U.S. patent application number 17/240028 was filed with the patent office on 2022-05-12 for associative polymers and related compositions, methods and systems.
The applicant listed for this patent is CALIFORNIA INSTITUTE OF TECHNOLOGY. Invention is credited to Julia A. KORNFIELD, Ming-Hsin WEI.
Application Number | 20220145012 17/240028 |
Document ID | / |
Family ID | |
Filed Date | 2022-05-12 |
United States Patent
Application |
20220145012 |
Kind Code |
A1 |
KORNFIELD; Julia A. ; et
al. |
May 12, 2022 |
ASSOCIATIVE POLYMERS AND RELATED COMPOSITIONS, METHODS AND
SYSTEMS
Abstract
Described herein are associative polymers capable of controlling
a physical and/or chemical property of non-polar compositions and
related compositions, methods and systems. Associative polymers
herein described have a non-polar backbone and functional groups
presented at ends of the non-polar backbone, with a number of the
functional groups presented at the ends of the non-polar backbone
formed by associative functional groups capable of undergoing an
associative interaction with another associative functional group
with an association constant (k) such that the strength of each
associative interaction is less than the strength of a covalent
bond between atoms and in particular less than the strength of a
covalent bond between backbone atoms.
Inventors: |
KORNFIELD; Julia A.;
(PASADENA, CA) ; WEI; Ming-Hsin; (PASADENA,
CA) |
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Applicant: |
Name |
City |
State |
Country |
Type |
CALIFORNIA INSTITUTE OF TECHNOLOGY |
PASADENA |
CA |
US |
|
|
Appl. No.: |
17/240028 |
Filed: |
April 26, 2021 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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16581603 |
Sep 24, 2019 |
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17240028 |
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15913828 |
Mar 6, 2018 |
10472470 |
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16581603 |
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14859181 |
Sep 18, 2015 |
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15913828 |
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62052355 |
Sep 18, 2014 |
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International
Class: |
C08G 83/00 20060101
C08G083/00; C08L 101/02 20060101 C08L101/02; C10L 1/16 20060101
C10L001/16; C10L 1/236 20060101 C10L001/236; C08L 101/08 20060101
C08L101/08; F17D 1/17 20060101 F17D001/17; C08G 61/08 20060101
C08G061/08; C10L 10/02 20060101 C10L010/02; C08K 5/00 20060101
C08K005/00; C10L 1/195 20060101 C10L001/195; C10L 10/08 20060101
C10L010/08 |
Goverment Interests
STATEMENT OF GOVERNMENT GRANT
[0002] The invention described herein was made in the performance
of work under a NASA contract NNN12AA01C, and is subject to the
provisions of Public Law 96-517 (35 USC 202) in which the
Contractor has elected to retain title.
Claims
1.-35. (canceled)
36. A system for controlling a physical and/or chemical property in
an non-polar composition, the system comprising at least two
between at least one host composition having a dielectric constant
equal to or less than 5, and at least one framing associative
polymer comprising a linear, branched, or hyperbranched polymer
backbone having at least two ends and a functional qroup presented
at two or more ends of the at least two ends of the linear,
branched, or hyperbranched polymer backbone; wherein the linear,
branched, or hyperbranched polymer backbone is substantially
soluble in the at least one host composition, and wherein a number
of the functional groups presented at the two or more ends is
formed by associative functional groups each capable of undergoing
an associative interaction with another associative functional
qroup in the at least one host composition with an association
constant (k) wherein in which R.sub.g is the radius of gyration of
the framing associative polymer in the non-polar composition in
nanometers, N.sub.a is Avogadro's constant; and n.sub.F is the
average number of the associative functional groups in the framing
associative polymer the at least one host composition and at least
one framing associative polymer for combined use to provide a
non-polar composition in which the at least at a concentration c
selected between from about 0.05c* to about 10c*, c * = 3 .times. M
W 4 .times. .pi. .function. ( R g 2 ) 3 / 2 .times. N a ,
##EQU00031## in which M.sub.w is the weight averaged molecular
weight, R.sub.g is the radius of gyration, and N.sub.a is
Avogadro's constant. depending on the weight averaged molecular
weight and/or Radius of gyration of the at least one framing
associative Polymer and on the Physical and/or chemical property to
be controlled.
37. The system of claim 36, wherein the at least one framing
associative polymer has a weight averaged molecular weight equal to
or lower than about 2,000,000 g/mol.
38. The system of claim 36, wherein the at least one framing
associative polymer has a weight averaged molecular weight
400,000<M.sub.w [g/mol].ltoreq.1,000,000.
39. The system of claim 36, wherein the association constant is
6<log.sub.10 k.ltoreq.14.
40. The system of claim 36, wherein the association constant is
6.9<log.sub.10 k.ltoreq.7.8.
41. The system of claim 36, wherein the associative functional
group is a carboxylic acid and the another associative functional
group is a carboxylic acid, or the associative functional group is
a carboxylic acid and the another associative functional group is
an amine, or the associative functional group is an alcohol and the
another associative functional group is an amine, or the
associative functional group is an alcohol and the another
associative functional group is a carboxylic acid, or the
associative functional group is a diacetamidopyridine and the
another associative functional group is a thymine, or the
associative functional group is a Hamilton Receptor and the another
associative functional group is a cyanuric acid, the associative
functional group is zinc sulfonate or palladated
sulfur-carbon-sulfur (SCS) pincer and the another associative
functional group is selected from pyridine or primary, secondary
and tertiary amines.
42. The system of claim 36, wherein the another associative
functional groups is presented at at least one end of a different
associative polymer.
43. The system of claim 36, wherein the at least one framing
associative polymer is e formed by at least two structure units
having formula [[FG-chain-[node].sub.z (1) and optionally one or
more structural units having formula -node-chain]- (11), wherein:
FG is an associative functional group (FGa); chain is a non-polar
polymer substantially soluble in a non-polar composition, the
polymer having formula: R1-[A].sub.nR2 (III) wherein: A is a
chemical and in particular an organic moiety forming the monomer of
the polymer; R.sub.1 and R.sub.2 are independently selected from
any carbon based or organic group with one of R.sub.1 and R.sub.2
linked to an FG or a node and the other one of R.sub.1 and R.sub.2
linked to an FG or a node; and n is an integer.gtoreq.1; z is 0 or
1; node is a covalently linked moiety linking one of R.sub.1 and
R.sub.2 of at least one first chain with one of the R.sub.1 and
R.sub.2 of at least one second chain; and wherein the FG, chain and
node of different structural units of the polymer can be the same
or different.
44. The system of claim 43, wherein the associative functional
group FGa is selected from diacetamidopyridine group, thymine
group, Hamilton Receptor group, cyanuric acid group, carboxylic
acid group, primary secondary or tertiary amine group, primary
secondary and tertiary alcohol group, zinc sulfonate, palladated
sulfur-carbon-sulfur (SCS) pincer pyridine or primary, secondary
and tertiary amines.
45. The system of claim 43, wherein A is a diene, olefin, styrene,
acrylonitrile, methacrylate or acrylate, vinyl acetate,
dichlorodimethylsilane, tetrafluoroethylene, acids, esters, amides,
amines, glycidyl ethers, or isocyanates, siloxane,
46. The system of claim 43, wherein n is equal to or greater than
200 or equal to or greater than 800.
47. The system of claim 36, wherein the at least one host
composition comprises a hydrocarbon composition, a fluorocarbon
composition or a silicone composition,
48. The system of claim 36, wherein the at least one host
composition comprises a mineral oil, a biofuel, pentane, hexane,
cyclohexane, benzene, toluene, chloroform and diethyl ether,
liquefied petroleum gas, liquid methane, butane, gasoline,
kerosene, jet fuel and diesel fuel.
49. The system of claim 36, wherein the at least one host
composition comprises crude oil or a refined fuel.
50. The system of claim 36, wherein the at least one host
composition comprises a refined fuel selected from Jet-A, Jet-A1,
kerosene, JP-8, gasoline and/or diesel.
51. The system of claim 36, wherein when the at least one
rheological property is selected from drag reduction, mist control,
lubrication and/or viscoelastic properties.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. application Ser.
No. 15/913,828 filed on Mar. 6, 2018 which is a continuation of
U.S. application Ser. No. 14/859,181 entitled "Associative Polymers
and Related Compositions, Methods and Systems" filed on Sep. 18,
2015, which claims priority to the U.S. Provisional Application
Ser. No. 62/052,355 entitled "Associative Polymers and Related
Compositions, Methods and Systems" filed on Sep. 18, 2014 with
docket number P1173-USP2, which may be related to provisional
application 61/799,670 entitled "Associative Polymers and related
Compositions Methods and Systems" filed on Mar. 15, 2013 with
docket number P1173-USP, to U.S. application Ser. No. 14/217,142
entitled Associative Polymers and related Compositions Methods and
Systems" filed on Mar. 17, 2014 with docket number P1173-US, and to
PCT application S/N PCT/US14/30772, entitled Associative Polymers
and related Compositions Methods and Systems" filed on Mar. 17,
2014 with docket number P1173-PCT, the contents of each of which is
incorporated herein by reference in its entirety.
FIELD
[0003] The present disclosure relates to associative polymers and
related compositions methods and systems. In particular, the
present disclosure relates to associative polymers suitable to be
used in connection with control of physical and/or chemical
properties of non-polar compositions.
BACKGROUND
[0004] Several non-polar compositions are known in the art for
which control of the related physical and/or chemical properties is
desired. For example, in hydrocarbon compositions which can be used
for combustion and energy production, control of properties such as
mist, drag, and combustion can be desirable.
[0005] Also in non-polar liquid hydrocarbon compositions suitable
to be used as ink, pesticide or fuel, control of properties such as
mist and drop breakup can be desirable.
[0006] However, despite development of several approaches, control
of those properties is still challenging.
SUMMARY
[0007] Provided herein are associative polymers which in several
embodiments can be used as additives in a non-polar composition,
and related compositions, methods, and systems. In particular
associative polymers herein described in several embodiments allows
control of physical and/or chemical properties, and in particular
rheological properties, thus allowing for example drag reduction,
mist control, lubrication, fuel efficiency and/or control of
viscoelastic properties of a non-polar composition.
[0008] In general associative polymers herein described have a
non-polar backbone and functional groups presented at ends of the
non-polar backbone, with a number of the functional groups
presented at the ends of the non-polar backbone being associative
functional groups. An associative functional group in associative
polymers herein described are capable of undergoing an associative
interaction with another associative functional group with an
association constant (k) such that the strength of each associative
interaction is less than the strength of a covalent bond between
atoms and in particular less than the strength of a covalent bond
between backbone atoms. In particular, in associative polymers
herein described associative functional groups can have an
association constant (k)
k .function. ( M - 1 ) .gtoreq. 4 3 .times. .pi. .function. ( R g 2
) 3 2 .times. N a n F .times. 10 - 23 ##EQU00001##
in which R.sub.g is the radius of gyration of the associative
polymer in a non-polar composition (R.sub.g in nanometers), N.sub.a
is Avogadro's constant; and n.sub.F is the average number of the
associative functional groups in the associative polymer. In some
embodiments, an associative polymer herein described can have an
overall weight average molecular weight, M.sub.w, equal to or lower
than about 2,000,000 g/mol, and/or a M.sub.w equal to or higher
than about 100,000 g/mol.
[0009] According to a first aspect, a linear or branched
associative polymer is described, herein also indicated as framing
associative polymer, which comprises a linear, branched, or
hyperbranched backbone having at least two ends and functional
groups presented at two or more ends of the at least two ends of
the backbone. In the framing associative polymer, the linear or
branched polymer backbone is substantially soluble in a non-polar
composition, and a number of the functional groups presented at the
two or more ends of the of the at least two ends of the backbone is
formed by associative functional groups. In some embodiments, the
linear or branched framing associative polymer has an overall
weight average molecular weight, M.sub.w, equal to or lower than
about 2,000,000 g/mol, and/or a Mw equal to or higher than about
100,000 g/mol.
[0010] According to a second aspect, a linear or branched
associative polymer is described, herein also indicated as capping
associative polymer, which comprises a linear, branched, or
hyperbranched polymer backbone having at least two ends and an
associative functional group presented at one end of the at least
two ends of the backbone. In the capping associative polymer, the
linear or branched backbone is substantially soluble in a non-polar
composition. In some embodiments the capping associative polymer
has an overall weight average molecular weight, M.sub.w, equal to
or lower than about 2,000,000 g/mol, and/or a Mw equal to or higher
than about 100,000 g/mol. In some embodiments, the terminal linear
or branched associative polymer is a linear polymer.
[0011] According to a third aspect, any one of the associative
polymers herein described and in particular any one of the framing
associative polymers and/or capping associative polymers herein
described, can have a weight averaged molecular weight equal to or
lower than 1,000,000 g/mol. In those embodiments, associative
polymer herein described can be shear resistant depending on the
structure of the backbone and on the presence, number and location
of secondary, tertiary and quaternary carbon atoms in backbone. In
some embodiments, framing associative polymers and/or capping
associative polymers herein described can have a weight averaged
molecular weight equal to or lower than 750,000 g/mol. In some
embodiments, framing associative polymers and/or capping
associative polymers herein described can have a weight averaged
molecular weight between 400,000 g/mol and 1,000,000 g/mol.
[0012] According to a fourth aspect a modified non-polar
composition is described, the modified non-polar composition
comprising a host composition having a dielectric constant equal to
or less than about 5 and at least one framing associative polymer
herein described, and optionally at least one capping associative
polymer herein described, the at least one framing associative
polymer and the at least one capping associative polymer
substantially soluble in the host composition. In particular, in
the modified non polar composition the at least one framing
associative polymer herein described can be comprised in the host
composition at a concentration from about 0.001 c* to 10c*, with
respect to an overlap concentration c* for the at least one framing
associative polymer relative to the host composition. In
embodiments where the capping associative polymer is comprised in
the non-polar composition, the capping associative polymer can be
comprised in an amount up to 20% of a total polymer concentration
of the non-polar composition.
[0013] According to a fifth aspect a method is described, to
control one or more physical and/or chemical properties and in
particular a rheological property of a non-polar composition. The
method comprises: providing a host composition having a dielectric
constant equal to or less than about 5; and providing at least one
framing associative polymer herein described substantially soluble
in the host composition and optionally at least one capping
associative polymer herein described. The method further comprises
combining the host composition and the at least one framing
associative polymer herein described at a selected concentration c
between from about 0.001 c* to 10c*, depending on the weight
averaged molecular weight and/or Radius of gyration of the at least
one framing associative polymer and on the physical and/or chemical
property to be controlled. In embodiments where the capping
associative polymer is provided, the method further comprises
combining the at least one capping associative polymer in the
non-polar composition in an amount up to 20% of a total polymer
concentration of the non-polar composition.
[0014] According to a sixth aspect a method is described, to
control resistance to flow and/or to control flow rate enhancement
of a non-polar composition alone or in combination with control of
another physical and/or chemical property of the non-polar
composition. The method comprises: providing a host composition
having a dielectric constant equal to or less than about 5; and
providing at least one framing associative polymer herein described
substantially soluble in the host composition and optionally at
least one capping associative polymer herein described. In the
method the framing associative polymer and the capping associative
polymer having a weight averaged molecular weight equal to or
higher to 200,000 g/mol. The method further comprises combining the
host composition and the at least one framing associative polymer
herein described at a selected concentration c between from about
0.001 c* to 1c*, depending on the weight averaged molecular weight
and/or Radius of gyration of the at least one framing associative
polymer and on the extent of drag reduction desired alone or in
combination with another physical and/or chemical property to be
controlled. In embodiments where the capping associative polymer is
provided, the method further comprises combining the at least one
capping associative polymer in the non-polar composition in an
amount up to 20% of a total polymer concentration of the non-polar
composition.
[0015] According to a seventh aspect a method to control sizes,
and/or to control distribution of sizes of the droplets of a fluid
(e.g. a fluid mist) in a non-polar composition alone or in
combination with another physical and/or chemical property is
described. The method comprises providing a host composition having
a dielectric constant equal to or less than about 5; providing at
least one framing associative polymer herein described and
optionally at least one capping associative polymer herein
described. In the method, the framing associative polymer and the
capping associative polymer are substantially soluble in the host
composition and have a weight averaged molecular weight equal to or
higher to 400,000 g/mol. The method further comprises combining the
host composition and the at least one framing associative polymer
herein described at a selected concentration c between from about
0.05c* to 3c*, depending on the weight averaged molecular weight
and/or Radius of gyration of the at least one framing associative
polymer and on the another physical and/or chemical property to be
controlled. In embodiments where the capping associative polymer is
provided, the method further comprises combining the at least one
capping associative polymer in the non-polar composition in an
amount up to 20% of a total polymer concentration of the non-polar
composition.
[0016] According to an eight aspect a method to provide an
associative polymer is described. The method comprises providing a
linear, branched or hyperbranched polymer backbone substantially
soluble in a non-polar composition and having at least two ends and
having a weight averaged molecular weight equal to or higher than
about 100,000 g/mol; and attaching an associative functional group
at one or more ends of the at least two ends of the backbone. In
particular in embodiments where the attaching is performed at two
or more ends of the at least two ends of the linear, branched or
hyperbranched backbone the method provides a framing associative
polymer. In some embodiments the associative polymer has an overall
weight average molecular weight, M.sub.w, equal to or lower than
about 2,000,000 g/mol, and/or a Mw equal to or higher than about
100,000 g/mol.
[0017] According to a ninth aspect a system is described for
controlling a physical or chemical property, and in particular a
rheological property, of a non-polar composition alone or in
combination with another physical and/or chemical property, and in
particular a rheological property, of the non-polar composition.
The system comprises at least two between at least one associative
polymer herein described and at least one host composition having a
dielectric constant equal to or less than 5. In some embodiments
the system can further comprise at least one terminal polymer
herein described.
[0018] The associative polymers, capping associative polymers and
related material compositions, methods and systems herein described
can be used in connection with applications wherein control of
physical and/or chemical properties of non-polar compositions is
desired with particular reference to drag reduction and/or flow
rate enhancement. Exemplary applications comprise fuels and more
particularly crude oils and refined fuels, inks, paints, cutting
fluids, drugs, lubricants, pesticides and herbicides as well as
synthetic blood, adhesive processing aids, personal care products
(e.g. massage oils or other non-aqueous compositions) and
additional applications which are identifiable by a skilled person.
Additional applications comprise industrial processes in which
reduction of flow resistance, mist control, lubrication, and/or
control of viscoelastic properties of a non-polar composition and
in particular a liquid non polar composition is desired.
[0019] The details of one or more embodiments of the disclosure are
set forth in the accompanying drawings and the description below.
Other features, objects, and advantages will be apparent from the
description and drawings, and from the claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] The accompanying drawings, which are incorporated into and
constitute a part of this specification, illustrate one or more
embodiments of the present disclosure and, together with the
detailed description and the examples, serve to explain the
principles and implementations of the disclosure.
[0021] FIGS. 1A-1B show a schematic illustration of supramolecular
structures of associative polymers according to embodiments herein
described. In particular, FIG. 1A shows schematics of telechelic
donor/acceptor interaction. FIG. 1B shows schematics of telechelic
self-associating interactions.
[0022] FIGS. 2A-2B show a schematic illustration of end to end
association in associative polymers herein described. FIG. 2A
describes an exemplary donor acceptor association FIG. 2B describes
an exemplary self-association.
[0023] FIG. 3 shows an exemplary associative polymer according to
an embodiment herein described. In the illustration of FIG. 3 x and
y can be independently selected between any integer.gtoreq.1. The
sum of x and y can be between 1,000 and 10,000.
[0024] FIG. 4 shows exemplary functional groups and related
exemplary associative interactions according to embodiments herein
described.
[0025] FIG. 5 shows exemplary architectures of associative polymers
herein described. In particular in the illustration of FIG. 5, a,
b, c, d, n, and e are independently integers.gtoreq.1.
[0026] FIG. 6 shows exemplary block architectures of associative
polymers herein described and of an exemplary chain or backbone
moiety. In particular in the illustration of FIG. 6, a, b, c, d, n,
x, and y are independently integers.gtoreq.1.
[0027] FIG. 7 shows a schematic representation of a method to
provide an associative polymer of the disclosure according to
embodiments herein described.
[0028] FIG. 8 shows a schematic representation of a reaction
suitable to provide an associative polymer of the disclosure using
chain transfer agents according to embodiments herein
described.
[0029] FIG. 9 shows exemplary chain transfer agents suitable to be
used in the reaction illustrated in FIG. 8 according to embodiments
herein described, and in particular, chain transfer agents with
internal olefins based on benzyl ether dendrons.
[0030] FIG. 10 shows a schematic representation of an exemplary
method to produce associative polymers herein described using chain
transfer agents according to embodiments herein described.
[0031] FIG. 11 shows a diagram illustrating GPC traces of 430K
di-TE PB (di-TE PB also called octa tBu ester PB herein) and the
resulting polymer of its hydrolysis reaction (in THF). In
particular, FIG. 11, shows a diagram illustrating the GPC traces of
a telechelic 1,4-PB with a backbone length of 430,000 g/mol
(M.sub.w) and end groups having 4 tert-butyl ester groups on each
(denoted TE groups hereinafter; the polymer is denoted 430K di-TE
PB hereinafter) and the resulting polymer of its hydrolysis
reaction (in THF). The resulting end-groups with 4 acid groups and
the polymer are hereinafter denoted TA groups and 430K di-TA PB
(di-TA PB also called octa acid PB herein), respectively.
[0032] FIG. 12 shows a diagram illustrating viscosity in function
of shear rate of the 1 wt % Jet-A solutions of the 430K di-TE PB
and 430K diTA PB herein also indicated as di-TE PB and (430K di-TA
PB).
[0033] FIG. 13 shows a diagram illustrating GPC traces of the 430K
octa chloro PB and the corresponding octa tertiary amine PB. In
particular, FIG. 13, shows a diagram illustrating the GPC traces of
telechelic 1,4-PB with a backbone length of 430,000 g/mol and
end-groups with 4 chloro groups on each and the corresponding
tertiary amine-terminated polymer (the end groups with 4 tertiary
amines are denoted TB groups, and the corresponding polymer is
denoted 430K di-TB PB hereinafter).
[0034] FIG. 14 shows a diagram illustrating viscosity in function
of shear rate of 1 wt % Jet-A solutions of 430K di-TE PB, di-TA PB,
di-TA PB, and 1:1 w/w di-TA PB/di-TB PB mixture herein also
indicated as 430K di-TE PB, di-TA PB, di-TB PB, and 1:1 w/w-di-TA
PB/di-TB PB mixture.
[0035] FIG. 15 illustrates properties of an exemplary hydrocarbon
composition according to the disclosure. In particular, FIG. 15,
Panel A shows that the exemplary composition remains stable for
months at -30.degree. C. and FIG. 15, Panel B shows that dewatering
operations occur as quickly and completely in the composition
(right) as in an untreated host (left).
[0036] FIG. 16 shows is a diagram illustrating the radius of
gyration of an exemplary backbone polymer (polystyrene) as a
function of its weight-average molecular weight (M.sub.w in g/mol)
in a representative theta solvent (cyclohexane) and in a
representative good solvent (toluene). In particular, FIG. 16 shows
an exemplary relationship between the radius of gyration R.sub.g of
a backbone polymer as a function of its weight average molecular
weight (M.sub.w in g/mol).
[0037] FIG. 17 shows a schematic representation of exemplary
interactions between conventional linear polymers of the
disclosure, in situation when the polymer concentration is equal to
the overlap concentration c*. The dotted lines represent the radius
of the single polymers (functional not shown). In particular the
schematic of FIG. 17, show an exemplary way polymer molecules can
pervade the entire solution when provided at their overlap
concentration C*.
[0038] FIGS. 18 and 19 show exemplary synthesis reactions for
exemplary CTAs suitable to make associative polymers in accordance
with embodiments herein described.
[0039] FIGS. 20 and 21 show exemplary covalent links linking node
to chain and node to FG according to embodiments herein
described.
[0040] FIG. 22 Shows a schematic illustration of the
self-association behavior of carboxyl-terminated telechelic 1,4-PBs
according to some embodiments herein described.
[0041] FIG. 23 shows a graph Specific viscosity of 1 wt % solutions
of test polymers in 1-chlorododecane (CDD) and tetralin (TL). FIG.
23, Panel A shows the effect of end functionality N=1, 2, 4, 8 for
polymers with Mw.about.220,000 g/mol (Table 3.1). Data are not
available for octa-carboxyl end groups (N=8) due to insolubility of
the material in both in CDD and TL. FIG. 23, Panel B shows results
of N=4 at Mw=76, 230 and 430,000 g/mol. Graphs are on different
scales.
[0042] FIG. 24 shows the effect of number of chain-end functional
groups (N) on the concentration dependence of the specific
viscosity of solutions of telechelic associative polymers with
Mw.about.230,000 g/mol. FIG. 24, Panel A shows the effect in
1-chlorododecane (CDD). FIG. 24, Panel B shows the effect in
tetralin (TL). Graphs are on different scales.
[0043] FIG. 25 shows the concentration dependence of specific
viscosity of solutions of telechelic 1,4-PBs with non-associative
and associative chain ends (N=4) as a function of Mw: from left to
right, 76,000 g/mol, 230,000 g/mol, and 430,000 g/mol. The overlap
concentration of the tertbutyl ester form of each polymer is
indicated by the marks on the concentration axis, circles and
squares for tetralin (TL) and triangles for 1-chlorododecane (CDD);
for 76K di-TE in CDD c*=1.4 wt % (offscale). Solid lines indicate
linear regression from 0.2 wt % to 1.5c* for di-TE; dashed lines
correspond to the solid line vertically shifted to the linear
portion of the di-TA data: red for TL and blue for CDD.
[0044] FIGS. 26A-26B show graphs depicting shear-thinning behavior
of CDD solutions and TL solutions. FIG. 26A shows CDD solutions of
di-TA 1,4-PBs at three concentrations (0.4, 0.7 and 1.0 wt %) as a
function of Mw: FIG. 26A, Panel, A 76,000 g/mol, FIG. 26A, Panel, B
Mw=230,000 g/mol, and FIG. 26A, Panel, C 430,000 g/mol. FIG. 26B
shows TL solutions of di-TA 1,4-PBs at three concentrations (0.4,
0.7 and 1.0 wt %) as a function of Mw: FIG. 26B, Panel, A 76,000
g/mol, FIG. 26B, Panel, B Mw=230,000 g/mol, and FIG. 26B, Panel, C
430,000 g/mol.
[0045] FIG. 27 shows expanded .sup.1H NMR (500 MHz) spectra of
CDCl.sub.3 solutions of telechelic polymers that have a 10,000
g/mol 1,4-PB backbone with end groups. FIG. 27, Panel A shows the
THY (thymine) spectrum. FIG. 27, Panel B shows DAAP
(diacetamidopyridine). FIG. 27, Panel C shows the spectrum of a
mixture of the two polymers with a mass ratio of 1:2, which
represents a stoichiometric ratio of approximately 1:2. The
concentration of polymer in solution is approximate 1 wt %.
[0046] FIG. 28 shows expanded .sup.1H NMR (500 MHz) spectra of
CDCl.sub.3 solutions of telechelic polymers. FIG. 28, Panel A shows
the spectrum of 1,4-PB of M.sub.w=50,000 g/mol with CA (cyanic
acid) end groups FIG. 28, Panel B shows the spectrum of 1,4-PB of
M.sub.w=24,000 g/mol with HR (Hamilton receptor) end groups. FIG.
28, Panel C shows a mixture of the two polymers with a mass ratio
of 1:1.4, which represents a stoichiometric ratio of CA:HR of
approximately 1:2. The concentration of polymer in solution is
approximate 1 wt %.
[0047] FIG. 29 shows expanded .sup.1H NMR (500 MHz) spectra of
CDCl.sub.3 solutions of telechelic polymers. FIG. 29, Panel A shows
the spectrum of 1,4-PB of M.sub.w=22,000 g/mol with TB end groups.
FIG. 29, Panel B shows the spectrum of a mixture of 1,4-PB of
M.sub.w=22,000 g/mol with TB end groups and 1,4-PB of
M.sub.w=22,000 g/mol with TA end groups two polymers with a mass
ratio of 1:1. The concentration of polymer in solution is
approximate 1 wt %.
[0048] FIG. 30 shows expanded .sup.1H NMR (500 MHz) spectra of
CDCl.sub.3 solutions of telechelic polymers. FIG. 30, Panel A shows
the spectrum of 1,4-PB of M.sub.w=288,000 g/mol with THY end
groups. FIG. 30, Panel B shows the spectrum of 1,4-PB of
M.sub.w=219,000 g/mol with DAAP end groups. FIG. 30, Panel C shows
the spectrum of a mixture of the two polymers with a mass ratio of
1:2. The concentration of polymer in solution is approximate 1 wt
%.
[0049] FIG. 31 shows expanded .sup.1H NMR (500 MHz) spectra of
CDCl.sub.3 solutions of telechelic polymers. FIG. 31, Panel A shows
the spectrum of 1,4-PB of M.sub.w=200,000 g/mol with CA end groups.
FIG. 31, Panel B shows the spectrum of 1,4-PB of M.sub.w=240,000
g/mol with HR end groups. FIG. 31, Panel C shows the spectrum of a
mixture of the two polymers with a mass ratio of 1:2. The
concentration of polymer in solution is approximate 1 wt %.
[0050] FIG. 32 shows expanded .sup.1H NMR (500 MHz) spectra of
CDCl.sub.3 solutions of telechelic polymers. FIG. 32, Panel A shows
the spectrum of 1,4-PB of M.sub.w=250,000 g/mol with TB end groups.
FIG. 32, Panel B shows the spectrum of a mixture of 1,4-PB of
M.sub.w=250,000 g/mol with TB end groups and 1,4-PB of
M.sub.w=230,000 g/mol with TA end groups two polymers with a mass
ratio of 1:1. The concentration of polymer in solution is
approximate 1 wt %.
[0051] FIG. 33 shows a plot of specific viscosity (25.degree. C.)
of 1 wt % CDD solutions of 230K di-TE 1,4-PB, 230K di-TA 1,4-PB,
250K di-TB 1,4-PB, and the 1:1 (w/w) mixture of 230K di-TA 1,4-PB
and 250K di-TB 1,4-PB at shear rates 1-3000 s.sup.-1.
[0052] FIG. 34 shows a plot of specific viscosity (25.degree. C.)
of 1 wt % CDD solutions of 230K di-DE 1,4-PB, 230K di-DA 1,4-PB,
250K di-DB 1,4-PB, and the 1:1 (w/w) mixture of 230K di-DA 1,4-PB
and 250K di-DB 1,4-PB at shear rates 1-3000 s.sup.-1.
[0053] FIG. 35 shows a plot of specific viscosity (25.degree. C.)
of 1 wt % Jet-A solutions of 430K di-TE 1,4-PB, 430K di-TA 1,4-PB,
430K di-TB 1,4-PB, and the 1:1 (w/w) mixture of 430K di-TA 1,4-PB
and 430K di-TB 1,4-PB at shear rates 1-3000 s.sup.-1.
[0054] FIG. 36 shows GPC-LS (THF, 35.degree. C.) traces of 230K
di-TE 1,4-PB, 230K di-TA 1,4-PB and the resultant polymer of LAH
reduction of 230K di-TA 1,4-PB.
[0055] FIG. 37 shows a schematic illustration of a synthesis of
di-TE 1,4-PB via two-stage ROMP of COD as the benchmark reaction
for the influence of the purity of VCH-free COD.
[0056] FIG. 38 shows a plot of the viscosities of a non-associative
polymer in an appropriate host at varying concentrations using a
rheometer wherein at c* a deviation from linearity is observed in
the plot of viscosity versus polymer concentration. Linear
regression is performed on the data from both dilute and
concentrated regimes, and the crossover of the two linear fits
represents the overlap concentration, c*.
[0057] FIG. 39A shows an image of an experimental setup to test the
associative polymers herein described in the control of drag
reduction in compositions (see, e.g. Example 13A).
[0058] FIG. 39B shows an image of an experimental setup to test the
associative polymers herein described in the control of long
lasting drag reduction in compositions (see, e.g. Example 13B).
[0059] FIG. 39C shows that 1:1 (w/w) 670K Di-DA PB/630K Di-DB PB
provides long-lasting drag reduction.
[0060] FIG. 40 shows a plot of an exemplary relationship between c*
and M.sub.w that can be generalized to be used to select a desired
M.sub.w of a backbone in an associative polymer as herein described
based on the desired concentration of the associative polymer
relative to c*.
[0061] FIG. 41 shows a schematic illustration of a two-stage
synthesis of tert-butyl ester-terminated telechelic 1,4-PBs. Step
(a): 50-100 equiv of COD, 1/30 equiv of second-generation of Grubbs
Catalyst, anhydrous dichloromethane (DCM), 40.degree. C., 30-60
min. Step (b): 1000-2000 equiv of COD for target Mw<300,000
g/mol, anhydrous dichloromethane (DCM), 40.degree. C., 16 h; 10000
equiv of COD for target Mw>400,000 g/mol, anhydrous
dichloromethane (DCM), 40.degree. C., <10 min.
[0062] FIG. 42 shows a schematic illustration of TFA hydrolysis of
tert-butyl ester polymer end groups.
[0063] FIG. 43 shows graphs of specific viscosity (25.degree. C.)
of 1 wt % 1-chlorododecane (CDD) and dodecane solutions of 288K
di-THY 1,4-PB, 219K di-DAAP 1,4-PB, and 1:2 (w/w) mixture of 288K
di-THY 1,4-PB and 219K di-DAAP 1,4-PB.
[0064] FIG. 44 shows a graph of Specific viscosity (25.degree. C.)
of 1 wt % 1-chlorododecane (CDD) and Jet-A solutions of 240K di-HR
1,4-PB, 200K di-CA 1,4-PB, and 1:2 and 2:1 (w/w) mixtures of 240K
di-HR 1,4-PB and 200K di-CA 1,4-PB.
[0065] FIG. 45, Panels A-B show a schematic illustration of a
synthesis of di-DB and di-TB 1,4-PBs via two-stage,
post-polymerization end-functionalization reaction.
[0066] FIGS. 46A-46B show a schematic representation of a synthesis
of bis-dendritic, tert-butyl ester-terminated chain transfer agents
(CTA). FIG. 46A shows a synthesis of a CTA with only one tert-butyl
ester on each side (compound 3). FIG. 46B shows a synthesis of a
CTA with only one tert-butyl ester on each side (compound 10), with
the conditions being: (a) 2.2 eq. of 2 or 2', K.sub.2CO.sub.3,
N,N-dimethylformamide (DMF), 80.degree. C., 5 h; (b) 4 eq. of
LiAlH.sub.4, THF, R.T., overnight; (c) 6 eq. of 2 or 2', 6 eq. of
PPh.sub.3, 6 eq. of DIAD, THF, 0.degree. C. then 40.degree. C.,
overnight; (d) 8 eq. of LiAlH.sub.4, THF, R.T., overnight; (c) 12
eq. of 3, 12 eq. of PPh.sub.3, 12 eq. of DIAD, THF, 0.degree. C.
then 40.degree. C., overnight.
[0067] FIGS. 47A-47C show FIG. 47A assembly of long telechelic
polymers (LTPs) into mega-supramolecules (right; linear and cyclic
(not shown)) compared to that of randomly functionalized
associative polymers (left) and prior end-associative telechelics
(middle) in terms of degree of polymerization (DP) and
conformations at rest and in elongational flow; FIG. 47B ring-chain
equilibrium distribution of cyclic (filled) and linear (open)
supramolecules; FIG. 47C synthesis of telechelics (non-associative
with FG end-groups, structures in FIG. 61 and FIG. 45A) and
post-polymerization conversion to associative telechelics (FGa,
bottom). (1): Grubbs II, dichloromethane (DCM), 40.degree. C., 1 h;
(2): Grubbs II, DCM, 40.degree. C., until stir bar stops (>5
min), equivalents of COD for desired molecular weight. DA: di-acid.
DB: di-base. TA: tetra-acid.
[0068] FIGS. 48A-48D show evidence of supramolecules in solutions
of equimolar mixture of .alpha.,.omega.-di(isophthalic acid) and
.alpha.,.omega.-di(di(tertiary amine)) polycyclooctadienes (DA/DB);
FIG. 48A effect of telechelics size (k.ident.kg/mol) on specific
viscosity of supramolecular solutions and controls in cyclohexane
(CH) at 2 mg/ml (0.25% wt, 25.degree. C.); FIG. 48B effect of
solvent on specific viscosity for 2 mg/ml (0.25% wt) solutions
(25.degree. C.) of telechelics having M.sub.w=670k due to both
polarity (dielectric constant, FIG. 80) and solvent quality for the
backbone (FIG. 63, Panel A); FIG. 48C, static light scattering
(35.degree. C.) shows that association of .about.670k DA with DB
chains in CH at 0.22 mg/ml (0.028% wt) produces supramolecules
(filled) with an apparent M.sub.w greater than 2,000 kg/mol, which
separate into individual building blocks (x) when an excess of a
small-molecule tertiary amine is added (open symbols, 10 ul/ml of
triethylamine, TEA; see FIG. 63, Panels A-B for its effect on
viscosity). Curves show predictions of the model for complementary
telechelics 1,000 kg/mol in solution at 1400 ppm (solid,
supramolecules; dashed, non-associated telechelics), details in
FIG. 63, Panel C; FIG. 63, Panel D concentration-normalized SANS
intensities (25.degree. C.) for 50k telechelics in
d.sub.12-cyclohexane at concentrations well below the overlap
concentration of NA (2 mg/ml for NA and DB; 0.05 mg/ml for DA and
DA/DB).
[0069] FIGS. 49A-49C show FIG. 49A the decrease of specific
viscosity for 4.2M PIB 1.6 mg/ml (0.2% wt) in Jet-A at 25.degree.
C. after approximately 60 passes through a Bosch fuel pump as shown
in FIG. 66, Panel A (sheared) relative to as-prepared (unsheared)
indicates shear degradation; FIG. 49B Specific viscosities of 2.4
mg/ml (0.3% wt) of a 1:1 molar ratio of
.alpha.,.omega.-di(isophthalic acid) and
.alpha.,.omega.-di(di(tertiary amine)) polycyclooctadienes
(.about.670 kg/mol DA/DB) in Jet-A at 25.degree. C., sheared vs.
unsheared; FIG. 49C Emission data using an unmodified long-haul
diesel engine. Control: untreated diesel. Treated: diesel treated
with 0.1% wt 670k DA/DB (details in Example 63).
[0070] FIGS. 50A-50B show impact test in the presence of ignition
sources (60 ms after impact, maximal flame propagation) for Jet-A
solutions treated with 4.2M PIB or
.alpha.,.omega.-di(di-isophthalic acid) polycyclooctadienes (TA):
FIG. 50A Jet-A with 4.2M PIB (0.35% wt) and Jet-A with 430k TA
(0.3% wt), "unsheared" and "sheared"; FIG. 50B effect of TA
molecular weight (76 kg/mol to 430 kg/mol) in Jet-A at 0.5% wt
(unsheared).
[0071] FIG. 51 shows model predictions for two different values of
the strength of interaction .epsilon.kT=14 kT (left),
.epsilon.kT=16 kT (middle) and .epsilon.kT=18 kT (right) (open
diamond: linear supramolecules; solid diamond: cyclic
supramolecules).
[0072] FIG. 52 shows molecular design for self-assembly of
telechelic polymeric building blocks into larger linear and cyclic
supramolecules via end association
[0073] FIG. 53 shows grouping of polymer components, where A and B
generically refer to A1 or A2 and B1 or B2 end-groups. Each group
is composed of all the different possible aggregates obtained by
the assembly of the A1 - - - A2 and B1 - - - B2 building
blocks.
[0074] FIG. 54 shows mapping of polymer loops into necklaces of 4
colors. The 4 colors correspond to: A1A2B1B2, A1A2B2B1, A2A1B1B2,
A2A1B2B1.
[0075] FIG. 55 shows that it is not possible to create a loop that
"reads" the same clockwise and counterclockwise, so every loop maps
into exactly two distinct necklaces. (Color assignments are given
in FIG. 54).
[0076] FIG. 56, Panels A-C show contact probabilities and
equilibria
[0077] FIG. 57 shows selection of the end-groups; FIG. 57, Panel A
chemical structures and molar masses of the end-associative
polymers (excepting isophthalic acid/tertiary amine functionalized
ones that are shown in FIG. 47C); FIG. 57, Panel B specific
viscosities of telechelic polymers at 8.7 mg/ml total polymer in
1-chlorododecane; FIG. 57, Panel C illustration of secondary
electrostatic interactions (SEIs) in THY/DAAP and HR/CA pair.
[0078] FIGS. 58 and 59 show incorporation of CTA into polymer
during the first stage of two-stage ROMP of COD, and chain
extension to long telechelics in the second stage: FIG. 58, .sup.1H
NMR of characteristic peaks for di(di-tert-butyl-isophthalate) CTA
(structure of end-group shown in FIG. 57), unreacted CTA (proton 1)
and CTA incorporated into macromer (proton 2), at three time
points; the integrations of the peaks were used to calculate the
percentage of unreacted CTA, shown in FIG. 59, Panel A. FIG. 59,
Panel A, Kinetic curves show that the peaks characteristic of the
unincorporated CTA are already difficult to quantify in the sample
taken after 40 min, and it is not evident for the sample taken at 1
hour (given the magnitude of the noise in the spectra, the amount
of unincorporated CTA is less than 3%). Dashed curve is calculated
based the data point at 10 min assuming exponential decay of
unreacted CTA. FIG. 59, Panel B, In an example with di-chloro PCOD,
the M.sub.n calculated by NMR is in good agreement with that
measured by GPC, considering the inherent uncertainty in NMR
integration and the inherent uncertainty in GPC measurement
(5-10%). FIG. 59, Panel C, GPC traces show no indication of macro
CTA (42 kg/mol) in the chain-extended telechelics (structure shown
in FIG. 59, Panel C, 497 kg/mol) produced in the second step.
[0079] FIG. 60 shows .sup.1H NMR spectra of increasingly purified
COD in the range from 3.4 to 5.9 ppm: FIG. 60, Panel A COD after
BH.sub.3.THF treatment and vacuum distillation (containing
.about.330 ppm of butanol based on integration); FIG. 60, Panel B
COD further purified with magnesium silicate/CaH.sub.2 treatments
(to show removal of butanol and the resulting purity of COD used as
monomer).
[0080] FIGS. 61A-61B show FIG. 61A, structures of non-associative
(NA) end-groups and the conversion from NA to associative
end-groups; FIG. 61B, isophthalic acid end groups obtained by
deprotection of the tBu groups in the tBu-ester-ended
non-associative precursor.
[0081] FIGS. 62A-62B show .sup.1H NMR spectra of tBu-ester ended
(DE) and isophthalic acid ended (DA) polycyclooctadiene
(M.sub.w=630 kg/mol) showing high degree of conversion of the
end-groups: FIG. 62A, the peaks for protons on the phenyl ring
(protons 1 and 2) shift due to the removal of tBu; FIG. 62B, the
peak for tBu group disappears in the spectrum for DA.
[0082] FIG. 62C shows .sup.1H NMR spectra of azide ended (DN.sub.3)
and tertiary amine ended (DB) polycyclooctadiene (M.sub.w=540
kg/mol) showing high degree of conversion of the end-groups.
[0083] FIG. 63 shows formation of supramolecules in equimolar
solutions of .alpha.,.omega.-di(isophthalic acid)
polycyclooctadiene, .alpha.,.omega.-di(di(tertiary amine))
polycyclooctadiene (DA/DB), with non-associated controls: FIG. 63,
Panel A, effect of chain length on specific viscosity of
telechelics in tetralin and Jet-A (2 mg/ml) at 25.degree. C.; FIG.
63, Panel B, effect of TEA (2.5 .mu.l/ml) on the viscosities of
associative telechelic polymers DA/DB; FIG. 63, Panel C, left:
static light scattering shows that association between DA and DB
chains (circle: 670k series; triangle: 300k series) in CH at 0.22
mg/ml (0.028%) produces supramolecules (filled), which separate
into individual building blocks (x) when an excess of a
small-molecule tertiary amine is added (open symbols, 10 .mu.l/ml
of triethylamine, TEA). Curves show predictions of the model (see
Examples 37-49); right: Zimm plot of the same static light
scattering data shown in Left part. Lines indicate the fitting to
the Zimm equation and dashed lines indicate the extrapolation that
was used to evaluate the intercept at zero concentration, zero
angle; the slope of the line and the value of the intercept are
used to evaluate the apparent M.sub.w and apparent R.sub.g; FIG.
63, Panel D, resulting values of apparent M.sub.w and R.sub.g for
the five polymer solutions in FIG. 63, Panel C.
[0084] FIG. 64 shows modeling of interplay of telechelic length and
concentration in a stoichiometric mixture of complementary
end-associative telechelics in the regime of long telechelics: FIG.
64, Panel A, effect of telechelic length on the distribution of the
number of telechelics in a supramolecule, given as the
concentration in ppm wt/wt of each species, cyclic (circles) or
linear (x or +), at a fixed total concentration of 1400 ppm; FIG.
64, Panel B, the same distributions as in FIG. 64, Panel A,
presented in terms of the molar mass of the supramolecules; the
weight-average molar mass of the supramolecules is given to the
left of the legend; FIG. 64, Panel C, effect of concentration on
the distribution of supramolecules for telechelics of 1M g/mol (see
Examples 37-49).
[0085] FIG. 65 shows .sup.1H NMR spectra of isophthalic acid ended
(DA) and di(tertiary amine) ended (DB) polycyclooctadienes
(M.sub.w=45 kg/mol) and 1:1 molar mixture of DA/DB in deuterated
chloroform (CDCl.sub.3) indicating that carboxylic acid-amine
hydrogen bonds dominate over carboxylic acid-carboxylic acid
hydrogen bonds: FIG. 65, Panel A, .sup.1H NMR peaks due to
hydrogens on carbons adjacent to nitrogens of tertiary amine groups
of DB (methylene protons 1; methyl protons 2) shift downfield when
they form charge-assisted hydrogen bonds with carboxylic acid
groups of DA; FIG. 65, Panel B, .sup.1H NMR peaks due to hydrogens
on the phenyl ring of DA shift upfield upon formation of
charge-assisted hydrogen bonds between carboxylic acids and
tertiary amines.
[0086] FIG. 66 shows: FIG. 66, Panel A, home-built apparatus for
"shear degradation" test; FIG. 66, Panel B, an initially 4,200
kg/mol PIB at a concentration of 0.35% in Jet-A shows the decrease
in specific viscosity indicative of shear degradation with
increasing number of passes through the pump; FIG. 66, Panel C, GPC
validation of "shear degradation" test using PIB and confirmation
that associative polymers resist degradation (see Example 61).
(symbols)
[0087] FIG. 67 shows FIG. 67, Panel A results of diesel engine
tests using The Federal Test Protocol (FTP); FIG. 67, Panel B work
and fuel efficiency data using an unmodified long-haul diesel
engine. Control: untreated diesel. Treated: diesel with 0.14% w/v
670k DA/DB (see Examples 63 and 64).
[0088] FIG. 68 shows average mass flow rate normalized to that of
"as prepared" 4.2M PIB solution for a 0.02% solution of 4.2M PIB in
Jet-A and a 0.1% solution of 670k DA/DB in Jet-A (similar to that
used in the diesel engine tests of FIG. 49C).
[0089] FIG. 69 shows FIG. 69, Panel A, apparatus for impact/flame
propagation experiments; FIG. 69, Panel B, frame at 60.4 ms for
untreated Jet-A. The rectangular box is the area within which
pixels were analyzed for brightness; FIG. 69, Panel C, average
brightness of the pixels in the rectangle of FIG. 69, Panel B as a
function of time during the first 300 ms after impact for five
compositions (untreated Jet-A, 0.35% wt 4.2M PIB unsheared, 0.35%
wt 4.2M PIB sheared, 0.3% wt 430k TA unsheared and 0.3% wt 430k TA
sheared).
[0090] FIG. 70 shows characterization of
.alpha.,.omega.-di(di(isophthalic acid)) (TA) polycyclooctadiene
used in Impact test: FIG. 70, Panel A, Effect of chain length (k
refers to kg/mol) on specific viscosity of TA in tetralin at 10
mg/ml. FIG. 70, Panel B, Specific viscosity of 2.4 mg/ml 430k TA in
Jet-A at 25.degree. C., sheared vs unsheared.
[0091] FIG. 71 shows a schematic representation of the
concentration-dependent self-association of telechelic associative
polymers (see FIG. 1B). Left: Telechelic associative chain at low
concentration. Middle: Flower-like micelle above a critical
concentration value. Right: Transient network at higher
concentration.
[0092] FIG. 72 shows specific viscosity of 1 wt % Jet-A solutions
of LTPs at 25.degree. C.: FIG. 72, Panel A, 430 kg/mol NA-, TA-,
TB-PCODs, and 1:1 (w/w) mixture of TA- and TB-PCODs; FIG. 72, Panel
B, 200 kg/mol NA-, DA-, DB-PCODs, and 1:1 (w/w) mixture of DA- and
DB-PCODs; FIG. 72, Panel C, 600 kg/mol NA-, DA-, DB-PCODs, and 1:1
(w/w) mixture of DA- and DB-PCODs. Note that all data reported are
averages over shear rates 10 to 100 s.sup.-1.
[0093] FIG. 73 shows representative examples of solutions of
associative LTPs in Jet-A after storage at -30.degree. C. over 13
months: 0.3 wt % Jet-A solution 1:1 (w/w) mixture of 430 kg/mol TA-
and TB-PCODs. (See FIG. 15, Panel A left panel for 0.5 wt % Jet-A
solution of 264 kg/mol TA-PCOD).
[0094] FIG. 74 shows shear viscosity of samples from shear
stability test and their unsheared controls. Right: 0.35 wt % Jet-A
solution of 4,200 kg/mol PIB; middle: 0.3 wt % Jet-A solution of
430 kg/mol TA-PCOD; left: 0.3 wt % Jet-A solution of 1:1 mixture of
600 kg/mol DA- and DB-PCODs.
[0095] FIG. 75, Panels A-B shows results of Jet-A in impact/flame
propagation test: FIG. 75, Panel A t=30 ms after impact FIG. 75,
Panel B t=60 ms after impact.
[0096] FIG. 76 shows results of 0.35 wt % Jet-A solution of 4,200
kg/mol PIB in impact/flame propagation test. Left: results of
unsheared solution; right: results of sheared solution.
[0097] FIG. 77 shows results of 0.3 wt % Jet-A solution of 430
kg/mol TA-PCOD in flame propagation test. Left: results of
unsheared solution. Right: results of sheared solution.
[0098] FIG. 78 shows molecular design considerations for backbone
selection for solubility in fuels and resistance to chain scission.
In contrast to polymers examined in prior literature ([6],[7]) on
mist control and drag reduction, the present polymers use a
backbone that has no tertiary or quaternary carbons nor any
heteroatoms in the repeat unit. The importance of these features is
illustrated by comparison with the two polymers that have received
the most attention in prior literature: 4,200 kg/mol
polyisobutylene (PIB) and a copolymer of acrylic and styrenic
monomers known as FM-9 (M.sub.w.about.3,000 kg/mol). Acrylate units
introduce heteroatoms that interfere with fuel solubility (a
problem that is exacerbated by the random incorporation of
carboxylic acid side groups). Polyisobutylene has quaternary
carbons in the backbone, making it particularly susceptible to
chain scission ([8]). The tertiary backbone carbons in FM-9 also
make the backbone more susceptible to chain scission than one that
has only secondary carbons. The solubility and strength of the
present polymers are enhanced by including carbon-carbon double
bonds in the backbone.
[0099] FIG. 79 shows physical properties of single component
solvents: Dielectric constant (F) and refractive index (n).
Dielectric constant serves as a measure of the polarity of
solvents: it increases from for cyclohexane (CH) and tetralin.
Increasing solvent polarity reduces the degree of end-association
for the telechelics. The difference between the refractive index of
solvents and that of PCOD (n.about.1.52) determines the contrast in
multi-angle laser light scattering (MALLS). Tetralin is excluded
from the MALLS experiment because of its low contrast with PCOD
(1.54 is too close to 1.52). Cyclohexane gives desirable contrast
in MALLS.
[0100] FIG. 80 shows preliminary ASTM data of untreated ("Base
fuel") and treated JP-8 (with 1:1 molar mixture of 500 kg/mol
.alpha.,.omega.-di(isophthalic acid) polycyclooctadiene and 600
kg/mol .alpha.,.omega.-di(di(tertiary amine)) polycyclooctadiene
(DA/DB)). .sup.(a)The concentration of polymer (mass/mass) added to
"Base fuel" JP-8, a military aviation fuel (specified by
MIL-DTL-83133), corresponding to Jet-A with three additional
additives: the Corrosion Inhibitor/Lubricity Enhancer, the Fuel
System Icing Inhibitor, and the Static Dissipater Additive.
.sup.(b)Flash Point (ASTM D93) is the lowest temperature at which
fuel will produce enough flammable vapors to ignite when an
ignition source is applied. Flash point is the most commonly used
property for the evaluation of the flammability hazard of fuels. As
expected, the mist-control polymers do not affect the flash point
because the polymer additive affects mechanical mist formation--not
the liquid-vapor equilibrium characteristics of the fuel. There is
no statistically significant difference in flash point among the
three samples. .sup.(c)Total Acid Number (ASTM D3242) organic acids
are naturally found in hydrocarbon fuels and others are created
during refining. The presence of acids in fuel is unwanted because
of the potential to cause corrosions or interfere with fuels water
separation. There is no statistically significant difference in
total acid number among the three samples. .sup.(d) Density at
-15.degree. C. (ASTM D4052) is used to verify fuel type, calculate
aircraft fuel load and range, gaging and metering and flow
calculations. .sup.(e) Kinematic Viscosity at -20.degree. C. (ASTM
D445) at low temperatures is specified to be 8.0 mm.sup.2/s or less
to ensure adequate fuel flow and atomization under low temperature
operations, particularly for engine relight at altitude. The
composition at 1000 ppm obeys this criteria.
[0101] FIGS. 81A-81H show associative polymer based on 2-arm linear
(e.g. FIG. 81A) and 3-arm star structure units (e.g. FIG. 81B) in
which each chain is connected to a least one node "N". Within the
class of molecules as described herein; in strong flow the molecule
is expected to tend to break near the middle or a node "N", so one
of the two resultant pieces may retain at least end functional
groups and efficacy is expected to remain substantially unchanged
(e.g. FIG. 81F). In an H shaped polymer as shown in the molecule
(e.g. FIG. 81H) breaks near the middle; resulting in two polymers
(each half of the H polymer which are themselves active for the
desired rheological effect, so efficacy is not lost.
DETAILED DESCRIPTION
[0102] Associative polymers, and related materials, compositions,
methods, and systems are described, which based in several
embodiments, allow control of physical and/or chemical properties,
of a non-polar composition.
[0103] "Chemical and/or physical properties" in the sense of the
present disclosure comprise properties that are measurable whose
value describes a state of a physical system and any quality that
can be established only by changing a substance's chemical
identity.
[0104] The term "non-polar compositions" in the sense of the
present disclosure indicates compositions having a dielectric
constant equal to or lower than 5 which can comprise compositions
of varying chemical nature. In particular, a non-polar composition
can comprise hydrocarbon compositions, fluorocarbon compositions or
silicone compositions. A hydrocarbon composition is a composition
in which the majority component is formed by one or more
hydrocarbons. A fluorocarbon composition is a composition in which
the majority component is formed by one or more fluorocarbons. A
silicone composition is a composition in which the majority
component is formed by one or more silicones.
[0105] In embodiments herein described, associative polymers are
provided which can be added to a non-polar composition to control
at least one physical and/or chemical property of the composition
as illustrated in the present disclosure. In particular, chemical
and/or physical properties that can be controlled by associative
polymers herein described include rheological properties. The term
"rheological properties" of a composition refers to properties
related to the deformation and flow of the composition, in liquid
or "soft" solid state, under stress, in particular, when a
mechanical force is exerted on the composition. Rheological
properties can be measured from bulk sample deformation using a
mechanical rheometer, or on a micro-scale by using a microcapillary
viscometer or an optical technique such as microrheology. Examples
of rheological properties include shear viscosity, elongational
viscosity, storage and loss moduli, viscoelastic properties, and
lubrication properties.
[0106] Accordingly, in some embodiments herein described,
associative polymers are provided which can be added to a non-polar
composition to perform drag reduction, mist control, lubrication,
fuel efficiency improvement and/or control of viscoelastic
properties of a non-polar composition.
[0107] In particular, the term "drag reduction" as used herein
refers to the reduction of the resistance to flow in turbulent flow
of a fluid in a conduit (e.g. a pipe) or pipeline thereby allowing
the fluid to flow more efficiently. A skilled person would realize
that drag reduction can be described in terms that include, for
example, a reduction in the friction factor at high Reynolds number
(e.g. higher than 5000, between 5000 and 25000 and higher than
25000), a reduction in the pressure drop required to achieve a
given volumetric flow rate, a reduction in hydraulic resistance,
and an increase in flow rate without raising operating pressure. In
particular, drag reduction can be measured by methods identifiable
to a skilled person, for example measurement of the flow rate of a
fluid though a conduit and/or by measurement of the change in
pressure of a fluid flowing through a conduit.
[0108] In particular, the term "mist control" as used herein refers
to the control of the properties of a fluid mist. In particular,
the properties that can be controlled can include the sizes, and/or
distribution of sizes, of the droplets of fluid. In some
embodiments, control of the sizes, and/or distribution of sizes, of
the droplets can control the flammability of the mist of a fluid
(e.g., to reduce the propagation of a flame through the fuel mist
in the event of an accident). In other embodiments, control of the
sizes, and/or distribution of sizes, of the droplets can increase
the deposition of a fluid on an intended surface (e.g., to reduce
pesticide wasted by convection away from the field to which it is
being applied). In particular, mist control can be measured by
techniques identifiable to a skilled person, such as measurement of
the sizes and size distribution of droplets when a fluid is
converted to a mist.
[0109] In particular, the term "lubrication" as used herein refers
to the reduction of wear and/or inhibition of movement between two
surfaces separated by a non-polar composition as herein described.
In particular, in some embodiments, the lubrication properties of a
non-polar composition can be controlled to improve the
wear-resistance and/or movement of the surfaces with respect to
each other when the non-polar composition is introduced as a
lubricant between the two surfaces (e.g. improving the
wear-resistance and/or movement of ball bearings in a ball bearing
structure, or improving the wear resistance and/or movement of a
piston in an engine). In particular, lubrication of a fluid can be
measured by techniques identifiable to a skilled person, such as
rheological measurements (e.g. measuring the coefficient of
friction when two surfaces with the fluid between them are slid
past each other).
[0110] In particular, the term "fuel efficiency" as used herein,
refers to the thermal efficiency with which the potential energy of
a fuel is converted to kinetic energy and/or work in the chemical
transformation undergone by the fuel (e.g. combustion of the fuel
in an engine). In particular, fuel efficiency can be measured by
techniques identifiable to a skilled person, such as measurement of
the amount of work performed by the chemical transformation of the
fuel (e.g. measuring the number of miles of travel an engine can
provide when combusting a given volume of fuel).
[0111] In particular, the term "viscoelastic properties" as used
herein refers to the manner in which a non-polar composition reacts
to external stresses such as deformation, in which the non-polar
fluid exhibits a combination of viscous response (e.g. production
of a permanent strain of the non-polar composition once it has been
distorted by the applied stress) and elastic response (deformation
of the non-polar composition during application of the stress, and
return to the original shape upon removal of the stress). In
particular, viscoelastic properties can be measured by methods
identifiable to a skilled person, such as rheological measurements
(e.g. measurement of the storage and loss moduli of the non-polar
composition).
[0112] Associative polymers herein described have a non-polar
backbone and functional groups presented at ends of the non-polar
backbone. In particular in the associative polymer the linear or
branched backbone is substantially soluble in the non-polar
composition. The term "substantially soluble" as used herein with
reference to a polymer and a nonpolar composition indicates the
ability of the polymer backbone to dissolve in the non-polar
liquid. Accordingly, the backbone of the associative polymers as
herein described can be substantially soluble in a nonpolar
composition when the polymer backbone and nonpolar composition have
similar Hildebrand solubility parameters (.delta.) which is the
square root of the cohesive energy density:
.delta. = .DELTA. .times. .times. H v - RT V m ##EQU00002##
wherein .DELTA.H.sub.v is equal to the heat of vaporization, R is
the ideal gas constant, T is the temperature, and Vm is the molar
volume. In particular, similar solubility parameters between a
polymer and a nonpolar composition can be found when the absolute
value of the difference between their solubility parameters is less
than about 1 (cal/cm.sup.3).sup.1/2 (see also Tables 3-5 herein). A
skilled person will realize that the ability of the backbone to
dissolve in the non-polar composition can be verified, for example,
by placing an amount of the homopolymer or copolymer to be used as
the backbone of the associative polymer in a host liquid as herein
described, and observing whether or not it dissolves under
appropriate conditions of temperature and agitation that are
identifiable to a skilled person.
[0113] In some embodiments, the backbone of associative polymers as
herein described can be substantially soluble in a nonpolar
composition when the difference in solubility parameters gives rise
to a Flory-Huggins interaction parameter (.chi.) of about 0.5 or
less. In particular, .chi. can be determined by the following
empirical relationship:
= s + H .apprxeq. 0.34 + v 0 RT .times. ( .delta. 1 - .delta. 2 ) 2
##EQU00003##
where .chi..sub.s is the entropic part of the interaction between
the associative polymer and nonpolar composition (generally
assigned an empirical value of 0.34, as would be apparent to a
skilled person), .chi..sub.H is the enthalpic part of the
interaction, v.sub.0 is the molar volume of the nonpolar
composition, .delta..sub.1 is the solubility parameter of the
polymer, and .delta..sub.2 is the solubility parameter of the host.
Additional exemplary empirical solubility parameters are
identifiable by a skilled person (see, e.g., [9] and other
available references known or identifiable by one skilled in the
art) An exemplary solubility determination of the backbone of an
associative polymer according to the disclosure with an exemplary
non-polar composition is reported in Example 12. Similarly, a
skilled person can determine if other associative polymer backbones
would be substantially soluble in other non-polar compositions by
applying the same calculations using the particular solubility
parameters for the particular non-polar composition.
[0114] In embodiments herein described, associative polymers are
polymers having a non-polar backbone and functional groups
presented at ends of the non-polar backbone and in particular at
two or more ends of the non-polar backbone.
[0115] The term "functional group" as used herein indicates
specific groups of atoms within a molecular structure that are
responsible for the characteristic physical and/or chemical
reactions of that structure and in particular to physical and/or
chemical associative interactions of that structure. As used
herein, the term "corresponding functional group" or "complementary
functional group" refers to a functional group that can react, and
in particular physically or chemically associate, to another
functional group. Thus, functional groups that can react, and in
particular physically or chemically associate, with each other can
be referred to as corresponding functional groups. In some
embodiments herein described functional end groups of polymers to
be added to a same non-polar compositions are corresponding
functional groups in the sense of the present disclosure.
[0116] In particular, exemplary functional groups can include such
groups as carboxylic acids, amines, and alcohols, and also
molecules such as, for example, diacetamidopyridine, thymine, the
Hamilton Receptor (see, e.g. [10]), cyanuric acid, and others
identifiable to a skilled person. In particular, some of the
exemplary functional groups can form pairs of complementary
functional groups, for example, carboxylic acids with other
carboxylic acids, carboxylic acids with amines, alcohols with
amines, alcohols with carboxylic acids, diacetamidopyridine with
thymine, the Hamilton Receptor with cyanuric acid, and others
identifiable to a skilled person (see, e.g., FIG. 4).
[0117] In particular, in some embodiments, functional groups as
herein described can be synthesized by installation of other
functional groups onto the backbone of the associative polymers at
a plurality of appropriate ends as herein described and transformed
according to methods identifiable to a skilled person (see, e.g.
[11]). In particular, in some of those embodiments the installation
can be performed in at least two ends of the associative polymers.
More particularly, installation at an end of the polymer can be
performed by installation of the functional group on the terminal
monomer of the polymer backbone, or on an internal monomer within a
range of approximately 1 to 100 monomers from the terminal
monomer.
[0118] In associative polymer herein described, a number of the
functional groups presented on ends of the backbone is formed by
"associative functional groups" (herein also indicated as FGas)
which are functional group able to associate with each other and/or
with corresponding functional groups in other associative polymers
in a same non-polar composition with an association constant (k) in
a range 0.1<log.sub.10 k<18 (preferably 2<log.sub.10
k<18), so that the strength of each associative interaction is
less than that of a covalent bond between backbone atoms.
[0119] In particular in associative polymer herein described
associative functional groups are capable of undergoing an
associative interaction one with another with an association
constant (k)
k .function. ( M - 1 ) .gtoreq. 4 3 .times. .pi. .function. ( R g 2
) 3 2 .times. N a n F .times. 10 - 23 ##EQU00004##
in which R.sub.g is the value of the radius of gyration of the
associative polymer in the non-polar composition in nanometers,
N.sub.a is Avogadro's constant; and n.sub.F is the average number
of associative functional groups per polymer molecule in the
associative polymer.
[0120] In some embodiments, associative polymers can further
comprise derivatizable functional group (herein also indicated as
FGd) presented at one or more ends of the at least two ends of the
backbone. The term "derivatizable functional groups" refers to
functional groups that cannot form associative interactions one
with another or with an associative functional group in the
non-polar composition and can undergo a derivatization reaction.
The term "derivatization" is commonly referred to a technique in
chemistry that transforms a chemical compound into a product of
similar chemical structure, also called a derivative. A
derivatizable functional groups refer to a specific type of
functional groups that participate in the derivatization reaction
and transform a polymer to its derivative having different chemical
and/or physical properties such as reactivity, solubility, boiling
point, melting point, aggregate state or chemical composition.
Derivatizable functional groups can be used in attach additional
functional moieties (e.g. polydrugs see Example 73) of the polymer
of interest. Exemplary derivatizable functional groups FGd suitable
for the associative polymers described herein are typically
non-polar FG that do not participate in hydrogen bonding and/or
metal ligand coordination interactions, and possibly allow coupling
of functional moieties to the polymer. Exemplary derivatizable
functional groups comprise an azido group, an alkynyl group, a
thiol group, a vinyl group, a maleimide group, and additional
groups identifiable by a skilled person (see e.g. FIG. 20 and FIG.
21)
[0121] In particular, in some embodiments, the at least two ends of
the associative polymers herein described presenting an associative
functional group in the sense of the disclosure, identify at least
two positions in the linear, branched or hyperbranched polymer
backbone of the associative polymer that are separated by an
internal span that has a length of at least 2,000 backbone bonds,
or an internal span between functional groups with a weight average
molar mass not less than 100,000 g/mol. In embodiments herein
described installation is performed so that the functional groups
are presented on the polymer.
[0122] The terms "present" and "presented" as used herein with
reference to a compound or functional group indicates attachment
performed to maintain the chemical reactivity of the compound or
functional group as attached. The term "attach" or "attached" as
used herein, refers to connecting or uniting by a bond, link, force
or tie in order to keep two or more components together, which
encompasses either direct or indirect attachment where, for
example, a first molecule is directly bound to a second molecule or
material, or one or more intermediate molecules are disposed
between the first molecule and the second molecule or material.
[0123] In particular, groups presented "at an end" of the polymer
backbone can comprise groups attached to a terminal monomer of a
polymer or to a monomer less than 100 monomers from a terminal
monomer of the polymer based on the specific structure and
configuration of the polymer as will be understood by a skilled
person upon reading of the present disclosure.
[0124] In various embodiments, functional end groups of associative
polymers herein described are able to associate in a donor/acceptor
association and/or in a self-association (FIG. 1 and FIG. 2). In
the donor/acceptor association the donor and acceptor can be
stoichiometric (e.g. equal numbers of donor and acceptor functional
groups) or non-stoichiometric (e.g. more donor groups than acceptor
groups or vice versa).
[0125] In various embodiments, the self-associative polymers, the
backbone can be linear or branched and following association of the
associative functional end groups the self-associating polymer can
form various supramolecular architectures (see Example 1). In
particular in some embodiments the backbone length can be such that
the backbone has a weight-average molecular weight of 250,000 g/mol
and more for individual chains.
[0126] More particularly, in various embodiments, the backbone can
be a nonpolar linear, branched or hyperbranched polymer or
copolymer (e.g. substituted or unsubstituted polydienes such as
poly(butadiene) (PB) and poly(isoprene), and substituted or
unsubstituted polyolefins such as polyisobutylene (PIB) and
ethylene-butene copolymers, poly(norbornene), poly(octene),
polystyrene (PS), poly(siloxanes), polyacrylates with alkyl side
chains, polyesters, and/or polyurethanes) providing a number of
flexible repeat units between associative functional end groups. In
some embodiments, the weight average molar mass (M.sub.w) of the
associative polymer can be equal to or lower than about 2,000,000
g/mol and in particular can be between about 100,000 g/mol and
about 1,000,000 g/mol.
[0127] In particular, in some embodiments, the backbone and
associative functional end groups can be selected to have a ratio
of carbon atoms to heteroatoms greater than about 1000:1 in the
associative polymers. For example, in some embodiments, a skilled
person can ensure that the heteroatom content is so low (e.g.
greater than 10,000:1) as to not affect burning (e.g. the emissions
produced by burning a fuel composition that contains some
associative polymers). In some embodiments, the associative polymer
can comprise functional groups within the backbone as shown
schematically in FIG. 6 and, therefore, in a location not limited
to the functional groups at one or more end of the polymer backbone
while still maintaining a ratio of carbon atoms to heteroatoms
greater than about 1000:1.
[0128] In some embodiments associative polymers herein described
and indicated as framing associative polymer, comprise associative
functional groups presented at two or more ends of at least two
ends of the backbone. In some embodiments associative polymers
herein described and indicated as capping associative polymer,
comprise an associative functional group presented at one end of
the at least two ends of the backbone.
[0129] In embodiments herein described, the framing associative
polymer can be used to control physical and/or chemical properties
and in particular rheological properties of a non-polar composition
alone or in combination with up to about 20% capping associative
polymers. In particular in embodiments where capping associative
polymers are combined with framing associative polymers, the
ability of the framing associative polymers to control the
properties of a non-polar composition is improved with respect to a
comparable composition comprising framing associative polymers only
(e.g. e.g. a 10% improved drag reduction). In some of those
embodiments, the use of capping associative polymers in combination
with framing associative polymers allows use of a reduced amount of
framing associative polymers (e.g. 10%)
[0130] In embodiments herein described framing associative polymer
and capping associative polymer can be linear, branched or
hyperbranched polymers with various structures as will be
understood by a skilled person
[0131] In particular embodiments, associative polymers herein
described can comprise one or more structural units of formula
[[FG-chain-[node].sub.z-- (I) and optionally the structural unit of
formula -node-chain]- (II)
wherein: [0132] FG is a functional group, which can comprise an
associative functional group FGa with one or more associative
moieties such that the functional group are capable of undergoing
an associative interaction with each other with an the association
constant (k) in a range 0.1<log.sub.10 k<18 (preferably
2<log.sub.10 k<18), so that the strength of each associative
interaction is less than that of a covalent bond between backbone
atoms, or FG can comprise a derivatizable functional group FGd with
one or more moieties capable of undergoing derivatization; [0133]
chain is a non-polar polymer substantially soluble in a non-polar
composition, the polymer having formula:
[0133] R.sub.1-[A].sub.nR.sub.2 (III) [0134] wherein: [0135] A is a
chemical and in particular an organic or silicone moiety forming
the monomers of the polymer; [0136] R.sub.1 and R.sub.2 are
independently selected from any carbon or silicon based or organic
group with one of R.sub.1 and R.sub.2 linked to an FG or a node and
the other one of R.sub.1 and R.sub.2 linked to an FG or a node; and
[0137] n is an integer.gtoreq.1; [0138] z is 0 or 1, depending on
the nature of the chemical link between a unit of Formula (I) or
Formula (II) and one or more units of Formula (I) and/or Formula
(II), [0139] node is a covalently linked moiety linking one of
R.sub.1 and R.sub.2 of at least one first chain with one of the
R.sub.1 and R.sub.2 of at least one second chain; [0140] and
wherein [0141] the FG, chain and node of different structural units
of the polymer can be the same or different.
[0142] In particular, in associative polymers herein described
including structural units of formula (I), FG groups presented "at
an end" of the polymer backbone can comprise groups attached to
either a terminal monomer of the chain or to a monomer less than 5%
and possibly less than 1% of the total number of monomers of the
chain from the terminal monomer of the chain in a structural unit
of Formula I).
[0143] Associative polymers and in particular framing associative
polymers and capping associative polymers in accordance with the
present disclosure can comprise one or more of the structural units
according to Formula (I) and/or Formula (II) in various
configurations as would be apparent to a skilled person upon
reading of the present disclosure.
[0144] For example in some embodiments herein described framing
associative polymers comprise at least two structural units of
Formula (I) wherein FG is an FGa. In some embodiments, framing
polymers herein described can comprise additional structural units
of Formula (I) and/or Formula (II) possibly presenting additional
FGas.
[0145] In some embodiments herein described, capping associative
polymers comprise one structural unit of Formula (I) wherein FG is
an FGa. In some embodiments, the capping associative polymers can
comprise additional structural units of Formula (II).
[0146] In some embodiments, framing associative polymers herein
described can be formed by three or more structural units of
Formula (I), wherein at least two of the structural units of
Formula (I) are attached one to another with a structural unit of
formula -node-chain]- (II) and wherein each [node] attaches three
structural unit of Formula (I). In some of those embodiments, all
the FGs are FGas. In some of those embodiments, structural unites
of Formula (I) can be distanced from one another.
[0147] In some embodiments, the framing associative polymer can be
formed by two structural units of Formula (I) wherein in the first
structural unit z is 0 and in the second structural unit z is 1 and
the node of the second structural unit links to one of R1 and R2 of
the first structural unit thus forming a linear polymer. In some of
those embodiments, the associative polymer is a framing associative
polymer and the FGs are FGas.
[0148] In polymers comprising structural units of Formula (I) and,
optionally, structural units of Formula (II), the longest span of
the polymer is of the form FG-chain-node-chain-FG in the case of
polymers that contain only structural units of Formula (I), or of
the form FG-chain-node-[chain-node].sub.n-chain-FG for chains that
include both types of units. Knowledge of the mean value of the
length of the -chain- units can be used to estimate the average
length of the longest span.
[0149] In the synthesis of branched polymers, the method of
synthesis often controls the type and extent of branching. In the
case of polymers that contain only structural units of Formula (I),
the architecture is either linear or star-type. If the average
degree of polymerization of the -chain-units is N.sub.c, the
average span of the polymer is 2N.sub.c for linear and star
polymers having a modest number of arms (e.g, 6 arms, or another
number that results in no crowding). For a polymer that has first
generation branches only (H-shaped or comb-shaped polymers), the
longest span is simply related to the number of structural units of
Formula (II) that separate the structural units of Formula (I) at
each end of the H- or comb-shaped polymer. For example, an H-shaped
polymer has an average number of monomer units in the longest span
that is 3N.sub.c. If branch-on-branch structure is present, similar
reasoning holds. For example, if the polymer has two generations of
tri-functional branching, the longest span contains, on average,
4N.sub.c repeat units.
[0150] An estimate of the number of monomer units in the longest
span can be used to estimate the radius of gyration that a branched
polymer will have, because R.sub.g of lightly branched polymers is
only slightly greater than it would be for a linear chain of the
same length as the longest span. In many applications of the
associative polymers herein described, the polymer backbone is
selected such that it dissolves substantially well in the host of
interest. Therefore, good solvent conditions usually prevail. Using
the scaling relationships for good solvent and the estimated degree
of polymerization, useful estimates of the radius of gyration can
be calculated. In turn, these can be used in preliminary design
calculations. Such preliminary calculations can guide the selection
of molecules to synthesize. Once the polymers have been prepared,
the value of R.sub.g can simply be measured using such methods as
static light scattering or viscometry.
[0151] In some embodiments herein described, FG indicates a
functional group FGa that is capable of undergoing an associative
interaction with another suitable functional group whereby the
association constant (k) for an interaction between associating
functional groups is in the range 0.1<log.sub.10 k<18, and in
particular in the range 4<log.sub.10 k<14 so that the
strength of each individual interaction is less than that of a
covalent bond between backbone atoms. In particular, in some
embodiments, the FGa can be chosen to have an association constant
that is suitable for a given concentration of the associative
polymer in the non-polar composition relative c*, as described
herein. For example, a skilled person will realize that if the
concentration of the associative polymer is high (e.g. greater than
3c*), a lower log.sub.10 k value (e.g. about 4 to about 6) can be
suitable, as can a higher log.sub.10 k value (e.g. about 6 to about
14). Additionally, a skilled person will also realize that if the
concentration of associative polymer is low (e.g. less than 0.5c*)
a higher log.sub.10 k value (e.g. about 6 to about 14) can be
suitable.
[0152] Exemplary FGaS comprise those that can associate through
homonuclear hydrogen-bonding (e.g. carboxylic acids, alcohols),
heteronuclear hydrogen-bonding donor-acceptor pairing (e.g.
carboxylic acids-amines), Lewis-type acid-base pairing (e.g.
transition metal center-electron pair donor ligand such as
palladium (II) and pyridine, or iron and tetraaceticacid, or others
identifiable to a skilled person as moieties that participate in
metal-ligand interactions or metal-chelate interactions),
electrostatic interactions between charged species (e.g.
tetraalkylammonium-tetraalkylborate), pi-acid/pi-base or quadrupole
interactions (e.g. arene-perfluoroarene), charge-transfer complex
formation (e.g. carbazole-nitroarene), and combinations of these
interactions (e.g. proteins, biotin-avidin). More than one type of
FGs and in particular of FGas may be present in a given polymer
structure.
[0153] In some embodiments, FGa can be selected among a
diacetamidopyridine group, thymine group, Hamilton Receptor group
(see, e.g. [10]), cyanuric acid group, carboxylic acid group,
primary secondary or tertiary amine group, primary secondary and
tertiary alcohol group, and others identifiable to a skilled
person.
[0154] In some embodiments, in the structural unit of Formula (I),
FG can be a derivatizable functional group (FGd). Exemplary
derivatizable FGds comprise of an azido group, an alkynyl group, a
thiol group, a vinyl group, a maleimide group, and additional
groups identifiable by a skilled person (see e.g. FIG. 20 and FIG.
21).
[0155] In the structural unit of Formulas (I) and (II) a chain can
be a polymer backbone that is substantially soluble in a liquid
host that has a dielectric constant equal to or less than 5. Such
chains can comprise for example polydienes such as poly(butadiene),
poly(isoprene), polyolefins such as polyisobutlyene, polyethylene,
polypropylene and polymers of other alpha olefins identifiable to a
skilled person, poly(styrene), poly(acrylonitrile), poly(vinyl
acetate), poly(siloxanes), substituted derivatives thereof, and
copolymers of these.
[0156] In the structural unit of Formulas (I) and (II) a node can
be a connecting unit between one or more and in particular two or
more [FG-chain] units such that the total molecular structure is
substantially terminated by FG species (e.g., a plurality of the
chain ends have a FG less than 100 repeat units from the chain
end). In some embodiments, the simplest such polymer is a linear
telechelic: two [FG-chain] units with their chains connected
end-to-end at a node: [FG-chain]-node-[chain-FG] or FG-chain-FG.
Alternative branched, hyperbranched, star, brush, partially-cross
linked or other multi-armed polymer structures can also be used,
provided that ends and/or other regions of the polymer chain are
functionalized according to the present disclosure. In particular,
a skilled person will understand from a reading of the present
disclosure the term "functionalized" according to the present
disclosure can be understood to mean that the functional groups can
be at the end of the polymer chains or other polymer structures, or
at different regions within the polymer chain (see, e.g., FIGS. 5
and 6).
[0157] In particular, in certain cases, the nodes can comprise one
or more FG units formed by FGa such that some degree of associative
functionality is present in the internal polymer structure. A node
is formed by any covalently bound group such as organic, siloxane,
and additional group identifiable by a skilled person. In
particular, a node can link two or more chains through suitable
covalent bonds and more particularly form branched polymers wherein
a node can link two to 10 chain -node-chain]- (II) (see e.g. FIG.
5). More than one type of nodes may be present in a given polymer
structure. In some embodiments the node can be a tertiary carbon, a
cycloaliphatic moiety or an aliphatic chain.
[0158] In particular in some embodiments, the chain can have a
formula R.sub.1[A].sub.n-R.sub.2 (III) in which A is a chemical
moiety suitable to be used as monomer and n can indicate the degree
of polymerization of the chain. In some embodiments, n can be an
integer equal to or greater than 200 and, in particular, equal to
or greater than 800. In some embodiments A can be an organic moiety
having secondary carbon atoms, tertiary carbon atoms and/or
quaternary carbon atoms, as will be understood by a skilled person.
In some of those embodiments A can be an organic moiety comprising
up to 10% of tertiary carbon atoms.
[0159] In some embodiments particular A can be a diene, olefin,
styrene, acrylonitrile, methyl methacrylate, vinyl acetate,
dichlorodimethylsilane, tetrafluoroethylene, acids, esters, amides,
amines, glycidyl ethers, isocyanates and additional monomers
identifiable by a skilled person. The term "olefins" as used herein
indicates two carbons covalently bound to one another that contain
a double bond (sp2-hybridized bond) between them. Olefins include
alpha olefins and internal olefin.
##STR00001##
E1, E2 and E3 are selected independently from hydrogen and linear,
branched or cyclic C1-C24 alkyl, preferably C1-C12 alkyl, more
preferably C1-C8 alkyl including methyl, ethyl, butyl, propyl,
hexyl, and ethylhexyl.
[0160] In particular, a skilled person will realize that the
particular moieties used as monomers can give rise to polymer
backbones that are suitable for combination with particular types
of nonpolar compositions. For example, styrene monomers, olefin
monomers, and in particular diene monomers can form polymers for
very non-polar compositions (e.g. compositions with a dielectric
constant of 1.5-2.5); amide, ester, epoxy, and urethanes can form
polymers for nonpolar compositions that have somewhat greater
dielectric constants (e.g., in the range 2.5-5); and fluorocarbon
monomers and silicone monomers can form polymers for fluorous
media. A skilled person will understand that additional types of
monomers would be suitable for other types of nonpolar
compositions.
[0161] In some embodiments, A in Formula (III) can be a moiety
selected to provide a chain of formula (IV):
##STR00002##
wherein R.sup.a-R.sup.n are independently selected from hydrogen,
C.sub.1-C.sub.12 substituted or unsubstituted alkyl, cycloalkyl,
alkeneyl, cycloalkenyl, alkynyl, cycloakynyl, and aryl groups and n
is in the range 200-20,000 and, in particular, in the range from
1000-10,000.
[0162] In some embodiments, A in formula (III) can be a moiety
selected to provide a chain of formulas (V)-(VIII):
##STR00003##
wherein R.sup.a-R.sup.j are independently selected from the group
consisting of hydrogen, C.sub.1-C.sub.12 substituted or
unsubstituted alkyl, cycloalkyl, alkenyl, cycloalkenyl, alkynyl,
cycloakynyl, and aryl groups and n is 1000-20,000.
[0163] In some embodiments, A in formula (III) can be a moiety
selected to provide a chain of formula (IX):
##STR00004##
wherein R.sup.a-R.sup.d are independently selected from the group
consisting of hydrogen, C.sub.1-C.sub.12 substituted or
unsubstituted alkyl, cycloalkyl, alkenyl, cycloalkenyl, alkynyl,
cycloakynyl, and aryl groups and n is 1000-40,000.
[0164] In some embodiments, A in formula (III) can be a moiety
selected to provide a chain of formula (X):
##STR00005##
wherein R.sup.a-R.sup.h are independently selected from the group
consisting of hydrogen, C.sub.1-C.sub.12 substituted or
unsubstituted alkyl, cycloalkyl, alkenyl, cycloalkenyl, alkynyl,
cycloakynyl, and aryl groups and n is 1000-20,000.
[0165] In some embodiments, A in formula (III) can be a moiety
selected to provide a chain of formula (XI):
##STR00006##
wherein R.sup.a-R.sup.e are independently selected from the group
consisting of hydrogen, C.sub.1-C.sub.12 substituted or
unsubstituted alkyl, cycloalkyl, alkenyl, cycloalkenyl, alkynyl,
cycloakynyl, and aryl groups and n is 1000-20,000.
[0166] In embodiments of the nodes of Formula (III) R.sub.1 and
R.sub.2 can be chemical moieties independently selected and capable
of forming a covalent bond. In some embodiments, either R.sub.1 or
R.sub.2 of at least one first chain can be linked to one of the
R.sub.1 and R.sub.2 of at least one second chain through a node. In
some embodiments, a node can comprise functional groups such as
arenes, perfluoroarenes, groups containing oxygen, groups
containing nitrogen and groups containing phosphorus and sulfur all
identifiable by a skilled person. In particular, functional groups
suitable for nodes can comprise a carboxylic acid, amine,
triarylphosphine, azide, acetylene, sulfonyl azide, thio acid and
aldehyde. In particular, for example, in forming covalent links
between node and chain and possibly between node and functional
group a first chemical moiety and a second corresponding chemical
moiety can be selected to comprise the following binding partners:
carboxylic acid group and amine group, sulfonyl azide and thio
acid, and aldehyde and primary amine. Additional chemical moieties
can be identified by a skilled person upon reading of the present
disclosure. Reference is also made to the exemplary nodes of
Example 11.
[0167] In some embodiments, R.sub.1 and/or R.sub.2 can be R1 and R2
are independently selected from a divalent group or atom.
[0168] In some embodiments where A is a moiety selected to provide
a chain of formula (IV)-(VIII), (X), or (XI), R.sub.1 and/or
R.sub.2 can be a moiety of formula (XII):
##STR00007##
wherein: q is 1 to 18; X is selected from the group consisting of
CH.sub.2, O, and S; and R.sup.a and R.sup.b are independently
hydrogen and/or a moiety of formula XIII-XVIII:
##STR00008##
provided that at least one of R.sup.a and/or R.sup.b is not
hydrogen. In particular R.sup.a and R.sup.b can be FGs connected to
the chain through R.sub.1 or R.sub.2 of Formula XII.
[0169] In some embodiments where A is a moiety selected to provide
a chain of formula (IV)-(VIII), (X), or (XI), R.sub.1 and/or
R.sub.2 can be a moiety of formula (XX):
##STR00009##
wherein: q is 1 to 18; X is selected from the group consisting of
CH.sub.2, O, and S; and R.sup.a and R.sup.b are independently a
moiety of formula (XIII)-(XVIII) as described herein. In particular
R.sup.a and R.sup.b can be FGs connected to the chain through
R.sub.1 or R.sub.2 of Formula (XX).
[0170] In some other embodiments where A is a moiety selected to
provide a chain of formula (IV)-(VIII), (X), or (XI), R.sub.1
and/or R.sub.2 can be a moiety of formula (XX):
##STR00010##
wherein: q is 1 to 18; X.sup.1, X.sup.2, and X.sup.3 are
independently selected from the group consisting of CH.sub.2, O,
and S; and R.sup.a-R.sup.d are independently hydrogen and/or a
moiety of formula (XIII)-(XVIII) as described herein; provided that
at least one of R.sup.a, R.sup.d, R.sup.c, and/or R.sup.b is not
hydrogen. In particular R.sup.a, R.sup.b, R.sup.c and R.sup.d can
be FGs connected to the chain through R.sub.1 or R.sub.2 of Formula
(XX).
[0171] In some other embodiments where A is a moiety selected to
provide a chain of formula (IV)-(VIII), (X), or (XI), R.sub.1
and/or R.sub.2 can be a moiety of formula (XXI):
##STR00011##
wherein: q, r and s are independently 1 to 18; X.sup.1, X.sup.2,
and X.sup.3 are independently selected from the group consisting of
CH.sub.2, O, and S; and R.sup.a-R.sup.d are independently hydrogen
and/or a moiety of formula (XIII)-(XVIII) as described herein;
provided that at least one of R.sup.a, R.sup.b R.sup.c, and/or
R.sup.d is not hydrogen. In particular R.sup.a, R.sup.b, R.sup.c
and R.sup.d can be FGs connected to the chain through R.sub.1 or
R.sub.2 of Formula (XXI).
[0172] In some embodiments nodes can also present additional groups
for binding with FG which can be introduced at the node according
to some embodiments. In some embodiments nodes comprise an organic
moiety, in some embodiments nodes comprise non organic moieties
such as Si--O and additional moieties identifiable by a skilled
person.
[0173] In some embodiments where A is a moiety selected to provide
a chain of formula (IX) R.sub.1 and/or R.sub.2 can be a moiety of
formula (XXII):
##STR00012##
wherein: q is 1 to 18; X is selected from the group consisting of
CH.sub.2, O, and S; and R.sup.a and R.sup.b are independently H
and/or a moiety of formula (XIII)-(XVIII) as described herein,
provided that at least one of R.sup.a and/or R.sup.b is not H. In
particular, R.sup.a and R.sup.b can be FGs connected to the chain
through R.sub.1 or R.sub.2 of Formula (XXII).
[0174] In some embodiments where A is a moiety selected to provide
a chain of formula (IX) R.sub.1 and/or R.sub.2 can be a moiety of
formula (XXIII):
##STR00013##
wherein: q is 1 to 18; X is selected from the group consisting of
CH.sub.2, O, and S; and R.sup.a and R.sup.b are independently a
moiety of formula (XIII)-(XVIII) as described herein. In
particular, R.sup.a and R.sup.b can be FGs connected to the chain
through R.sub.1 or R.sub.2 of Formula (XXIII).
[0175] In some other embodiments where A is a moiety selected to
provide a chain of formula (IX) R.sub.1 and/or R.sub.2 can be a
moiety of formula (XXIV):
##STR00014##
wherein: q is 1 to 18; X.sup.1, X.sup.2, and X.sup.3 are
independently selected from the group consisting of CH.sub.2, O,
and S; and R.sup.a-R.sup.d are independently H and/or a moiety of
formula (XIII)-(XVIII) as described herein; provided that at least
one of R.sup.a, R.sup.b, R.sup.c, and/or R.sup.d is not H. In
particular R.sup.a, R.sup.b, R.sup.c and R.sup.d can be FGs
connected to the chain through R.sub.1 or R.sub.2 of Formula
(XXIV).
[0176] In some other embodiments where A is a moiety selected to
provide a chain of formula (IX) R.sub.1 and/or R.sub.2 can be a
moiety of formula (XXV):
##STR00015##
wherein: q, r and s are independently 1 to 18; X.sup.1, X.sup.2,
and X.sup.3 are independently selected from the group consisting of
CH2, O, and S; and R.sup.a-R.sup.d are independently H and/or a
moiety of formula (XIII)-(XVIII) as described herein; provided that
at least one of R.sup.a, R.sup.b, R.sup.c, and/or R.sup.d is not H.
In particular R.sup.a, R.sup.b, R.sup.c and R.sup.d can be FGs
connected to the chain through R.sub.1 or R.sub.2 of Formula
(XXV).
[0177] In some other embodiments where A is a moiety selected to
provide a chain of formula (IX) R.sub.1 and/or R.sub.2 can be a
moiety of formula (XXVI):
##STR00016##
wherein: q is 1-18; R.sup.a-R.sup.b are independently H and/or a
moiety of formula (XIII)-(XVIII) as described herein; and R.sup.c
is hydrogen or C.sub.1-C.sub.12 substituted or unsubstituted alkyl;
provided that at least one of R.sup.a, R.sup.b, and/or R.sup.c is
not H. In particular, R.sup.a, R.sup.b, and R.sup.c can be FGs
connected to the chain through R.sub.1 or R.sub.2 of Formula
(XXVI).
[0178] In some other embodiments where A is a moiety selected to
provide a chain of formula (IX) R.sub.1 and/or R.sub.2 can be a
moiety of formula (XXVII):
##STR00017##
wherein: q is 1 to 18; R.sup.a-R.sup.d are independently H and/or a
moiety of formula (XIII)-(XVIII) as described herein; and
R.sup.f-R.sup.g are independently hydrogen or C.sub.1-C.sub.12
substituted or unsubstituted alkyl; provided that at least one of
R.sup.a, R.sup.b, R.sup.c, and/or R.sup.d is not H. In particular,
R.sup.a, R.sup.b, R.sup.c and R.sup.d can be FGs connected to the
chain through R.sub.1 or R.sub.2 of Formula (XXVII).
[0179] In particular in some embodiments the [chain-node] segments
have weight average molecular weight equal to or greater than
10,000 g/mol. In some embodiments the span of [chain-node]m between
FGs has average molar mass>50,000 g/mol (in particular when
dispersion in the host composition despite the "solvent-phobic"
FGas is desired). In some embodiments, the largest span of the
molecule can be equal to or less than 500,000 g/mol (for example,
when resistance to shear degradation is desired). In some
embodiments the largest span of the molecule, expressed as weight
average molecular weight can be equal to or less than 1,000,000
g/mol.
[0180] In some embodiments, associative polymers herein described
can be telechelic.
[0181] In some embodiments, associative polymers herein described
have a total polymer molecular weight is M.sub.w.ltoreq.2,000,000
g/mol and in particular can be between 100,000 g/mol and 1,000,000
g/mol. In some embodiments the largest span between nodes is less
than 500,000 g/mol in particular when the associative polymers are
branched polymers.
[0182] In some embodiments, selection of molecular weight for an
associative polymer herein described can be performed in view of
factors herein described and in particular values of the binding
constant in view of available or desired FGas, and a desired
concentration in view of effect to be controlled. Additional
factors that can be considered comprise a desired viscosity of the
host composition (e.g. high M.sub.w at low concentration to
minimize impact on the shear viscosity of the host and lower
M.sub.w at high concentration to increased impact on the shear
viscosity of the host), a desired density of FGs and in particular
FGas presented in connection with a desired effect (e.g. in order
to obtain gelation, concentrations near or greater than the overlap
concentration of the polymers are preferred), and duration of the
control in view of the shear degradation (e.g. if a longer duration
of the control is desired, the longest span of the molecules can be
reduced below the threshold chain length for shear degradation in
the application of interest)
[0183] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight equal to or higher than
about 100,000 g/mol.
[0184] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight between 400,000 to
1,000,000 g/mol.
[0185] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight between 630,000 g/mol
to 730,000 g/mol.
[0186] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight between 100,000 g/mol
to 300,000 g/mol.
[0187] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight between 300,000 g/mol
to 700,000 g/mol
[0188] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight between 700,000 g/mol
to 1,000,000 g/mol.
[0189] In some embodiments, associative polymers herein described
can have a weight averaged molecular weight between 1,000,000 g/mol
to 2,000,000 g/mol.
[0190] In some embodiments associative polymers herein described
can have an atomic composition with heteroatoms (i.e., other than C
or H) present at less than 1 heteroatom per 1000 carbons. In some
embodiments, heteroatoms are placed predominantly in correspondence
of the functional groups.
[0191] In some embodiments associative polymers herein described
can have a significant level of unsaturation (e.g. with a ratio of
H to C less than 1.8), which can improve low temperature liquid
behavior. However, fully-saturated chains can also be considered
effective and are included in the scope of the current
disclosure.
[0192] In various embodiments herein described, the associative
polymers of the disclosure can interact to form supramolecular
structures following interactions of the FGa having association
constant (k) of from 0.1<log.sub.10 k<18 and in particular
from 6<log.sub.10 k<14, in cases drag reduction and/or flow
rate enhancement are desired.
[0193] In some embodiments, selection of binding constant for an
associative polymer herein described can be performed in view of
factors herein described and in particular values of M.sub.w
desired, available or desired FGaS, and a desired concentration in
view of effect to be controlled. Additional factors that can be
considered comprise the specific host composition in which the
polymer is used, and additional factors identifiable by a skilled
person upon reading of the present disclosure.
[0194] In some embodiments, associative polymers herein described
can have an association constant 2.ltoreq.log.sub.10
k.ltoreq.18.
[0195] In some embodiments, associative polymers herein described
can have an association constant 4.ltoreq.log.sub.10
k.ltoreq.14.
[0196] In some embodiments, associative polymers herein described
can have an association constant 4.ltoreq.log.sub.10
k.ltoreq.12.
[0197] In some embodiments, associative polymers herein described
can have an association constant 6.ltoreq.log.sub.10
k.ltoreq.14.
[0198] In some embodiments, associative polymers herein described
can have an association constant 6.9.ltoreq.log.sub.10
k.ltoreq.7.8
[0199] In some embodiments, associative polymers herein described
can have an association constant log.sub.10 k.ltoreq.14 in
particular when the weight averaged molecular weight equal to or
lower than about 2,000,000 g/mol
[0200] In some embodiments, associative polymers herein described
can have an association constant 5.5.ltoreq.log.sub.10 k in
particular when the weight average molecular weight equal to or
higher than about 100,000 g/mol.)
[0201] In some embodiments, associative polymers herein described
can have an association constant 7.ltoreq.log.sub.10 k.ltoreq.9, in
particular when the weight averaged molecular weight is between
400,000 to 1,000,000 g/mol.
[0202] In some embodiments, associative polymers herein described
can have an association constant 6.9.ltoreq.log.sub.10 k.ltoreq.7.8
in particular when the weight averaged molecular weight is between
630,000 g/mol to 730,000 g/mol.
[0203] In some embodiments, associative polymers herein described
can have an association constant 6.ltoreq.log.sub.10 k.ltoreq.14,
preferably 6.ltoreq.log.sub.10 k.ltoreq.7.5, in particular when the
weight averaged molecular weight is between 100,000 g/mol to
300,000 g/mol.
[0204] In some embodiments, associative polymers herein described
can have an association constant 6.9.ltoreq.log.sub.10 k.ltoreq.14,
preferably 6.9.ltoreq.log.sub.10 k.ltoreq.7.8 in particular when
the weight averaged molecular weight between 300,000 g/mol to
700,000 g/mol.
[0205] In some embodiments, associative polymers herein described
can have an association constant 7.ltoreq.log.sub.10 k.ltoreq.14,
and preferably 7.ltoreq.log.sub.10 k.ltoreq.9 in particular when
the weight averaged molecular weight between 700,000 g/mol to
1,000,000 g/mol
[0206] In some embodiments, associative polymers herein described
can have an association constant 7.5.ltoreq.log.sub.10 k.ltoreq.14,
preferably 7.5.ltoreq.log.sub.10 k.ltoreq.12, in particular when
the weight averaged molecular weight between 1,000,000 g/mol to
2,000,000 g/mol. In particular, in embodiments herein described
where drag reduction is desired in flows having a Reynolds number
between 5,000 and 25000, polymers and related FGs can be selected
to have an FGaS with an association constant between 4.ltoreq.log
10 k.ltoreq.12, and in particular 5.5.ltoreq.log 10 k.ltoreq.12 and
in flows having a Reynolds number equal to or higher than 25,000
polymers and related FGs can be selected to have an association
constant between: 6.ltoreq.log 10 k.ltoreq.14.
[0207] In particular, in embodiments of supramolecular structures,
FGa associations can be due to, for example reversible noncovalent
interaction between the associative polymers that enables a
discrete number of molecular subunits or components to be
assembled, typically with an individual interaction strength less
than that of a covalent bond. Exemplary interactions include, for
example, self-associative hydrogen bonds (H-bonds), donor-acceptor
H-bonds, Bronsted or Lewis acid-base interactions, electrostatic
interactions, pi-acid/pi-base or quadrupolar interactions, charge
transfer complex formation, or other supramolecular
interactions.
[0208] In various embodiments herein described, the associative
polymers of the present disclosure can be used in connection with a
non-polar composition to control rheological properties, such as
drag reduction and/or flow rate enhancement, sizes, and/or size and
size distribution the droplets of a fluid mist, and viscoelastic
properties of the composition alone or in combination with other
physical and/or chemical properties of the composition. In
particular, in some embodiments, the non-polar compositions
comprise a host composition and at least one framing associative
polymer herein described.
[0209] The terms "host" and "host composition," as used herein,
refer to a majority component in a non-polar composition in which
the physical and/or chemical properties are sought to be
controlled. In particular, the host or host composition can be a
single substance such as a solvent like hexane or benzene, or the
host or host composition can be a substance which is a mixture such
as gasoline, diesel, olive oil, or kerosene. The host or host
composition can also be a mixture such as a paint or ink.
[0210] In some embodiments, the host composition can be a
hydrocarbon composition, a fluorocarbon compositions or a silicone
composition, In some embodiments, the host composition can be a
biofuel, a mineral oil, crude oils, pentane, hexane, cyclohexane,
benzene, toluene, chloroform and diethyl ether, dimethyl ether,
liquefied petroleum gas, liquid methane, butane, gasoline,
kerosene, jet fuel and diesel fuel.
[0211] In particular, in non-polar compositions herein described a
range of hosts can have dielectric constant less than 5, with hosts
having dielectric constant less than 2.5 being particularly well
suited to applications herein described as will be understood by a
skilled person upon reading of the disclosure. Non-polar
compositions with the above mentioned dielectric constants
encompasses a wide range of liquids that are relevant to
applications that comprise fuels (such as gasoline, kerosene, jet
fuel, diesel and additional fuels identifiable by a skilled
person), foods and pharmaceuticals (such as olive oil, linseed oil,
castor oil and additional foods identifiable by a skilled person),
solvents used as cleaning fluids (such as turpentine, toluene and
additional solvents identifiable by a skilled person), and adhesive
formulations (such as pinene and additional formulations
identifiable by a skilled person).
[0212] In embodiments of non-polar composition of the present
disclosure, the dielectric constant of a given host will vary with
temperature, which can be taken into account by one skilled in the
art.
[0213] Exemplary non-polar compositions, and in particular host
liquids, with a dielectric constant less than 5 are illustrated in
the table below (Table 1A). The table also provides exemplary hosts
that can be recognized as unfavorable for the modified non-polar
compositions herein described (see Table 1B).
TABLE-US-00001 TABLE 1A Dielectric Entry Fluid Temperature/.degree.
C. constant .di-elect cons. Exemplary Favorable Hosts 1 Benzene 20
2.3 2 Carbon disulfide 2.64 3 Carbon tetrachloride 20 2.23 4 Castor
oil 15.6 4.7 5 Chloroform 20 4.8 6 Cotton seed oil 3.1 7 Cumene 20
2.4 8 Decane 20 2 9 Dodecane 20 2 10 Ether 20 4.3 11 Fluorine
refrigerant R-12 25 2 12 Fluorine refrigerant R-22 25 2 13 Furan 25
3 14 Gasoline 21.1 2 15 Heptane 20 1.9 16 Hexane -90 2 17 Jet fuel
21.1 1.7 18 Kerosene 21.1 1.8 19 Linoleic acid 0 2.6-2.9 20 Linseed
oil 3.2-2.5 21 Naphthalene 20 2.5 22 Octane 20 2 23 Olive oil 20
3.1 24 Palmitic acid 71.1 2.3 25 Pentane 20 1.8 26 Phenol 10 4.3 27
Pinene 20 2.7 28 Styrene 25 2.4 29 Terpinene 21.1 2.7 30 Toluene
2.0-2.4 31 Turpentine (wood) 20 2.2 32 Vacuum (by definition) 1
32.1 Cyclohexane 2.0 32.2 Liquid methane -280 1.7 32.3 Liquid
Butane -1 1.4 32.4 Heavy oil 3 32.5 Petroleum oil 2.1 32.6 Liquid
asphalt 2.5-3.2
TABLE-US-00002 TABLE 1B Dielectric Entry Fluid Temperature/.degree.
C. constant .di-elect cons. Exemplary Unfavorable Hosts 33 Acetone
25 20.7 34 Alcohol, ethyl (ethanol) 25 24.3 35 Alcohol, methyl
(methanol) 20 35.1 36 Alcohol, propyl 20 21.8 37 Ammonia (aqua) 20
15.5 38 Aniline 20 7.3 39 Cresol 17.2 10.6 40 Ethylamine 21.1 6.3
41 Ethylene glycol 20 37 42 Furfural 20 42 43 Glycerine 47.68 44
Glycerol 25 42.5 45 Hexanol 25 13.3 46 Hydrazine 20 52 47 Pyridine
20 12
[0214] In particular, in some embodiments, host composition that
have dielectric constant equal to or less than about 5 are pentane,
hexane, cyclohexane, benzene, toluene, chloroform and diethylether.
In some embodiments, which can be used for fuel applications host
composition can also have dielectric constant less than 5,
including liquified petroleum gas, liquid methane, butane,
gasoline, kerosene, jet fuel and diesel fuel.
[0215] In embodiments, herein described polymer dielectric
constants can further provide an indication of their compatibility
with a chosen non-polar composition that is in the range indicated
in above. Reference is made for example to the exemplary list
provided in the table below (Table 2).
TABLE-US-00003 TABLE 2 Dielectric Plastic Material Constant -
.di-elect cons. - Acetal 3.7-3.9 Acrylic 2.1-3.9 ABS* 2.9-3.4
Polybutadiene approximately 2 Polycarbonate 2.9-3.8 Polyester, TP
3.0-4.5 Polypropylene 2.3-2.9 Polysulfone 2.7-3.8
Polydimethylsiloxane (Silicone Rubber) 3.0-3.2 Polyphenylene
sulfide 2.9-4.5 Polyacrylate 2.6-3.1 *ABS is Acrylonitrile
Butadiene Rubber
[0216] In particular, in some embodiments, for a given host
determined to have a dielectric constant within the threshold
herein disclosed, at least one framing associative polymer and
optionally one or more capping associative polymers herein
described are selected that are substantially soluble in the host
in accordance with the present disclosure.
[0217] In particular, appropriate associative polymers for a given
host can be identified by a skilled person in view of the present
disclosure. For example the backbone substantially soluble in the
host composition can be identified by comparison of the solubility
parameters (.delta.) of the polymer backbone and host composition,
as well as by determining the Flory-Huggins interaction parameter
(.chi.) from the solubility parameters according to calculations
described herein. In an exemplary embodiment, one or more
polymer-solvent pairs can have silicone backbones for use in one or
more fluorocarbon liquids.
[0218] In particular, an exemplary reference providing solubility
parametes is the website
www.sigmaaldrich.com/etc/medialib/docs/Aldrich/General_Infonnation/polyme-
r_solutions.Par.0 001.File.tmp/polymer_solutions.pdf at the time of
filing of the present disclosure (see Tables 3-5). More
particularly, a skilled person will know that Sigma-Aldrich and
other chemical companies provide exemplary tables showing exemplary
solubility parameter values for various non-polar compositions and
polymers. A skilled person can also refer to sources such as the
Polymer Handbook to find solubility parameter values [9].
TABLE-US-00004 TABLE 3 Table II: Solubility Parameters for
Plasticizers and Solvents (Alphabetical sequence) .delta. H-Bonding
.delta. H-Bonding Solvent (cal/cm.sup.3)F Strength.sup.3 Solvent
(cal/cm.sup.3).sup.1/2 Strength.sup.3 Acetone 9.9 m Dioctyl
sebacate 8.6 m Acetonitrile 11.9 p 1,4-Dioxane 10.0 m Amyl acetate
8.5 m Di(propylene glycol) 10.0 s Aniline 10.3 s Di(propylene
glycol) 9.3 m Benzene 9.2 p monomethyl ether Butyl acetate 8.3 m
Dipropyl phthalate 9.7 m Butyl alcohol 11.4 s Ethyl acetate 9.1 m
Butyl butyrate 8.1 m Ethyl amyl ketone 8.2 m Carbon disulfide 10.0
p Ethyl n-butyrate 8.5 m Carbon tetrachloride 8.6 p Ethylene
carbonate 14.7 m Chlorobenzene 9.5 p Ethylene dichloride 9.8 p
Chloroform 9.3 p Ethylene glycol 14.6 s Cresol 10.2 s Ethylene
glycol diacetate 10.0 m Cyclohexanol 11.4 s Ethylene glycol diethyl
ether 8.3 m Diamyl ether 7.3 m Ethylene glycol dimethyl ether 8.6 m
Diamyl phthalate 9.1 m Ethylene glycol monobutyl ether 9.5 m
Dibenzyl ether 9.4 m (Butyl Cellosolve .RTM.) Dibutyl phthalate 9.3
m Ethylene glycol monoethyl ether 10.5 m Dibutyl sebacate 9.2 m
(Cellosolve .RTM.) 1,2-Dichlorobenzene 10.0 p Furfuryl alcohol 12.5
s Diethyl carbonate 8.8 m Glycerol 16.5 s Di(ethylene glycol) 12.1
s Hexane 7.3 p Di(ethylene glycol) monobutyl 9.5 m Isopropyl
alcohol 8.8 m ether (Butyl Carbitol .RTM.) Methanol 14.5 s
Di(ethylene glycol) monoethyl 10.2 m Methyl amyl ketone 8.5 m ether
(Carbitol .RTM.) Methylene chloride 9.7 p Diethyl ether 7.4 m
Methyl ethyl ketone 9.3 m Diethyl ketone 8.8 m Methyl isobutyl
ketone 8.4 m Diethyl phthalate 10.0 m Propyl acetate 8.8 m
Di-n-hexyl phthalate 8.9 m 1,2-Propylenecarbonate 13.3 m Diisodecyl
phthalate 7.2 m Propylene glycol 12.6 s N,N-Dimethylacetamide 10.8
m Propylene glycol methyl ether 10.1 m Dimethyl ether 8.8 m
Pyridine 10.7 s N,N-Dimethylformamide 12.1 m
1,1,2,2-Tetrachloroethane 9.7 p Dimethyl phthalate 10.7 m
Tetrachloroethylene 9.3 p Dimethylsiloxanes 4.9-5.9 p
(perchloroethylene) Dimethyl sulfoxide 12.0 m Tetrahydrofuran 9.1 m
Dioctyl adipate 8.7 m Toluene 8.9 p Dioctyl phthalate 7.9 m Water
23.4 s .sup.2`Polymer Handbook`, Eds. Brandrup, J.; Immergut, E.
H.; Grulke, E. A., 4th Edition, John Wiley, New York, 1999
VII/675-711. Aldrich Catalog Number .sup.3H-Bonding: p = poor; m =
moderate; s = strong
TABLE-US-00005 TABLE 4 Table III: Solubility parameters (.delta.)
for Plasticizers and Solvents (Increasing .delta. value sequence)
.delta. H-Bonding Solvent (cal/cm.sup.3).sup.1/2 Strength.sup.4
Dimethylsiloxanes 4.9-5.9 p Diisodecyl phthalate 7.2 m Hexane 7.3 p
Diamyl ether 7.3 m Diethyl ether 7.4 m Dioctyl phthalate 7.9 m
Butyl butyrate 8.1 m Ethyl amyl ketone 8.2 m Ethylene glycol
diethyl ether 8.3 m Butyl acetate 8.3 m Methyl isobutyl ketone 8.4
m Methyl amyl ketone 8.5 m Amyl acetate 8.5 m Ethyl n-butyrate 8.5
m Ethylene glycol dimethyl ether 8.6 m Carbon tetrachloride 8.6 p
Dioctyl sebacate 8.6 m Dioctyl adipate 8.7 m Isopropyl alcohol 8.8
m Diethyl carbonate 8.8 m Propyl acetate 8.8 m Diethyl ketone 8.8 m
Dimethyl ether 8.8 m Toluene 8.9 p Di-n-hexyl phthalate 8.9 m Ethyl
acetate 9.1 m Diamyl phthalate 9.1 m Tetrahydrofuran 9.1 m Dibutyl
sebacate 9.2 m Benzene 9.2 p Tetrachloroethylene 9.3 p
(perchloroethylene) Di(propylene glycol) 9.3 m monomethyl ether
Chloroform 9.3 p Dibutyl phthalate 9.3 m Methyl ethyl ketone 9.3 m
Dibenzyl ether 9.4 m Ethylene glycol monobutyl ether 9.5 m (Butyl
Cellosolve .RTM.) Di(ethylene glycol) monobutyl 9.5 m ether (Butyl
Carbitol .RTM.) Chlorobenzene 9.5 p Methylene chloride 9.7 p
Dipropyl phthalate 9.7 m 1,1,2,2-Tetrachloroethane 9.7 p Ethylene
dichloride 9.8 p Acetone 9.9 m 1,2-Dichlorobenzene 10.0 p Diethyl
phthalate 10.0 m Ethylene glycol diacetate 10.0 m Di(propylene
glycol) 10.0 s Carbon disulfide 10.0 p 1,4-Dioxane 10.0 m Propylene
glycol methyl ether 10.1 m Di(ethylene glycol) monoethyl 10.2 m
ether (Carbitol .RTM.) Cresol 10.2 s Aniline 10.3 s Ethylene glycol
monoethyl 10.5 m ether (Cellosolve .RTM.) Pyridine 10.7 s Dimethyl
phthalate 10.7 m N,N-Dimethylacetamide 10.8 m Cyclohexanol 11.4 s
Butyl alcohol 11.4 s Acetonitrile 11.9 p Dimethyl sulfoxide 12.0 m
Di(ethylene glycol) 12.1 s N,N-Dimethylformamide 12.1 m Furfuryl
alcohol 12.5 s Propylene glycol 12.6 s 1,2-Propylenecarbonate 13.3
m Methanol 14.5 s Ethylene glycol 14.6 s Ethylene carbonate 14.7 m
Glycerol 16.5 s Water 23.4 s .sup.4H-Bonding: p = poor; m =
moderate; s = strong Carbitol and Cellosolve are registered
trademarks of Union Carbide Corp.
TABLE-US-00006 TABLE 5 Table IV: Solubility Parameters for
Homopolymers.sup.5 Repeating Unit .delta.(cal/cm.sup.3).sup.1/2
Repeating Unit .delta.(cal/cm.sup.3).sup.1/2 (Alphabetical
Sequence) (Increasing .delta. Value Sequence) Acrylonitrile 12.5
Tetrafluoroethylene 6.2 Butyl acrylate 9.0 Isobutyl methacrylate
7.2 Butyl methacrylate 8.8 Dimethylsiloxane 7.5 Cellulose 15.6
Propylene oxide 7.5 Cellulose acetate (56% Ac groups) 27.8
Isobutylene 7.8 Cellulose nitrate (11.8% N) 14.8 Stearyl
methacrylate 7.8 Chloroprene 9.4 Ethylene 8.0 Dimethylsiloxane 7.5
1,4-cis-Isoprene 8.0 Ethyl acrylate 9.5 Isobornyl methacrylate 8.1
Ethylene 8.0 Isoprene, natural rubber 8.2 Ethylene terephthalate
10.7 Lauryl methacrylate 8.2 Ethyl methacrylate 9.0 Isobornyl
acrylate 8.2 Formaldehyde (Oxymethylene) 9.9 Octyl methacrylate 8.4
Hexamethylene adipamide (Nylon 6/6) 13.6 n-Hexyl methacrylate 8.6
n-Hexyl methacrylate 8.6 Styrene 8.7 Isobornyl acrylate 8.2 Propyl
methacrylate 8.8 1,4-cis-Isoprene 8.0 Butyl methacrylate 8.8
Isoprene, natural rubber 8.2 Ethyl methacrylate 9.0 Isobutylene 7.8
Butyl acrylate 9.0 Isobornyl methacrylate 8.1 Propyl acrylate 9.0
Isobutyl methacrylate 7.2 Propylene 9.3 Lauryl methacrylate 8.2
Chloroprene 9.4 Methacrylonitrile 10.7 Tetrahydrofuran 9.4 Methyl
acrylate 10.0 Methyl methacrylate 9.5 Methyl methacrylate 9.5 Ethyl
acrylate 9.5 Octyl methacrylate 8.4 Vinyl chloride 9.5 Propyl
acrylate 9.0 Formaldehyde (Oxymethylene) 9.9 Propylene 9.3 Methyl
acrylate 10.0 Propylene oxide 7.5 Vinyl acetate 10.0 Propyl
methacrylate 8.8 Methacrylonitrile 10.7 Stearyl methacrylate 7.8
Ethylene terephthalate 10.7 Styrene 8.7 Vinylidene chloride 12.2
Tetrafluoroethylene 6.2 Acrylonitrile 12.5 Tetrahydrofuran 9.4
Vinyl alcohol 12.6 Vinyl acetate 10.0 Hexamethylene adipamide(Nylon
6/6) 13.6 Vinyl alcohol 12.6 Cellulose nitrate (11.8% N) 14.8 Vinyl
chloride 9.5 Cellulose 15.6 Vinylidene chloride 12.2 Cellulose
acetate (56% Ac groups) 27.8 .sup.5Values reported are for
homopolymers of the Repeating Unit. Reported .delta. values vary
with the method of determination and test conditions. Averaged
values are given in this table.
[0219] In some embodiments, the host composition can be formed by
crude oils, refined fuel, and in particular kerosene (e.g., Jet-A,
Jet-A1, and military fuel JP-8), gasoline, and diesel and other
refined fuels identifiable by a skilled person.
[0220] As used herein the term "refined" can be considered to have
its usual meaning in the art. Thus, a refined hydrocarbon liquid
composition is one that has been subjected to at least one process
that is intended to purify it from a crude petroleum (crude
oils/crudes) starting material. Thus, a refined fuel is a
hydrocarbon liquid composition which has undergone at least one
process that can be considered to be a distillation, upgrading or
conversion process, that is known to a person of skill in the art.
Typically, a refined fuel is one that has undergone more than one
refining procedure in a refinery, such as a combination of
distillation, upgrading and conversion. Therefore, in some
instances the refined fuel composition can meet known,
predetermined quality parameters. In some instances, a refined
hydrocarbon liquid composition can also include chemical additives
that have been introduced to meet desirable fuel specifications.
Exemplary refined fuels comprise Jet A and Jet A1 which are a
kerosene-type aviation fuel comprising a mixture of a large number
of different hydrocarbons with carbon number distribution between
about 8 and 16 (carbon atoms per molecule) identifiable by a
skilled person. An additional exemplary refined fuel comprise JP-8
or JP8 (for "Jet Propellant 8") which is a kerosene type jet fuel,
specified by MIL-DTL-83133 and British Defence Standard 91-87 also
identifiable by a skilled person. In particular, in some
embodiments, the associative polymer can be selected depending on
the regime of flows where drag reduction and/or flow rate
enhancement is desired as well as any other particular physical
and/or chemical properties of the non-polar composition to be
controlled.
[0221] In some embodiments the host composition can be formed by a
mineral oil. The term "mineral oil" refers to various colorless,
odorless, light mixture of higher alkanes from a mineral source. In
some embodiments, mineral oil can be a liquid by-product of
refining crude oil to make gasoline and other petroleum products.
This type of mineral oil is a transparent, colorless oil composed
mainly of alkanes and cycloalkanes, related to petroleum jelly and
has a density of around 0.8 g/cm.sup.3. Three basic classes of
mineral oils are alkanes, based on n-alkanes, naphthenic oils,
based on cycloalkanes, and aromatic oils, based on aromatic
hydrocarbons. Mineral oils can be in light or heavy grades, in
which heavy grades mean higher viscosity. The viscosity of a
mineral oil is correlated to its temperature, specifically, the
higher the temperature, the lower the viscosity.
[0222] In particular, in some embodiments, the chemical and/or
physical property can be controlled by controlling concentration of
one or more framing associative polymers in the host composition
relative to the overlap concentration c* of the one or more framing
associative polymers in the host concentration. Accordingly one or
more framing associative polymers can be comprised in the host in a
concentration of a fractional or integer multiple of the overlap
concentration (c*).
[0223] The terms "overlap concentration", or "c*", as used herein
refer to the concentration at which molecules of a non-associative
form of the framing associative polymer (e.g. obtained from
literature sources on the backbone of interest or from experimental
methods described herein using the polymer of interest modified to
inactivate the functional groups to prevent association, for
example by esterifying carboxylic acids or blocking carboxylic acid
with triethylamine) dissolved in the host begin to overlap each
other, as opposed to being separated as they would be in a more
dilute solution. In particular, c* for particular polymers in
particular hosts can be identified by methods and calculations
identifiable to a skilled person (see, e.g. [12] and Example
23).
[0224] In particular, the chain length of the backbone can be
chosen such that the backbone is long enough to ensure that a small
concentration of the polymer will suffice to produce a desired
effect using relationships between chain length and the c* of the
associative polymer described herein. For example, a polymer that
is effective at concentrations less than 1% by weight can be
obtained by choosing a backbone length that gives c* less than or
approximately equal to 1% by weight. In particular, the
relationship between chain length (e.g., expressed as the weight
averaged molecular weight) and c* can be determined from references
identifiable by a skilled person or determined by calculations as
described herein.
[0225] In particular, for a non-associative polymer chain, the
overlap concentration is given by:
c * = 3 .times. M w 4 .times. .pi. .function. ( R g 2 ) 3 / 2
.times. N a , ##EQU00005##
wherein M.sub.w is the weight averaged molecular weight, R.sub.g is
the radius of gyration, and N.sub.a is Avogadro's constant. The
overlap concentration represents a concentration equal to one
polymer molecule per spherical volume of radius R.sub.g, as
illustrated for example in the exemplary schematic of FIG. 17.
Throughout this disclosure, reference is made to c* when describing
the concentration of associative polymer required to achieve each
type of desired chemical or physical property. Generally the
pairings of polymer and host represent good solvent (e.g. a solvent
in which the polymer-solvent interactions are more
thermodynamically favorable than polymer-polymer interactions; see
e.g. [13]) conditions for the polymer backbone. In good solvent
conditions, R.sub.g increases approximately as the 2/3 power of
M.sub.w, so the expression for c* above shows that c* decreases as
M.sub.w increases. For a specific choice of polymer backbone and
host liquid, c* scales approximately as 1/M.sub.w. For example,
doubling the length of the polymer backbone approximately reduces
by half the concentration of associative polymer required to
achieve a given effect.
[0226] In several exemplary embodiments, many polymers' data
relating R.sub.g to M.sub.w are available for commonly used
solvents [14]. When experimental values are not available, an
indicative estimate can be made using a theoretical chain model as
herein described. For example, the estimate of R.sub.g using the
ideal chain model provides a conservative estimate c*of the
concentration of polymer required to achieve a desired effect. A
skilled person will realize upon a reading of the present
disclosure that the polymer backbone is in a good solvent condition
when dissolved in the host, so the actual c* of the polymer in the
host can be less than the value of c* estimated using the ideal
chain model.
[0227] For the purpose of selecting the degree of polymerization to
use for the span of the polymer (which is the backbone length in
the simple case of a linear telechelic structure), an equivalent
expression can be written that refers to tabulated parameters,
including e.g. parameters available for many polymers. In
particular, tabulated values of the characteristic ratio,
c.sub..infin., and the length and equivalent mass of a "Kuhn
segment" (b and M.sub.o) can be used to estimate the chain length
that will confer a desired effect with a selected concentration.
For example, for mist control, the polymer can be present at its
overlap concentration. In applications in which a polymer
concentration is desired to be at most c.sub.max, a chain can be
used that has sufficiently many Kuhn segments, N, so that the
polymer begins to overlap when its concentration is approximately
c.sub.max or less. Such chain can be given by:
N 3 / 2 = 9 .times. 6 2 .times. .pi.b 3 .times. c max
##EQU00006##
where N is the number of Kuhn segments and corresponds to a linear
polymer (or span of a branched polymer) having molar mass NM.sub.o,
where M.sub.o is the mass per Kuhn segment. Therefore, one can
synthesize for example a polymer that has a span of molar mass
NM.sub.o (and functional groups, selected with guidance below) and
introduce the synthesized polymer to a composition at a
concentration c* to provide mist control. A skilled person will
realize that when using approximate expressions for c*, mist
control is expected to improve by increasing or decreasing the
concentration relative to the estimated value of c*. In particular,
in experiments that examine the extent of mist control with
associative polymer, concentrations of associative polymer of 0.5c*
and 2c* can be suitable. Similar reasoning can be applied for other
effects herein described as will be understood by a skilled
person.
[0228] A list of exemplary tabulated parameters is indicated below
(Table 6; [15], p. 53):
TABLE-US-00007 TABLE 6 Characteristic ratios, Kuhn lengths, and
molar masses of Kuhn monomers for common polymers at 413 K Polymer
Structure C.sub..infin. b (.ANG.) .rho. (g cm.sup.-3) M.sub.0 (g
mol.sup.-1) 1,4-Polyisoprene (PI)
--(CH.sub.2CH.dbd.CHCH(CH.sub.3))-- 4.6 8.2 0.830 113
1,4-Polybutadiene (PB) --(CH.sub.2CH.dbd.CHCH.sub.2)-- 5.3 9.6
0.826 105 Polypropylene (PP) --(CH.sub.2CH.sub.2(CH.sub.3))-- 5.9
11 0.791 180 Poly(ethylene oxide) (PEO) --(CH.sub.2CH.sub.2O)-- 6.7
11 1.064 137 Poly(dimethyl siloxane) (PDMS)
--(OSi(CH.sub.3).sub.2)-- 6.8 13 0.895 381 Polyethylene (PE)
--(CH.sub.2CH.sub.2)-- 7.4 14 0.784 150 Poly(methyl methacrylate)
(PMMA) --(CH.sub.2C(CH.sub.3)(COOCH.sub.3))-- 9.0 17 1.13 655
Atactic polystyrene (PS) --(CH.sub.2CHC.sub.6H.sub.5)-- 9.5 18
0.969 720
[0229] In addition, a skilled person can also identify the
relationship between chain length and c* by experimental
measurement, e.g. by measuring the shear viscosity of the host
composition including the non-associative form of the polymer as a
function of the concentration of the polymer.
[0230] In particular, the overlap concentration of the backbone can
be determined from conventional shear viscosity measurements of
solutions containing various concentrations of the non-associative
form of the polymer. Alternatively, it can be evaluated using the
weight average molecular weight of the longest span of the polymer,
which is often characterized as part of the synthesis and
purification of a synthetic polymer.
[0231] In particular, c* can be determined at a given temperature
by measuring the viscosities of a non-associative polymer in an
appropriate host at varying concentrations using a rheometer
wherein at c* a deviation from linearity is observed in the plot of
viscosity versus polymer concentration. Linear regression is
performed on the data from both dilute and concentrated regimes,
and the crossover of the two linear fits represents the overlap
concentration, c* (see, e.g. [15, 16] and FIG. 38).
[0232] In particular, in some embodiments, a way to identify a
"desired overlap concentration" is to consider the type of
beneficial effect that is needed. For example, for a desired effect
of mist control, a concentration of polymer can be used that is
approximately equal to the overlap concentration. In particular, in
embodiments herein described where control of drag reduction and/or
flow rate enhancement and related duration is desired, a
concentration range of the associative polymer can be selected
between from about 0.001 c* to 1c*, depending on the extent drag
reduction desired alone or in combination with another physical
and/or chemical property to be controlled.
[0233] In embodiments where control of additional physical or
chemical property is desired the specific c* value can be selected
taking into account the c* values associated with the control of
the additional physical and/or chemical property.
[0234] For example a concentration range suitable for mist control
can be between 0.5c* to 2c*. In embodiments in which a desired
effect is enhancing fuel efficiency, a polymer concentration can be
used in the non-polar compositions herein described that is less
than c*, and in particular can be between 0.1c* and 0.5c*. In
embodiments in which the desired effects are drag reduction and
enhanced lubrication, a polymer concentration can be a
concentration below or approximately equal c*, and in particular
can be between 0.05c* to c*. In embodiments in which a desired
effect is converting a liquid into a gel, a concentration greater
than c* can be provided and in particular a concentration from 2c*
to 10c*.
[0235] Selection of one or more specific associative polymers that
can be comprised within the composition at a concentration relative
to the c* selected to control a set of one or more chemical and/or
physical properties can be performed in view of the characteristics
of functional groups, chain structures, and weight average
molecular weight of associative polymers herein described
[0236] In some embodiments, the functional groups described herein
at the ends of the backbone of the associative polymer can be
selected to ensure association occurs with the range of the polymer
concentrations selected. In conjunction with the selection of
functional groups, the synthetic chemistry is selected to be
appropriate for introduction of such groups.
[0237] A skilled person will realize that characteristics of the
host that influence the selection of functional groups include, for
example, its dielectric constant and whether or not it contains
protic species or species that offer a lone pair of electrons.
Non-polar liquids generally contain molecules made mainly of atoms
with similar electronegativities, such as carbon and hydrogen (for
example, hydrocarbons that dominate fuels and many lubricants).
Bonds between atoms with similar electronegativities lack partial
charges, making the molecules non-polar. A common way of
quantifying this polarity is the dielectric constant. A skilled
person will also realize that another characteristic of components
in the host liquid is whether or not they have O--H or N--H bonds
that can participate in hydrogen bonding. A skilled person would
recognize these as protic molecules. Examples of protic species
that may be present in host liquids in the disclosed ranges of
dielectric constants include, for example secondary amines with
substantial hydrocarbon content (e.g., Diisobutylamine, which has
dielectric constant 2.7; dipropylamine, which has dielectric
constant 2.9; Methylbenzylamine, which has dielectric constant
4.4), carboxylic acids with substantial hydrocarbon content (e.g.,
palmitic acid, which has dielectric constant 2.3; linoleic acid,
which has dielectric constant 2.6; oleic acid, which has dielectric
constant 2.5), and alcohols with substantial hydrocarbon content
(e.g., hexadecanol, which has dielectric constant 3.8). In
addition, a skilled person will also realize that other protic
species (e.g., protic species that in their pure state can have a
dielectric constant greater than 5, such as aniline and phenol) can
be present as minor species in a host liquid that has dielectric
constant less than 5.
[0238] A skilled person will realize that another relevant
characteristic of components in the host liquid is whether or not
they present a lone pair of electrons that can participate in
hydrogen bonding. Examples of species with lone pairs that may be
present in host liquids in the disclosed ranges of dielectric
constants include alkyl-quinoxalines (e.g.,
2,3-Dimethylquinoxaline, which has dielectric constant 2.3),
tertiary amines (e.g., triethylamine, which has dielectric constant
2.4) and nonconjugated esters (e.g., isoamylvalerate, which has
dielectric constant 3.6). In addition, a skilled person will also
realize that other lone-pair species (that in their pure state
might have a dielectric constant greater than 5, such as pyridine
and methylethylketone) can be present as minor species in a host
liquid that has dielectric constant less than 5. In addition, a
skilled person will realize that components that are used as
additives when the host liquid is formulated can also be present.
For example, metal chelating agents (e.g.,
N,N-Disalicylidene-1,2-propanediamine) can be present in a host
liquid that is a fuel. A skilled person will realize that the
presence of these constituents influences the selection of
functional groups depending on the presence of protic species or
species that offer a lone pair of electrons as described
herein.
[0239] A skilled person will also realize the presence of protic
species can, in some circumstances, interfere with FG, and in
particular with FGa, association mediated by hydrogen bonding. The
skilled person will realize that one way to overcome the
interference is to increase the number of hydrogen bond moieties at
the chain ends. The skilled person will also realize that another
way to overcome the interference is to reduce the concentration of
protic species in the host. A skilled person would recognize that
these two approaches can be used together. In addition, a skilled
person will also realize that, all other factors being equal,
increasing the dielectric constant of the host weakens the
interaction (e.g., conventional hydrogen bonds, charge-assisted
hydrogen bonds, charge transfer interaction, metal-ligand
interactions). For example, increasing the dielectric constant from
2.4 (toluene) to 4.8 (chloroform) decreases the association
constant for the Hamilton receptor and cyanuric acid by an order of
magnitude. Accordingly, FGas that provide a stronger association
(e.g., charge-assisted hydrogen bonding or a metal-ligand
interaction) are expected to be beneficial when the dielectric
constant is greater than 2.5. A skilled person would realize that
the selection of FGas that provide strong association can be used
together with increasing the number of associative groups at the
chain ends and with reducing the concentration of host components
that have high dielectric constants.
[0240] In particular, in some embodiments, the value of the
concentration of the associative polymer relative to overlap
concentration c* can be governed by the selection of chain-host
pair and can be insensitive to the specific choice of FGa. A
skilled person will understand that the overlap concentration can
vary with temperature, in a manner that is particular to a specific
chain-host pair. For example, the selection of polymer backbone and
host governs the solvent quality; and, for a given solvent quality,
the degree of polymerization is chosen to adjust c* once the
chain-host pair is selected. In this connection selecting a greater
degree of polymerization, provides a greater R.sub.g and,
consequently, a reduced c* as will be understood by a skilled
person.
[0241] In some embodiments herein described, the chain structure
between the nodes (e.g. the chain being a polyolefin, polydiene, or
other structure identifiable to a skilled person upon a reading of
the present disclosure) can be chosen such that it interacts
favorably with the host, the state of the backbone can be estimated
using good solvent (e.g. a solvent in which the polymer-solvent
interactions are more thermodynamically favorable than
polymer-polymer interactions; see e.g. [13]) scaling for its
pervaded volume. Over most of the molecular weight range of
interest, the ideal chain approximation (e.g. approximation of the
polymer chain as a random walk and neglecting any kind of
interactions among monomers; see e.g. [15]) can also be useful: it
provides a lower bound on R.sub.g that is usually within a factor
of 2 of the good solvent chain dimensions, as shown in FIG. 16 for
the case of polystyrene for a good solvent such as toluene, and a
theta solvent (e.g. a solvent in which the polymer-solvent
interactions are approximately as equally thermodynamically
favorable as polymer-polymer interactions; see e.g. [13]) such as
cyclohexane. In particular, the value of the radius of gyration can
be used to estimate the concentration at which polymer molecules
would begin to overlap one another: the overlap concentration c*
corresponds to the value that gives approximately one polymer
molecular per (R.sub.g.sup.2).sup.3/2.
[0242] Additional factors related to applications of the resulting
compositions (e.g. distribution through a pipeline, storage for a
certain time period and other factors identifiable by a skilled
person), can also be taken into account in the selection of the
specific associative polymer or combination thereof and/or in the
selection of the related concentration in the host composition
relative to c* within a range associated to control of one or more
chemical and/or physical properties.
[0243] In embodiments in which a low concentration of polymer is
desired, a reduction in the concentration of the associative
polymer relative to c* can be obtained by selecting a polymer with
high degree of polymerization. In some of those embodiments, the
degree of polymerization of the polymer is low enough that the
polymers do not degrade during necessary handling. For example, in
embodiments in which the non-polar compositions are fuel or other
liquid and the liquid is intended to travel through a distribution
system, minimization of the degradation of the polymer upon passage
through pumps and filters, and/or minimization of degradation
during turbulent flow in transport pipelines or hoses can be
desirable. In this connection, in exemplary embodiments in which
the polymers comprise linear chains, keeping the weight-average
molar mass below 1,000,000 g/mol can give adequate stability with
respect to shear degradation. In exemplary embodiments in which the
polymer comprises lightly branched molecules, having
node-chain-node segments that are individually greater than 10,000
g/mol, the longest span of the molecule can be kept below the
threshold for shear degradation (typically less than 1,000,000
g/mol).
[0244] In embodiments wherein conversion of liquid to gel is
desired, a solution or gel that has dielectric constant less than 5
and comprises a polymer that has weight average molar mass between
100,000 g/mol and 1,000,000 g/mol, can comprise the polymer at a
concentration that is between 0.1c* and 10 c*. The specific
concentration can be determined based on the measured length and
backbone composition of the polymer, and the polymer molecules
manifestly associate with one another as evidenced by shear
viscosity that is anomalously enhanced relative to a
non-associative polymer of the same molar mass and backbone
structure or by light scattering showing structures that are much
larger than a non-associative polymer of the same molar mass and
backbone structure. The latter measurements can be performed for
example by removing the polymer from the composition and
reconstituting them in a solvent that has a dielectric constant
that is close to that of the composition (.+-.20%) at a
concentration of c* based on the weight-average molecular weight
determined by GPC equipped with multi-angle static light
scattering.
[0245] In some embodiments when the concentration of the framing
associative polymer is equal to or lower than 0.02 c* the
associative polymer can have a weight averaged molecular weight
equal to or higher than 10,000,000 g/mol. In some of those
embodiments, the associative polymer can be used for drag reduction
in the non-polar composition.
[0246] In some embodiments when the concentration of the framing
associative polymer is between than 0.05 c* to 0.1 c*the
associative polymer can have a weight averaged molecular weight
equal to or higher than 10,000,000 g/mol In some of those
embodiments, the associative polymer can be used for mist control
in the non-polar composition.
[0247] In some embodiments when the concentration of the framing
associative polymer is between 0.02 c* and 0.05 c*, the associative
polymer can have a weight averaged molecular weight between
2,000,000 g/mol to 10,000,000 g/mol In some of those embodiments,
the associative polymer can be used for drag reduction in the
non-polar composition.
[0248] In some embodiments when the concentration of the framing
associative polymer is between 0.05 c* and 0.1c*, the associative
polymer can have a weight averaged molecular weight between 500,000
g/mol to 2,000,000 g/mol, and in particular 1,000,000 g/mol to
2,000,000 g/mol. In some of those embodiments, the associative
polymer can be used for drag reduction and/or mist control in the
non-polar composition.
[0249] In some embodiments when the concentration of the framing
associative polymer is between 0.1 c* and c*, the associative
polymer can have a weight averaged molecular weight between 400,000
g/mol to 1,000,000 g/mol In some of those embodiments, the
associative polymer can be used for drag reduction and/or mist
control in the non-polar composition. In particular, when the
weight averaged molecular weight is at least 400,000 g/mol the
associative polymer can be used at concentration is between 0.1c*
and 0.5c* for drag reduction of the host composition; at a
concentration of about 0.5c* for drag reduction and possibly for
mist control of the host composition depending on the molecular
weight of the polymer, and at a concentration of less than
approximately c* for drag reduction and mist control of the host
composition.
[0250] In some embodiments when the concentration of the framing
associative polymer is between 0.5 c* and c*, the associative
polymer can have a weight averaged molecular weight between 400,000
g/mol to 1,000,000 g/mol. In some of those embodiments, the
associative polymer can be used for drag reduction, mist control
and/or lubrication in the non-polar composition.
[0251] In some embodiments when the concentration of the framing
associative polymer is between c* and 2c*, the associative polymer
can have a weight averaged molecular weight between 400,000 g/mol
to 1,000,000 g/mol. In some of those embodiments, the associative
polymer can be used for mist control, lubrication, and/or
viscoelastic properties of the non-polar composition.
[0252] In some embodiments when the concentration of the framing
associative polymer is between c* and 2c*, he associative polymer
can have a weight averaged molecular weight between 100,000 g/mol
to 400,000 g/mol. In some of those embodiments, the associative
polymer can be used for drag reduction, lubrication and/or
viscoelastic properties of the non-polar composition.
[0253] In some embodiments when the concentration of the framing
associative polymer is between c* and 3c*, the associative polymer
can have a weight averaged molecular weight between 400,000 g/mol
to 1,000,000 g/mol. In some of those embodiments, the associative
polymer can be used for mist control, lubrication and/or control of
viscoelastic properties in the non-polar composition.
[0254] In some embodiments when the concentration of the framing
associative polymer is between c* and 3c*, the associative polymer
can have a weight averaged molecular weight between 100,000 g/mol
to 400,000 g/mol In some of those embodiments, the associative
polymer can be used for lubrication, and/or control of viscoelastic
properties in the non-polar composition.
[0255] In some embodiments when the concentration of the framing
associative polymer is between 2c* to 10c*, the associative polymer
can have a weight averaged molecular weight between 100,000 g/mol
to 400,000 g/mol In some of those embodiments, the associative
polymer can be used for lubrication, and/or viscoelastic properties
of the non-polar composition.
[0256] In some embodiments when the concentration of the framing
associative polymer is between 2c* to 10c*, the associative polymer
can have a weight averaged molecular weight between 100,000 g/mol
to 1,000,000 g/mol In some of those embodiments, the associative
polymer can be used for lubrication, and/or viscoelastic properties
and in particular gelification of the non-polar composition.
[0257] In some embodiments when the concentration of the framing
associative polymer is between 3c* and 10c*, the associative
polymer can have a weight averaged molecular weight between 100,000
g/mol to 1,000,000 g/mol In some of those embodiments, the
associative polymer can be used for lubrication, and/or control of
viscoelastic properties and in particular gelification in the
non-polar composition.
[0258] In embodiments in which the composition comprise liquid
fuels, such as gasolines, diesel fuels, kerosene and jet fuels,
such compositions can comprise polymers with molar mass between
100,000 g/mol and 1,000,000 g/mol having backbones that, as bulk
polymers, have dielectric constant less than 3 and are present in
the composition at a concentration that is between 0.1c* and 10c*,
based on the measured weight averaged molar mass and backbone
composition of the polymer, and the polymer molecules manifestly
associate with one another as evidenced by shear viscosity that is
enhanced relative to a non-associative polymer of the same molar
mass and backbone structure or by light scattering showing
structures that are much larger than a non-associative polymer of
the same molar mass and backbone structure. The latter measurements
can be performed for example by removing the polymer from the
composition and reconstituting them in toluene at a concentration
of c* based on the weight-average molar mass determined by GPC
equipped with light scattering. In several examples of the current
disclosure toluene is indicated as a reference host because it has
a dielectric constant of approximately 2.2, which is at the upper
range of diverse fuels and, therefore, gives a conservative
diagnostic of association. That is, a polymer that forms
intermolecular associations in toluene will form intermolecular
associations in gasoline, diesel, kerosene and jet fuel, among
others.
[0259] In some embodiments, polymer for improving fuel efficiency
can be effective at 10000 ppm or less with weight average molecular
weight below 1,000,000 g/mol, possibly after more than 10 passages
of the fuel through a fuel pump. In some embodiments, associative
polymers can remain uniformly dissolved for at least 2 weeks or
even months even at -30.degree. C.
[0260] In some embodiments, with weight average molecular weight
400,000 g/mol chains, droplet behavior of non-polar composition
comprising associative polymers herein described is expected to
match 4,200,000 g/mol (weight average) polyisobutylene, a commonly
used standard material to achieve mist control effect using high
molecular weight polymer, compared at the same, concentration of
0.3%.
[0261] In some embodiments, if for a particular application the
polymer concentration is desired to be kept low, this can be
achieved by increasing the length of the polymer chain between
associative groups. The reason for this is that polymers tend to
adopt compact conformations in isolated clusters when the
concentration is far below their overlap concentration; increasing
the length of the polymer between associative groups decreases the
overlap concentration, thereby allowing desired properties to be
achieved with a lower concentration of polymer.
[0262] In some embodiments, if for a particular application the
polymer additive is desired to survive passage through pumps and
turbulent pipe flow, this can be achieved by keeping the length of
the polymer below the threshold at which chain scission occurs in
intense flows. For a number of polymers, the literature provides
values of the chain length above which chains scission occurs (e.g.
polyisobutylene) For any choice of polymer backbone structure, the
threshold length (or equivalently, degree of polymerization or
molar mass) above which chain scission occurs upon passage through
pumps or turbulent pipe flow can be determined as will be
understood by a skilled person.
[0263] In some embodiments, for the purpose of creating additives
that deliver valuable effects at low polymer concentration, use of
chain segments having molar mass between 100,000 g/mol and 500,000
g/mol between FG, and in particular FGa, and node can be desired.
This range of structures can associate at low concentrations to
give desired properties. For example, in the context of fuels, the
resulting polymers can inhibit misting in order to reduce the risk
of post-crash fires; can control atomization to increase fuel
efficiency and/or reduce emissions; can confer drag reduction that
reduces pumping costs and improves throughput through existing
pipelines; and improve lubrication. In particular, polymers of the
present disclosure can survive prolonged, severe shear with little
degradation; the polymers do not interfere with filtering fuel; the
polymers do not interfere with dewatering fuel.
[0264] According to the above indication and to the additional
indication provided in the disclosure, in some embodiments, one
skilled in the art can identify whether or not a host of interest
(e.g., a particular lubricant oil) is suitable for application of
the associative polymers based on the dielectric constant of the
host, and the skilled person can identify suitable monomer
structures using knowledge of the dielectric constant or solubility
parameter of the resulting polymer, and thus select the degree of
polymerization (e.g. by synthesizing a polymer backbone of a
particular weight-averaged molecular weight) to achieve a desired
c*.
[0265] In some embodiments herein described once the suitability of
a potential host is determined, as well as the selection of the
monomer and the selection of the degree of polymerization are made,
functional groups can be selected that are able to associate
according to the indicated association constant. In particular, in
some embodiments when the host has a relatively low dielectric
constant (e.g. .epsilon.<2) and little or no participation in
hydrogen bonds, there are many associative groups that are
effective as will be understood by a skilled person. Therefore,
secondary considerations can be applied to narrow down the
selection (such as cost, sensitivity to ionic species, nature of
combustion products, and other considerations identifiable to a
skilled person). For example, in some instances, with increasing
dielectric constant of the host, many of the useful interactions
(hydrogen bonding, charge transfer, acid-base, and others
identifiable to a skilled person) become progressively weaker.
Therefore, clusters of functional groups may be required to confer
adequate association. Consequently, for solvents that have
dielectric constant greater than 2.5, dendrimeric FG can be used
that include multiple associative groups (examples are shown for FG
that each present four or eight copies of a chosen associative
group).
[0266] For example, in embodiments herein described where drag
reduction (e.g. the flow resistance of a non-polar composition
through a conduit such as an oil pipeline or fuel line in a
vehicle) is the property sought to be controlled, a skilled person
can identify the solubility parameter of the fluid, and then can
identify polymer backbones that are substantially soluble in the
fluid (e.g. by comparing the solubility parameters and/or using the
solubility parameters to determine the Flory-Huggins interaction
parameter as described herein). The selection of particular
polymers for the backbone of the associative polymer suitable to be
included at a concentration relative to c* below c* can be further
refined based on, for example, on the cost of the polymers, or the
ease and/or expense of the polymerization chemistry, as would be
identifiable to a skilled person.
[0267] In particular, for drag reduction, a skilled person would
realize it can be desirable to minimize the amount of polymer used
for two reasons: to minimize cost and to avoid undue increase in
the shear viscosity of the mixture. Accordingly, the length
(expressed as the weight-averaged molecular weight) of the backbone
of the associative polymer can be near the threshold imposed by
shear degradation, which a skilled person would understand to be in
the range of approximately 500,000 g/mol for hydrocarbon polymers
such as polyisobutylene, polybutadiene, polyolefins, and others
identifiable to a skilled person.
[0268] In particular, a skilled person can verify that the chain
length selected resists shear degradation by performing analyses
known to the skilled person. For example, the viscosity of a
non-polar composition comprising the associative polymers described
herein can be measured before and after recirculation through a
conduit (e.g. by using a fuel pump to recirculate a sample of the
non-polar composition) and determining if there is a difference in
viscosity between the two time points (e.g., if the viscosity
decreases after recirculation, the associative polymer can be
considered to have undergone shear degradation).
[0269] As another example, if mist control is among the properties
of the nonpolar composition desired to be controlled, the polymer
backbone selection among the possible polymers to be included at a
concentration relative to c* between 0.5c* to 2c* can be based on
solubility of the in nonpolar composition as described herein (e.g.
solubility parameters and/or Flory-Huggins interaction parameter),
with the additional consideration of the associative polymer having
negligible effect on the calorific value of the nonpolar
composition in which mist control is desired, as would be
identifiable to a skilled person (e.g. by using the calorimetric
method ASTM D240-09). The functional groups described herein at the
ends of the backbone of the associative polymer can be chosen to
ensure that association occurs at desired concentration such that
heteroatom content is so low as to not affect burning. For example,
association can be measured using titration techniques identifiable
to a skilled person (see, e.g., [17]). Using the titration methods,
the skilled person can identify a concentration at which the
particular associative polymers (with a given number of end groups
containing heteroatoms) associate; if the concentration is suitable
based on c* considerations (e.g. the particular concentration of
the associative polymer relative to c* to control a particular
property such as mist control) the skilled person can then measure
the calorific value using ASTM D240-09. If the concentration is not
suitable, the number of end groups can be changed accordingly (e.g.
by increasing the number for greater association at a given
concentration, or by decreasing the number for lesser association),
the titration re-performed, and the calorific value
re-measured.
[0270] In various embodiments, associative polymers herein
described can be made with methods in which a backbone polymer is
provided which is then functionalized with suitable FGs and in
particular with FGas.
[0271] In some embodiments, in which the backbone has a structural
unit of formula -4node-chain]- (II), wherein [0272] chain is a
non-polar polymer substantially soluble in a non-polar composition,
the polymer having formula
[0272] R.sub.1-[A].sub.nR.sub.2 (III) [0273] in which [0274] A is
an organic moiety forming the monomer of the polymer; [0275]
R.sub.1 and R.sub.2 are independently selected from any carbon
based or organic group; and [0276] n is an integer.gtoreq.1; and
[0277] node is a chemical moiety covalently linking one of R.sub.1
and R.sub.2 of at least one first chain with one of the R.sub.1 and
R.sub.2 of at least one second chain; [0278] and wherein the chain
and node of different structural units of the polymer can be the
same or different and the polymer presents two or more terminal
R.sub.1 and R.sub.2 groups the method can comprise: providing the
polymer having structural unit of formula -node-chain]- (II) and
attaching functional groups FG herein described to terminal R.sub.1
and/or R.sub.2 groups of the polymer.
[0279] In some embodiments, an associative polymer can be provided
by forming a polymer chain through a method of polymerization of a
suitable monomer such as those described in [9], so that the
desired architecture (linear, branched, star, and other
architectures identifiable to a skilled person) is generated and
individual polymer chains are substantially terminated by chemical
groups that are amenable to functionalization. The end groups can
already be functionalized by FGs and in particular FGas or formed
by precursors that are converted to FGs, and in particular FGas
(e.g., by deprotection or functional groups that are suitable for
covalent attachment of FGs). This prepolymer can then be reacted
with a molecule containing the desired FG, so that FGs are
introduced to the polymer chain through chemical transformations
commonly described as functional group interconversions. Thus, in
some embodiments the desired polymer composition can be achieved in
a two-step process, in which after the first step reaction of the
monomer gives a polymer that does not substantially include the
desired FG or FGs, which are introduced in the second step. For
example, the prepolymer may be synthesized as substantially
terminated with functional groups known in the art to be "leaving
groups" such as halide, triflate or tosylate, and the desired FG or
FGs introduced to the polymer chain through nucleophilic
substitution reaction.
[0280] In some embodiments, suitable monomers comprise dienes,
olefins, styrene, acrylonitrile, methyl methacrylate, vinyl
acetate, dichlorodimethylsilane, tetrafluoroethylene, acids,
esters, amides, amines, glycidyl ethers, isocyanates, and mixtures
of these.
[0281] In some embodiments, the associative polymer suitable for
drag reduction can be selected based on the Reynolds number of the
host composition in the flow pattern where the control is desired,
wherein when the Reynolds number of the host composition is in the
range of about 5,000.ltoreq.Re.ltoreq.25,000 or possibly up to
1,000,000 Re, the association constant (k) is in the range of
4.ltoreq.log.sub.10 k.ltoreq.12; and when the Reynolds number is in
the range of about Re.gtoreq.25,000, the association constant (k)
is in the range of 6.ltoreq.log.sub.10 k.ltoreq.14.
[0282] In some embodiments, associative polymers that can be used
for drag reduction in flow having Reynolds numbers equal to or
higher than 5000 comprise one or more of a telechelic 1,4-PB
polymer with each end-group having one tertiary amine group
(Di-MB), a telechelic 1,4-PB polymer with each end-group having two
tertiary amine groups (Di-DB) a telechelic 1,4-PB polymer with each
end-group having four tertiary amine groups (Di-TB), a telechelic
1,4-PB polymer with each end-group having eight tertiary amine
groups (Di-OB), a telechelic 1,4-PB polymer with each end-group
having one carboxyl groups (Di-MA), a telechelic 1,4-PB polymer
with each end-group having two carboxyl groups (Di-DA), a
telechelic 1,4-PB polymer with each end-group having four carboxyl
groups (Di-TA), a telechelic 1,4-PB polymer with each end-group
having eight carboxyl groups (Di-OA), a telechelic 1,4-PB polymer
with each end-group having one tert-butyl ester groups (Di-ME), a
telechelic 1,4-PB polymer with each end-group having two tert-butyl
ester groups (Di-DE), a telechelic 1,4-PB polymer with each
end-group having four tert-butyl ester groups (Di-TE), and/or a
telechelic 1,4-PB polymer with each end-group having eight
tert-butyl ester groups (Di-OE). In particular in those embodiments
the molecular weight of the polybutene can have any values among
the ones described, e.g. an overall weight average molecular
weight, M.sub.w, equal to or lower than about 2,000,000 g/mol,
and/or a Mw equal to or higher than about 100,000 g/mol.
[0283] In some embodiments, associative polymers that can be used
for drag reduction in flow having Reynolds numbers equal to or
higher than 5000 comprise the following pairs: Di-TA/Di-MB (1
tertiary amine), Di-TA/Di-DB, Di-TA/Di-TB; Di-TB (4 tertiary
amines)/Di-MA, Di-TB/Di-DA; Di-OB (8 tertiary amines)/Di-MA,
Di-OB/Di-DA, and Di-OB/Di-TA.
[0284] The association polymers described herein can be synthesized
by methods known to a skilled person. For example, the backbone can
be synthesized by Ring-Opening Metathesis Polymerization (ROMP)
chemistry and functionalized at the ends of the backbone using
appropriate chain transfer agents (see, e.g., Examples section
herein and [18]). In addition, anionic polymerization,
Atom-transfer Radical-Polymerization (ATRP), Reversible
Addition-Fragmentation chain Transfer polymerization (RAFT) and
other polymerization techniques identifiable to a skilled person
(including an alternative overview of metathesis techniques) can be
used to synthesize several types of backbones (e.g. block, star,
branched and other architectures) and introduce of many different
types of functional groups at the ends of the polymer chain (or
elsewhere if desired) (see, e.g. [19, 20]).
[0285] In certain embodiments, an associative polymer in accordance
with the present disclosure can be provided by forming a polymer
chain such that the desired architecture is generated, and
individual polymer chains are substantially terminated by the
desired FG, in situ. Thus, in some embodiments the desired polymer
composition can be achieved in a single step process, and reaction
of the monomer affords a polymer that includes the desired FG or
FGs. In yet other embodiments, the desired FGs can be introduced to
the polymer chain in a form such that the ultimate function of such
FGs is masked by a chemical substitution (e.g. the FGs feature one
or more "protecting groups"), and the desired functionality of the
FGs can then be enabled for example through removal of such a
"protecting group" through chemical transformation in subsequent
steps. However, in some embodiments, the desired polymer
composition can still be achieved in a single step process, and the
polymer as synthesized includes the desired FG or FGs in protected
form. In some of those embodiments, suitable monomers include
cyclic olefins and acyclic .alpha.,.omega.-dienes.
[0286] Suitable methods of polymerization in accordance with some
embodiments herein described, comprise ring-opening metathesis
polymerization (ROMP) and acyclic diene metathesis polymerization
(ADMET), in the presence of suitable chain transfer agent (CTA)
typically consisting of the FG suitably disposed about a reactive
olefinic functionality (e.g. cis-double bond). The FG or FGs can be
in their ultimate functional form in this CTA, or can be in
"protected" form such that unmasking of the ultimate functional
form may be achieved through removal of this "protecting group"
through chemical transformation.
[0287] Suitable "protecting groups" in accordance with some
embodiments herein described, comprise those described in
"[21].
[0288] For example, in some embodiments where the polymer backbone
is made by a ROMP polymerization (e.g. using cyclooctadiene to
synthesize a backbone of repeating
.dbd.CHCH.sub.2CH.sub.2CH.dbd.CHCH2CH2CH.dbd. units), the ends of
the polymer backbone can be functionalized with appropriate chain
transfer agents to provide functionalized ends of the backbone
which can be further transformed to provide functional groups
capable of being corresponding functional groups, as shown for
example in Examples 1-3 where carboxylic acid functional groups are
installed. A skilled person will realize upon a reading of the
present disclosure that analogous reactions can be performed to
synthesize other backbones such as poly(vinylacetate) (e.g. RAFT
polymerization as shown, for example in [22]; or free radical
polymerization of vinyl acetate using a free radical initiator
comprising FG groups as shown, for example, in [23]).
[0289] In particular, as exemplified in Example 3, chain transfer
agents can be used to attach moieties substituted with chloro
groups, which can then be displaced with azide groups (e.g. using
trimethylsilyl (TMS) azide by methods identifiable to a skilled
person). A moiety comprising attached alkyne groups can then be
reacted with the azide groups via reactions such as the
azide-alkyne Huisgen cycloaddition (e.g. click reaction) to attach
the moiety to thereby attach the FG to the backbone (see, e.g.
Example 3).
[0290] In yet further embodiments, an associative polymer in
accordance with the present disclosure can be provided by
metathesis applied to a high molecular weight (M.sub.w>5,000,000
g/mol) poly(diene) such as poly(butadiene) in the presence of
suitable CTA and metathesis catalyst to give a shorter poly(diene)
substantially terminated by an FG and in particular FGas, with the
diene:CTA ratio chosen to afford the desired molecular weight for
the product telechelic polymer. In particular methods of these
particular embodiments, the starting high molecular weight
poly(diene) can be linear and substantially free of 1,2-vinyl
groups in the polymer backbone.
[0291] In exemplary methods to make a polymer of the present
disclosure, the polymer can be made by ROMP in a continuous
process. In particular, methods of these particular embodiments the
continuous process can use reactions in series (FIG. 10). In
relation to compositions that are used as liquid fuels the
continuous production of the associative polymers herein described
can be performed near or inside a petrochemical refinery and
incorporated into a product continuously.
[0292] In exemplary methods to make a polymer of the present
disclosure, the polymer can be made by ring-opening metathesis
polymerization (ROMP) to obtain desired end-functional telechelic
polymers of weight averaged molecular weight 100,000 to 1,000,000
g/mol.
[0293] In exemplary methods to make a polymer of the present
disclosure, the polymer can be made by related polymerization
and/or functionalization methods to make functional telechelics of
molecular weight 100,000 to 1,000,000 g/mol.
[0294] In some embodiments, a mixture of framing associative
polymers and capping associative polymers are produced
simultaneously.
[0295] In various embodiments, associative polymers herein
described can be used in methods and systems to control physical
and/or chemical properties of a non-polar composition herein
described, in particular to obtain a controlled drag reduction
and/or flow rate enhancement effect alone or in combination with
other physical and/or chemical properties as herein described.
[0296] The method comprises providing a host composition having a
dielectric constant equal to or less than about 5; and providing at
least one framing associative polymer substantially soluble in the
host composition; and combining the host composition and the at
least one framing associative polymer herein described at a
concentration c between from about 0.001c* to about 10c* selected
based on the molecular weight of the at least one framing
associative polymer (and/or radius of gyration) and on a physical
and/or chemical property and in particular rheological property to
be controlled.
[0297] In some embodiments, the method can further comprise
selecting a concentration c of the at least one framing associative
polymer in the host composition, the concentration depending on the
averaged molecular weight and/or radius of gyration of the at least
one framing associative polymer and on a physical and/or chemical
property to be controlled based on the factors herein described
before the combining. A skilled person will be able to select the
specific Mw, Radius of gyration and concentration of the at least
one framing associative polymer in the host composition in view of
the present disclosure.
[0298] In particular in exemplary embodiments, framing associative
polymer can be used, alone or in combination with capping
associative polymers, in a method to control resistance to flow
and/or flow rate enhancement of a non-polar composition In some of
those embodiments additional physical and/or chemical property of
the non-polar composition can also be controlled. The method
comprises providing a host composition having a dielectric constant
equal to or less than about 5; and providing at least one framing
associative polymer substantially soluble in the host composition
and having a weight averaged molecular weight equal to or higher to
200,000 g/mol. The method comprises combining the host composition
and the at least one framing associative polymer herein described
at a concentration c between from about 0.001c* to about 1c*
selected based on the molecular weight of the at least one framing
associative polymer and on a physical and/or chemical property and
in particular rheological property to be controlled.
[0299] In some embodiments, the method can further comprise
selecting a concentration c of the at least one associative polymer
in the host composition between from about 0.001c* to about 1c*
depending on the averaged molecular weight of the at least one
associative polymer and on a physical and/or chemical property to
be controlled based on the factors herein described before the
combining.
[0300] In some embodiments, the method can further comprise
determining an overlap concentration c* for the at least one
framing associative polymer before performing the selecting.
[0301] In some embodiments, the non polar composition resulting
from the method to control resistance to flow and/or flow rate
enhancement herein described is capable of maintaining
substantially constant flow rate enhancement. In some of those
embodiments, the at least one framing associative polymer has a
weight averaged molecular weight of 650,000 g/mol to 750,000 g/mol
and can be comprised at a concentration of about 0.5c*. In some of
those embodiments the flow rate enhancement can be about 28%.
[0302] In some embodiments, in the non polar composition resulting
from the method to control resistance to flow and/or flow rate
enhancement herein described the flow rate enhancement is at least
20%. In some of those embodiments, the at least one framing
associative polymer can have a weight averaged molecular weight of
650,000 g/mol to 750,000 g/mol and can be comprised at a
concentration greater than 0.2c*.
[0303] In some embodiments, the non polar composition resulting
from the method to control resistance to flow and/or flow rate
enhancement herein described is capable of maintaining a
substantially constant flow rate enhancement in a pipeline of at
least 8 kilometers. In some of those embodiments, the at least one
framing associative polymer has a weight averaged molecular weight
greater than 650,000 g/mol and can be comprised at a concentration
greater than 0.1c* possible 0.05c*. In some of those embodiments
the composition can be in a flow having Reynolds number equal to or
higher than 5000, In some of those embodiments, if minimization of
shear degradation is desired the at least one framing associative
polymer can be provided at a weight averaged molecular weight
650,000 g/mol to 750,000 g/mol.
[0304] In some embodiments, the association constant of the at
least one framing associative polymer used in the method to control
resistance to flow and/or flow rate enhancement of a non-polar
composition is between 7.ltoreq.log.sub.10 k.ltoreq.14.
[0305] In some embodiments, the method to control resistance to
flow and/or flow rate enhancement herein described can be applied
to compositions in a flow having Reynolds number between about
5,000.ltoreq.Re, and in particular greater than 25,000 Re and the
at least framing associative polymer as an association constant (k)
in the range of 7.ltoreq.log.sub.10 k.ltoreq.14.
[0306] In some embodiments the method to control resistance to flow
and/or flow rate enhancement herein described can be applied to
compositions in a flow having Reynolds number Re.gtoreq.25,000 and
the at last one framing associative polymer has an association
constant (k) in the range of 7.ltoreq.log.sub.10 k.ltoreq.14.
[0307] In some embodiments, of the method to control resistance to
flow and/or flow rate enhancement herein described, the
concentration c is about 0.5 c* or between about 0.5c* to 1c* and
the another physical and/or chemical property is mist control.
[0308] In some embodiments, of the method to control resistance to
flow and/or flow rate enhancement herein described, the
concentration c is less than approximately c* and the another
physical and/or chemical property is fuel efficiency.
[0309] In some embodiments, of the method to control resistance to
flow and/or flow rate enhancement herein described, the
concentration c is between 0.1c* and 0.5c* and the another physical
and/or chemical property is fuel efficiency.
[0310] In some embodiments, of the method to control resistance to
flow and/or flow rate enhancement herein described, the
concentration c is below or approximately equal c* and the another
physical and/or chemical property is enhanced lubrication.
[0311] In some embodiments, of the method to control resistance to
flow and/or flow rate enhancement herein described, the
concentration c is between 0.05c* to c* and the another physical
and/or chemical property is enhanced lubrication.
[0312] In some embodiments of the method to control resistance to
flow and/or flow rate enhancement herein described, one or more
capping associative polymers having a weight averaged molecular
weight equal to or higher than 200,000 g/mol can be comprised in an
amount up to 20 wt % of a total polymer concentration in the
composition. In some of those embodiments, the one or more capping
associative polymers can be provided at 5 wt % of the total polymer
concentration in the composition. In some of those embodiments, the
one or more capping associative polymers can be provided at 10 wt %
of the total polymer concentration in the composition.
[0313] In some embodiments, framing associative polymer can be
used, alone or in combination with capping associative polymers, in
a method to control sizes, and/or distribution of sizes, of the
droplets of fluid (e.g. to control fluid mist) in a non-polar
composition. In some of those embodiments one or more additional
physical and/or chemical properties of the non-polar composition
can also be controlled. The method comprises providing a host
composition having a dielectric constant equal to or less than
about 5 and providing at least one framing associative polymer
substantially soluble in the host composition and having a weight
averaged molecular weight equal to or higher to 400,000 g/mol. The
method further comprises combining the host composition and the at
least one associative polymer herein described at a concentration c
selected between from about 0.05c* to about 3c* based on the
averaged molecular weight of the at least one associative polymer
and on a physical and/or chemical property to be controlled.
[0314] In some embodiments, the method can further comprise
selecting a concentration c of the at least one associative polymer
in the host composition, the concentration c selected between from
about 0.05c* to about 3c* depending on the averaged molecular
weight and/or radius of gyration of the at least one framing
associative polymer and on a physical and/or chemical property to
be controlled based on the factors herein described before the
combining.
[0315] In some embodiments, the method can further comprise
determining an overlap concentration c* for the at least one
associative polymer before performing the selecting.
[0316] In some embodiments, in the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the at least one framing associative polymer has a weight averaged
molecular weight equal to or higher than 1,000,000 g/mol, possible
about 10,000,000 g/mol and can be comprised at a concentration from
0.05 c* to 0.1 c*. in some of those embodiments, the at least one
framing associative polymer provided in the has a weight averaged
molecular weight between 1,000,000 g/mol to 4,000,000 g/mol, or
preferably 2,000,000 g/mol to 4,000,000 g/mol, or between 1,000,000
and 2,000,000 g/mol if a longer lasting effect is desired.
[0317] In some embodiments, in the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the at least one framing associative polymer has a weight averaged
molecular weight between 400,000 g/mol to 1,000,000 g/mol and can
be comprised at a concentration between 0.5 c* and c*.
[0318] In some embodiments, in the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the at least one framing associative polymer has a weight averaged
molecular weight between 400,000 g/mol to 1,000,000 g/mol, and can
be comprised at a concentration between c* and 3c*.
[0319] In some embodiments, the association constant of the at
least one framing associative polymer used in the method to control
sizes, and/or distribution of sizes, of the droplets of the fluid
mist herein described is between 7.ltoreq.log.sub.10
k.ltoreq.14.
[0320] In some embodiments, of the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the concentration c is about 0.5 c* or between about 0.5c* to 1c*
and the another physical and/or chemical property is drag
reduction.
[0321] In some embodiments, of the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the concentration c is less than approximately c* and the another
physical and/or chemical property is fuel efficiency.
[0322] In some embodiments, of the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the concentration c is between 0.1c* and 0.5c* and the another
physical and/or chemical property is fuel efficiency.
[0323] In some embodiments, of the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the concentration c is below or approximately equal c* and the
another physical and/or chemical property is enhanced
lubrication.
[0324] In some embodiments, of the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
the concentration c is between 0.05c* to c* and the another
physical and/or chemical property is enhanced lubrication.
[0325] In some embodiments of the method to control sizes, and/or
distribution of sizes, of the droplets of a fluid herein described,
one or more capping associative polymers having a weight averaged
molecular weight equal to or higher to 400,000 g/mol can be
comprised in an amount up to 20 wt % of a total polymer
concentration in the composition. In some of those embodiments, the
one or more capping associative polymers can be provided in a 5 wt
% of the total polymer concentration in the composition. In some of
those embodiments, the one or more capping associative polymers can
be provided in a 10 wt % of the total polymer concentration in the
composition.
[0326] In some embodiments of the associative polymers, and related
compositions, methods and systems herein described any one of the
associative polymers herein described and in particular any one of
framing associative polymers and/or capping associative polymers
herein described can have a weight averaged molecular weight equal
to or lower than 1,000,000 g/mol. In those embodiments, shear
resistant associative polymers can be provided. The wording "shear
resistant" as used herein in connection with a polymer indicates a
polymer that, under a mechanical stress sufficient to break a
carbon-carbon covalent bond, shows a decrease in its weight
averaged molecular weight Mw equal to or lower than 5% and can be
detected by techniques identifiable by a skilled person. When a
polymer is in a composition the mechanical stress applied to
different portions of the polymer are transmitted within the
polymer backbone and differently apply to different carbon-carbon
covalent bonds of the chain based on the structure and
configuration of the polymer as well as characteristics of flow as
will be understood by a skilled person.
[0327] In embodiments where shear resistant associative polymers
are desired, selection of one or more desired weight averaged
molecular weight can be performed based on the structure of the
backbone and presence, number and location of secondary, tertiary
and quaternary carbon atoms in backbone as will be understood by a
skilled person.
[0328] In some embodiments, framing associative polymers and/or
capping associative polymers herein described can have a weight
averaged molecular weight the equal to or lower than 750,000 g/mol.
In some embodiments, framing associative polymers and/or capping
associative polymers herein described can have a weight averaged
molecular weight between 400,000 g/mol and 1,000,000 g/mol. In
particular in some of those embodiments shear resistant associative
polymers can be a linear polymer.
[0329] In some embodiments, shear resistant associative polymers
herein described can substantially maintain (.+-.10%) control of
one or more physical and/or chemical properties in a non-polar
composition after application of a mechanical stress that is
sufficient to break a carbon-carbon covalent bond (e.g. 150 kT
where k is Boltzmann constant). For example such mechanical stress
can be applied when a fluid passes through liquid handling
operations, including pumping, turbulent pipeline flow, filters and
the like as will be understood by a skilled person. Accordingly,
shear resistant associative polymers herein described, and in
particular shear resistant framing associative polymers herein
described can be used to provide non-polar composition where a long
lasting control of one or more properties is desired, and in
particular where control of one or more desired effect is
maintained after repeated exposure of the non-polar composition
comprising the associative polymer to the mechanical stress
sufficient to break a carbon-carbon covalent bond. In particular
the mechanical stress sufficient to break a carbon-carbon covalent
bond depends on various factors such as the chemical nature of the
chain, the concentration and longest span of a polymer and
additional factors identifiable by a skilled person.
[0330] In particular in some embodiments, in which associative
polymers herein described are resistant to shear degradation (e.g.
chain scission upon passage through pumps, during prolonged
turbulent flow in pipelines, tubes or hoses, during passage through
filters), the associative polymer of the present disclosure can be
introduced at early steps in the preparation of non-polar host
compositions. In many applications the host composition can be
itself a mixture.
[0331] In particular in exemplary embodiments in which a modified
non polar composition comprising associative polymers herein
described is provided in connection with production of inks or
paints that can comprise a carrier liquid, pigments, stabilizers
and other components, the associative polymer can be added to the
carrier liquid prior to incorporation of the remaining components,
with the possibility that a central depot of carrier liquid can
feed production lines for diverse colors or grades of ink or paint.
In some of these embodiments, the efficacy of the polymer can be
retained after pumping, filtering, mixing and other processing
steps.
[0332] Similarly, in exemplary embodiments in which a modified non
polar composition comprising associative polymers herein described
is provided in connection with lubricant applications, the
associative polymers herein described can be incorporated into the
base oil that is subsequently combined with diverse additive
packages. At concentrations up to c*, the associative polymers are
expected to survive and are expected to not interfere with
processes that include but are not limited to filtering,
dewatering, pumping and mixing operations.
[0333] In exemplary embodiments in which a modified non polar
composition comprising associative polymers herein described is
provided in connection with fuel applications (e.g. use as drag
reducing agents, enhancers of fuel efficiency, emission reducing
agents, or mist control agents), the ability to incorporate the
associative polymer herein described at any point along the
distribution system allows for example incorporation at the
refinery; or in the intake line of a storage tank; or in the intake
line of a tanker ship, railway tank car, tank of a tanker truck; or
in the intake line to a major site of use, such as an airport or a
military depot; or in the transfer line from a storage tank into a
vehicle; or as a solution added to the tank of a vehicle at the
time of fueling.
[0334] In exemplary embodiments in which a modified non polar
composition comprising associative polymers herein described is
provided in connection with drag reducing agents in the transport
of petrochemicals (especially crude oil) through very long
pipelines, the present polymers resist shear degradation upon
passage through pumps; therefore, fewer injection stations are
required. In some cases, introduction of the associative polymer at
a single location prior to the intake of the pipeline will provide
drag reduction throughout the entire length of the pipeline.
[0335] In some embodiments herein described associative polymers
are not interfacial agents, so that such polymers can be added
prior to dewatering operations (including but not limited to fuel
handling) and defoaming operations (including but not limited to
production of paints and inks); at concentrations up to c*, the
associative polymers do not interfere with these essential
processing steps and the processing steps have a minimal effect on
the associative polymers.
[0336] In some embodiments, associative polymers herein described
can be used as a fuel additive with one or more of the following
features: i) effective at low concentrations (acceptable
viscosity), ii) introduced at the refinery; iii) resistant to
non-intentional degradation; iv) soluble over wide temperature
range (-50.degree. C. to 50.degree. C.); v) permit dewatering and
filtering, vi) permit optimization in engine combustion chamber;
vii) clean burning, and viii) affordable.
[0337] In some embodiments, the associative polymers and related
compositions herein described can be used in connection with
application where passage of a fluid in a pipeline is performed. A
turbulent drag, which is usually expressed in terms of frictional
pressure drop, plays a crucial role in pipeline transportation of
non-polar liquids as will be understood by a skilled person: it
increases the energy cost for moving the liquid through the
pipeline and thus limits the capacity of the system. Introducing a
drag reducing agent (DRA) to the fluid, which dampens turbulent
regions near the pipe wall and consequently decreases turbulent
flow and increases laminar flow, provides a reduction in the
frictional pressure drop along the pipeline length. The benefits
provided by DRAs include maintaining the same flow rate with a
significantly lower energy cost, and alternatively resulting in a
much higher flow rate using the same amount of energy as will be
understood by a skilled person.
[0338] In some embodiments, the associative polymers here described
can be designed to provide drag reduction to non-polar liquid in
turbulent pipeline flow. In some of those embodiments when exposed
to high shear flow in pump, aggregates of FGs serve as sacrificial
weak links that can reversibly respond to the high shear by
dissociation so as to protect the backbone from degradation. Once
the polymer chains leave the pump, they can re-form supramolecules
via association of FGs and continue to provide drag reduction to
the pipeline flow. In some instances identifiable by a skilled
person, associative polymers herein described can greatly simplify
the practice of reducing energy cost for pipeline transportation of
non-polar hosts and/or increasing the capacity of existing pipeline
system using drag reducing additives.
[0339] As disclosed herein, the associative polymers and non-polar
composition herein described can be provided as a part of systems
to control at least one rheological property of the drag reduction
and/or flow rate enhancement alone or in combination with another
physical and/or chemical properties herein described, including any
of the methods described herein.
[0340] The systems can be provided in the form of kits of parts. In
a kit of parts, polymers (e.g. backbone polymers, associative
polymers or precursor thereof), compositions and other reagents to
perform the methods can be comprised in the kit independently. One
or more polymers, precursors, compositions and other reagents can
be included in one or more compositions alone or in mixtures
identifiable by a skilled person. Each of the one or more polymers,
precursors, compositions and other reagents can be in a composition
alone or together with a suitable vehicle.
[0341] Additional reagents can include molecules suitable to
enhance reactions (e.g. association of one or more associative
polymers herein described with a related host composition)
according to any embodiments herein described and/or molecules
standards and/or equipment to facilitate or regulate the reaction
(e.g. introduction of the associative polymer to the host)
[0342] In particular, the components of the kit can be provided,
with suitable instructions and other necessary reagents, in order
to perform the methods here described. The kit can contain the
compositions in separate containers. Instructions, for example
written or audio instructions, on paper or electronic support such
as tapes or CD-ROMs, for carrying out reactions according to
embodiments herein described (e.g. introduction of associative
polymer in a host composition), can also be included in the kit.
The kit can also contain, depending on the particular method used,
other packaged reagents and materials.
[0343] Further advantages and characteristics of the present
disclosure will become more apparent hereinafter from the following
detailed disclosure by way of illustration only with reference to
an experimental section.
EXAMPLES
[0344] The associative polymers, materials, compositions, methods
system herein described are further illustrated in the following
examples, which are provided by way of illustration and are not
intended to be limiting.
[0345] In particular, the following examples illustrate exemplary
associative polymers and related methods and systems. A person
skilled in the art will appreciate the applicability and the
necessary modifications to adapt the features described in detail
in the present section, to additional associative polymers,
compositions, methods and systems according to embodiments of the
present disclosure.
Example 1: Exemplary Associative Polymer and Architectures
[0346] Exemplary associative polymers and related exemplary
architectures are illustrated in FIGS. 3 to 6.
[0347] In particular in the illustration of FIG. 3 a linear polymer
backbone of 1,4-polybutadiene is illustrated in which end groups
are <1 wt % of the polymer and contain <0.2 wt % heteroatoms.
When added to fuel, polymers of this type burn cleanly and maintain
the caloric content of the fuel.
[0348] The illustration of FIG. 4 provides exemplary functional
groups which can be used with the backbone of FIG. 3 or other
backbones as will be understood by a skilled person. The
illustration of FIGS. 5 and 6 shows exemplary branched
architectures (FIG. 5) and exemplary block-polymer architecture
(FIG. 6) which can be created with the backbone of and/or other
backbones as will be understood by a skilled person. When the
associative polymer is added to a host composition the FGs form
physical associations according to their nature (e.g. self to self,
donor-acceptor, pairwise, or multidentate). The illustration of
FIGS. 1 and 2 show exemplary types of supramolecular structures
thus formed.
Example 2: Methods of Making Associative Polymers and Related
Architectures
[0349] A schematic illustration of exemplary reactions and methods
suitable to make associative polymers herein described is provided
in FIGS. 7 to 10.
[0350] In particular FIG. 7 shows a schematic of an exemplary
method to provide an associative polymer herein described
illustrated making specific reference to embodiments where a
corresponding non-polar composition is a fuel.
[0351] FIGS. 8 and 9 show an exemplary ROMP +Chain Transfer Agent
(CTA) reaction (FIG. 8) and exemplary chain transfer agents (FIG.
9). This exemplary reaction allows in several cases precise control
of the number of associating groups. It will be appreciated by a
skilled person that it can be straightforward to synthesize and
purify at large scale associative polymers compatible with
non-polar compositions, with the backbone and associative groups
chosen for a particular application as described in the
specification (see, e.g., [18-20]).
[0352] FIG. 10 shows a schematic of an exemplary method to
synthesize an associative polymer using CTAs.
Example 3: Synthesis of High Molecular Weight Di-TE PB by ROMP
[0353] 6.7 mg of octa-functional tert-butyl ester CTA is loaded
into a 50 ml Schlenk flask (charged with a magnetic stir bar). The
flask is later sealed with a septum. The content is then
deoxygenated by 5 times of pulling vacuum/filling argon. 0.5 ml of
deoxygenated DCM is added to dissolve the CTA. 0.13 ml of 1 mg/ml
DCM solution of Grubbs II catalyst is injected into the flask, and
then 0.03 ml of freshly vacuum distilled, purified COD (.ident.50
eq. w.r.t. CTA) is immediately injected.
[0354] The mixture is stirred at 40.degree. C. for 33 minutes to
allow complete incorporation of CTA into the polymer. Another 0.13
ml of freshly prepared 1 mg/ml DCM solution of Grubbs II catalyst
is then injected, followed by 5.6 ml of freshly vacuum distilled,
purified COD (.ident.10,000 eq.) in 12 ml of deoxygenated DCM. The
reaction is stopped by adding 30 ml of oxygen-containing DCM as the
mixture turns viscous enough to completely stop the motion of
magnetic stir bar. The diluted mixture is precipitated into 400 ml
of acetone at room temperature. The resulting polymer is collected
and dried in vacuo at room temperature overnight. GPC results of
the polymer: M.sub.w=430,000 g/mol, PDI=1.46.
##STR00018##
Example 4: Deprotection of the Acid End Groups
[0355] 1 g of the aforementioned polymer is loaded into a 50 ml
Schlenk flask (charged with a magnetic stir bar), and degassed by 5
times of pulling vacuum/filling argon). 30 ml of deoxygenated is
then syringe-transferred into the flask. The mixture is homogenized
at room temperature. Once complete homogenization is achieved, 1.25
ml of deoxygenated trifluoroacetic acid (TFA) is
syringe-transferred into the flask. The mixture is then stirred at
room temperature overnight.
[0356] Upon the completion of TFA hydrolysis, the mixture is
diluted with 20 ml of DCM, and the resulting solution is
precipitated into 400 ml of acetone at room temperature. The
resulting polymer is further purified by 2 times of
re-precipitation from THF into acetone.
##STR00019##
Example 5: Synthesis of High Molecular Weight Di-TB PB by ROMP
[0357] Synthesis of high M.W di-TB PB by ROMP is performed
according to the following steps:
[0358] Step 1: Prepolymer Synthesis
[0359] 5 mg of octa-functional chloro CTA is loaded into a 50 ml
Schlenk flask (charged with a magnetic stir bar). The flask is
later sealed with a septum. The content is then deoxygenated by 5
times of pulling vacuum/filling argon. 0.5 ml of deoxygenated DCM
is added to dissolve the CTA. 0.13 ml of 1 mg/ml DCM solution of
Grubbs II catalyst is injected into the flask, and then 0.03 ml of
freshly vacuum distilled, purified COD (.ident.50 eq. w.r.t. CTA)
is immediately injected. The mixture is stirred at 40.degree. C.
for 33 minutes to allow complete incorporation of CTA into the
polymer. Another 0.13 ml of freshly prepared 1 mg/ml DCM solution
of Grubbs II catalyst is then injected, followed by 5.6 ml of
freshly vacuum distilled, purified COD (.ident.10,000 eq.) in 12 ml
of deoxygenated DCM. The reaction is stopped by adding 30 ml of
oxygen-containing DCM as the mixture turns viscous enough to
completely stop the motion of magnetic stir bar. The diluted
mixture is then precipitated into 400 ml of acetone at room
temperature. The resulting polymer is collected and dried in vacuo
at room temperature overnight. GPC results of the polymer:
M.sub.w=430,000 g/mol, PDI=1.46.
##STR00020##
[0360] Step 2: End-Azidation of Prepolymer
[0361] 1 g of the aforementioned chloro-terminated prepolymer is
loaded into a 50 ml Schlenk flask, and dissolved into 30 ml of
anhydrous THF. Upon complete homogenization, 0.73 g of
azidotrimethylsilane (.ident.1200 eq w.r.t. polymer) and 1.57 g of
tetrabutylammonium fluoride (.ident.1200 eq w.r.t. polymer) are
added into the flask. The resulting mixture is degassed by 2
freeze-pump-thaw cycles to prevent crosslinking by dissolved
oxygen. Then, the mixture is stirred at 60.degree. C. overnight.
The mixture is precipitated into 300 ml of methanol at room
temperature. The resulting polymer is further purified by 2 more
times of reprecipitation from THF into acetone. The resulting
polymer is dried in vacuo at room temperature overnight.
##STR00021##
[0362] Step 3: Attachment of Tertiary Amine Groups to Polymer Chain
Ends
[0363] 0.68 g of the aforementioned azido-terminated prepolymer is
loaded into a 50 ml Schlenk flask, and dissolved into 25 ml of
anhydrous THF. Once homogenization is complete, 0.23 g of
3-Dimethylamino-1-propyne (.ident.1,200 eq. w.r.t. the polymer),
along with 0.02 g of N,N,N',N',N''-pentamethyldiethylenetriamine
(PMDETA, .ident.50 eq. w.r.t. the polymer) are added into the
flask. The mixture is then deoxygenated by 2 freeze-pump-thaw
cycles. Later it is frozen and pumped again, and then 0.016 g of
copper (I) bromide (.ident.50 eq. w.r.t. the polymer)) is added
into the flask under the protection of argon flow when the mixture
is still frozen. After thawing the mixture and filling the flask
with argon, the mixture is stirred at room temperature for 20
minutes in order to homogenize the copper (I) catalyst. The mixture
is stirred at 50.degree. C. overnight. 2 ml of methanol is slowly
injected into the mixture in order to remove copper from the amine
end groups. The mixture is precipitated into 300 ml of methanol at
room temperature. The resulting polymer is further purified by 2
more times of reprecipitation from THF into methanol. It is later
dried in vacuo at room temperature overnight.
##STR00022##
Example 6: Effect of Self-Association in Exemplary Associative
Polymers
[0364] Proof of effect of self-association in exemplary associative
polymers herein described is illustrated in FIG. 11 and FIG. 12. In
the exemplary associative of Example 5 the aforementioned method of
recovering the end acid groups does not crosslink the polybutadiene
backbone, as proved in the superposition of GPC traces of 430K
di-TE PB and the resulting polymer of its hydrolysis reaction (in
THF) illustrated in FIG. 11.
[0365] In the illustration of FIG. 11, the slight increase in the
population of high molecular weight species is due to the weak
self-association of chain-end acid clusters. The apparent M.sub.w
increases by 20% after TFA hydrolysis.
[0366] A further confirmation is provided by the illustration of
FIG. 12. In particular, FIG. 12 shows the rheology data of the 1 wt
% Jet-A solutions of the 430K di-TE PB and 430K di-TA PB
respectively. The viscosities of 1 wt % Jet-A solution of 430K
di-TA PB are significantly higher than those of the ester
prepolymer. Since the GPC results show the extent of backbone
crosslinking during removal of tert-butyl groups is negligible, it
is reasonable to say that the self-association of acid clusters
accounts for the increase in viscosities.
Example 7: Effect of End-to-End Donor Acceptor Association in
Exemplary Associative Polymers
[0367] A proof of the effect of end-to-end donor/acceptor
association is provided in FIG. 13 and FIG. 14. In particular FIG.
13, shows the superposition of GPC traces of the 430K octa chloro
PB and the corresponding octa tertiary amine PB.
[0368] In the illustration of FIG. 13, the polybutadiene backbone
is mainly intact after two end-functionalization reactions.
[0369] FIG. 14 shows the rheology data of 1 wt % Jet-A solutions of
430K di-TE PB, di-TA PB, di-TB PB, and 1:1 w/w di-TA PB/di-TB PB
mixture. In the illustration of FIG. 14, the 1:1 mixture shows
significantly higher viscosities than the other solutions. Since
none of the two polymer components are crosslinked, it suggests
that the end-to-end acid/base interaction results in the formation
of supramolecular species.
Example 8: Effect of an Exemplary Associative Polymer on Fuel
Compositions
[0370] Effect of di-TA PB synthesized according to Example 5, was
tested in Jet A fuel. In particular a composition comprising 0.5%
of di-TA PB with a backbone length of 264,000 g/mol (denoted 264K
di-TA PB) in jet A fuel has been provided as illustrated in FIG.
15.
[0371] In the illustration of FIG. 15 is shown that the exemplary
associative di-TA PB of Example 5 showed no phase separation and
was able to stay in solution (crystal clear) even at -30.degree. C.
for months (see FIG. 15, Panel A).
[0372] Additionally, dewatering operations appeared to occur as
quickly and completely in the composition with associative di-TA PB
of Example 5, as in the untreated host Jet A (see FIG. 15, Panel B
left vial v. right vial).
Example 9: High-Speed Impact/Flammability Test
[0373] To demonstrate the effect of exemplary polymers on the
mist-control of kerosene, a series of high-speed
impact/flammability test were conducted at California Institute of
Technology. The high-speed impact test is designed to simulate a
scenario in which fuels can be atomized into droplets due to
impact, whereas the continuously provided ignition sources are used
to obtain an indication of the flammability of resulting droplets.
The following samples were loaded into 50 ml aluminum cans, fixed
on a stage, and impacted by a 5 cm.times.3 cm steel cylinder
travelling at 200 km/hr (three continuously burning propane torches
were set up along the path of splashed samples): Jet-A, 0.35 wt %
Jet-A solutions of 4.2 M polyisobutylene (PIB) with and without
recirculation by a Bosch 69100 In-line turbine fuel pump for 1
minutes, 0.3 wt % of Jet-A solutions of 430K di-TA PB with and
without recirculation by a Bosch 69100 In-line turbine fuel pump
for 1 minutes. The results for each sample are described below:
Jet-A: Significant amount of fine droplets was generated upon
impact. The fine droplets travelling along the path of the
projectile were ignited by the burning torches within 50
milliseconds, and then evolved into a propagating fire ball.
[0374] 0.35 wt % Jet-A solution of 4.2M PIB, without shear: Large
droplets and filaments were generated by the impact. Sparkles were
observed as the fluid elements passed over the torches, but they
failed to propagate.
[0375] 0.35 wt % Jet-A solution of 4.2M PIB, with 1 min. of shear:
Fine droplets were generated by the impact. The fine droplets
travelling along the path of the projectile were ignited by the
burning torches within 50 milliseconds, and then evolved into a
propagating fire ball.
[0376] 0.3 wt % Jet-A solution of 430K di-TA PB, without shear:
Droplets were generated by the impact. Sparkles were observed as
the fluid elements passed over the torches, but they failed to
propagate.
[0377] 0.3 wt % Jet-A solution of 430K di-TA PB, with 1 min. of
shear: Droplets were generated by the impact. Sparkles were
observed as the fluid elements passed over the torches, but they
failed to propagate.
Example 10: Synthesis of Octa Functional CTAs
[0378] Reaction schemes for exemplary Octa functional CTAs in
accordance with the present disclosure are shown in the
illustration of FIG. 18 and FIG. 19.
Example 11: Exemplary Node to Chain and Node to FG Interactions
[0379] Exemplary pairs of reactive groups that are useful at end
positions such as R.sub.1 or R.sub.2 in the structure of formula
(III) or in di- or multi-valent crosslinkers and the product of
their reaction, which can be used for covalently linking a chain
and a FG, or linking chains to a node or attaching FG to a node in
accordance with the present disclosure, are shown in the
illustration of FIG. 20 and FIG. 21.
Example 12: Polymer-Composition Solubility Determination
[0380] Solubility of an exemplary polymer 1,4-polybutadiene (PB) in
a non-polar composition has been determined. The nonpolar
composition is kerosene, which can be considered to be a mixture of
hydrocarbons that contain 6-16 carbon atoms per molecule, the
v.sub.0 of octane (160 cm.sup.3/mol) can be chosen as a
representative value for kerosene.
[0381] Accordingly, when 1,4-polybutadiene (PB) is used as the
backbone of invented associative polymers, the value of
.delta..sub.1 is .about.8 (cal/cm.sup.3).sup.0.5 (see, e.g. [9,
24]). To evaluate .delta..sub.2 for kerosene, the following
relationship (dispersive Hansen parameter) can be used:
.delta.=9.55n.sub.D-5.55
where n.sub.D is the refractive index of the host, and n.sub.D can
be well-approximated by the square root of the dielectric constant
(F) of the host. Given .epsilon..sub.kerosene is 1.8 at 20.degree.
C., .delta..sub.2 is .about.9.55.times.(1.8).sup.0.5-5.55=7.26.
[0382] Accordingly, the interaction parameter for the associative
polymer with a 1,4-polybutadiene backbone in kerosene at ambient
temperature can be estimated as follows:
.apprxeq. 0.34 + 1 .times. 6 .times. 0 1 . 9 .times. 8 .times. 7
.times. 2 .times. 9 .times. 8 . 1 .times. 5 .times. ( 8 - 7 . 2
.times. 6 ) 2 = 0 .times. .49 . ##EQU00007##
[0383] The calculated value of .chi. of 0.49 indicates that the PB
associative polymer with a 1,4-polybutadiene backbone would be
expected to be substantially soluble in a non-polar composition of
kerosene.
[0384] A skilled person can determine based on the above Example if
other associative polymer backbones would be substantially soluble
in other non-polar compositions by applying the same calculations
using the particular solubility parameters for the particular
non-polar composition.
Example 13A: Drag Reduction Test
[0385] 0.2 grams of telechelic 1,4-PB of M.sub.w 630,000 g/mol,
terminated by 2 acid groups (denoted 630K di-DA PB) and 0.2 grams
of telechelic 1,4-PB of M.sub.w 540,000 g/mol, terminated by 2
tertiary amine groups (denoted 540K di-DB PB) were dissolved in
39.6 grams of Jet-A at room temperature over 16 hours.
[0386] The resulting 1 wt % Jet-A solution of 1:1 w/w 630K di-DA
PB/540K di-DB PB was further diluted with 1293 grams of Jet-A to a
concentration of 300 ppm (.about.0.1c* of the non-associative
backbone). A Bosch 69100 In-line turbine fuel pump with its outlet
connected to a piece of TYGON.RTM. tubing (inner diameter=6.34 mm;
length=40 cm) and inlet outlet connected to a piece of TYGON.RTM.
tubing (inner diameter=3.17 mm; length=2.14 m) was used to transfer
the fuel sample from its reservoir to a collecting jar over a
period of 20 seconds (FIG. 39A).
[0387] The pump was primed with .about.200 mL of the sample before
the test. The collecting jar was weighed before and after the
transfer in order to determine the amount of fuel collected. The
same procedure was also performed on the unmodified host Jet-A. The
measured mass flow rate of unmodified Jet-A was 24.17 g/s, which
corresponded to a Reynolds number of 6458. As for the Jet-A sample
with 300 ppm of 1:1 donor/acceptor polymer pair, the measured mass
flow rate was 24.92 g/s. Hence, an increase of 3.2% in mass flow
rate was achieved, indicating that the presence of 1:1 (w/w)
mixture of 630K di-DA PB and 540K di-DB PB at 300 ppm in Jet-A
reduced the effect of turbulent drag on flow rate.
[0388] A skilled person will realize that the above test can be
applied to other associative polymers in order to determine the
extent of drag reduction.
Example 13B: Long Lasting Drag Reduction Test
[0389] 0.7 grams of telechelic 1,4-PB of Mw 670,000 g/mol,
terminated by two acid groups (denoted 670K di-DA PB) and 0.7 grams
of telechelic 1,4-PB of Mw 630,000 g/mol, terminated by 2 tertiary
amine groups (denoted 630K di-DB PB) were dissolved in 139 grams of
Jet-A at room temperature over 16 hours. The resulting 1 wt % Jet-A
solution of 1:1 w/w 670K di-DA PB/630K di-DB PB was further diluted
with 1133 grams of Jet-A to a concentration of 1,100 ppm
(.about.0.37c* of the nonassociative backbone). [00373] 3.2 grams
of polyisobutylene of M.sub.w 4,200,000 g/mol (denoted 4.2M PIB)
were dissolved in 637 grams of Jet-A at room temperature over 48
hours. 52 grams of the resulting 0.5 wt % Jet-A solution was
further diluted with 1133 grams of Jet-A to a concentration of 217
ppm.
[0390] The apparatus for drag reduction study is shown in FIG. 39B.
A 2.5-gallon cylindrical steel air tank (Viair 91208, 200 psi
rated) was used as a pressurizable sample reservoir, which was
fitted with a pressure gauge, a high-pressure gas inlet, a 200-psi
safety relief valve, and a ball valve as the sample outlet. A
10-liter polyethylene (PE) bottle with a tubulation connector at
the bottom was used as the sample receiving container. A 9.15-meter
long piece of PTFE tubing (I.D.=3.17 mm) connecting the outlet
valve of the air tank and the tubulation connector of the PE bottle
was used as a miniature pipeline where turbulent drag took
place.
[0391] Test samples include untreated Jet-A as the reference, Jet-A
solution of 4.2M PIB at 217 ppm as the control, and Jet-A solution
of 1:1 (w/w) 670K Di-DA PB/630K Di-DB PB at 1,100 ppm. Gravity flow
was used to transfer the test sample from the 10-liter PE bottle
into the air tank over a period of 35 min. The test fluid was
pressurized to 200 psi by means of high-pressure nitrogen. Flow
rates were determined via a catch-and-weigh technique: The test
fluid was driven through the PTFE tubing over a period of 21 s to
the 10-liter PE bottle, which was weighed before and after the test
to determine the average mass flow rate and the corresponding
Reynolds number (Re). Five passes were performed on each sample.
When untreated Jet-A was tested, a Re of 10,770 was achieved, which
indicates the apparatus was able to generate turbulent flow.
Results are expressed as % flow enhancement defined as 100* (Jet-A
solution flow rate-Jet-A flow rate)/(Jet-A flow rate) with all flow
rates compared at common initial pressure (200 psi) and final
pressure (192 psi). The results are shown in FIG. 39C and FIG.
68.
[0392] Compared to untreated Jet-A, the presence of 4.2 M PIB at
217 ppm in Jet-A initially helped improve the flow rate by 37.4%.
The flow rate enhancement steadily decreased as the number of
passes through the system increased: at the 5th pass, the flow rate
enhancement by 4.2M PIB at 217 ppm in Jet-A was reduced to 26.2%,
indicating shear degradation of 4.2 M PIB in turbulent flow.
[0393] The flow rate enhancement by 1:1 (w/w) 670K Di-DA PB/630K
Di-DB PB at 1,100 ppm in Jet-A was found long-lasting throughout
the five passes: no measurable decrease in flow rate enhancement
was observed (average=28.2%, standard deviation=0.27%). The results
show that at 1,100 ppm in Jet-A, 1:1 (w/w) 670K Di-
[0394] DA PB/630K Di-DB PB resist shear degradation in turbulent
flow and thus provide long-lasting drag reduction thus supporting
the conclusion that the flow rate enhancement can be maintained
constant with flow having a high Reynolds number (e.g. higher than
5000 or 25000) and/or along a long pipeline (e.g. 8 Km or more)
Example 14: Detection of Rehological Properties of Solutions
[0395] The methods presented in Examples 2-5 to synthesize
telechelic 1,4-PBs with M.sub.w up to 430,000 g/mol capped at each
end with well-defined tert-butyl ester-terminated dendrons (FIG.
41) provides facile access to matched pairs of non-associative and
associative telechelic 1,4-PBs (FIG. 42). In this example, these
model polymers were used to study the relationship between
molecular properties (e.g., polymer molecular weight and the number
of carboxyl groups on chain ends) and association behavior,
particularly its effects on the rheological properties in solution.
The present study of the self-association behavior of
carboxyl-terminated telechelic 1,4-PBs provides a foundation for
comparative studies of complementary association illustrated in
FIG. 22.
[0396] The following materials and methods were used: Solvents
1-chlorododecane (CDD) and tetralin (TL) were both obtained from
Aldrich in 97% and 99% purity, respectively. All tert-butyl
ester-terminated telechelic 1,4-PBs and their corresponding
carboxyl-terminated telechelic 1,4-PBs were prepared as described
herein. Four values of the number of functional groups on polymer
chain ends, N, and three polymer backbone lengths (in terms of
M.sub.w by GPC-LS) were selected for the present study: A series of
polymers with approximately matched backbone length (nominally
220,000 g/mol) were prepared with N=1, 2, 4 and 8; and a series of
polymers with N=4 was prepared with three backbone lengths of
76,000, 230,000, and 430,000 g/mol. (Table 3.1). To simplify the
nomenclature of materials, polymer end-groups with N=1, 2, 4, and 8
tert-butyl ester groups are denoted ME, DE, TE, and OE (for mono-,
di-, tetra-, octa-ester end groups, respectively), respectively.
Similarly, polymer end-groups with N=1, 2, 4, and 8 carboxyl groups
are denoted MA, DA, TA, and OA (for mono-, di-, tetra-, octa-acid
end groups, respectively), respectively
[0397] Procedure for Sample Preparation: Solutions of tert-butyl
ester terminated polymers for viscosity measurements were prepared
by combining polymer and solvent in clean 20 mL scintillation vials
or larger 50 mL glass jars which were placed on a Wrist-Action
Shaker (Burrell Scientific) for up to 24 h to allow complete
homogenization.
[0398] Solutions of carboxyl-terminated polymers were prepared as
follows: To 150 to 200 mg of carboxyl-terminated polymer in a 50-mL
Schlenk flask was added necessary amount of solvent for 1 wt %
stock. The contents of the Schlenk flask were degassed by 3
freeze-pump-thaw cycles, and then stirred overnight at 70.degree.
C.
[0399] Viscosity Measurements: Steady shear viscosity was measured
in a cone-plate geometry (60 mm diameter aluminum, 1.degree. cone,
29 .mu.m truncation) using an AR1000 rheometer from TA Instruments
(temperature controlled at 25.degree. C.). Solutions of tert-butyl
ester terminated polymers were probed in the shear rate range 1-200
s.sup.-1 logarithmically (5 shear rates per decade). The range was
extended to 3000 s.sup.-1 for carboxyl-terminated polymers to
better capture shear-thinning behavior. All viscosity data were
reported in terms of specific viscosity (.eta..sub.sp,
.ident.(.eta..sub.solution-.eta..sub.solvent)/.eta..sub.solvent,
where .eta..sub.solvent=2.72 mPas for CDD and 2.02 mPas for TL at
25.degree. C.) which reflects the contribution of the polymer to
the viscosity [25].
Example 15: Dissolution Behavior
[0400] All six tert-butyl ester-terminated 1,4-PBs (Table 7) were
found readily soluble in both CDD and TL. With increasing carboxyl
content, it became more difficult to dissolve carboxyl-terminated
polymers: For N=1, the corresponding polymer (226K di-MA 1,4-PB)
was found soluble in both CDD and TL at room temperature; at N=2
and 4, the corresponding polymers (230K di-DA 1,4-PB; 76K, 230K,
and 430K di-TA 1,4-PBs) were not soluble in either model solvent at
room temperature, but they dissolved into CDD and TL when heated at
70.degree. C. and remained in solution thereafter. At N=8, the
polymer 207K di-OA 1,4-PB did not dissolve completely into either
solvent even when heated at elevated temperatures (>110.degree.
C.) overnight. The difficulty of dissolving 207K di-OA 1,4-PB is
not due to crosslinking: The polymer dissolves readily in THF, it
passes easily through filters, and GPC-LS analysis showed that 207K
di-OA 1,4-PB has a unimodal distribution similar to the other
polymers in the series of similar M.sub.w (near 220,000 g/mol; see
Table 7, which shows molecular weight (M.sub.w) and number of
chain-end functional groups (N) of tert-butyl ester- and
carboxyl-terminated telechelic 1,4-PBs).
TABLE-US-00008 TABLE 7.sup.a Nominal M.sub.w N 76 220 430 1 226
(1.4) 2 230 (1.5) 4 76 (1.5) 230 (1.4) 430 (1.5) 8 207 (1.5)
.sup.aGPC was performed for in THF for 35.degree. C. for the
tert-butyl ester form; results are shown for M.sub.w in kg/mol
followed by PDI in parentheses.
Example 16: Steady-Flow Shear Viscosity of 1 wt % Polymer
Solutions
[0401] Specific viscosity (.eta..sub.sp) of 1 wt % polymer
solutions averaged over shear rates from 10-100 s.sup.-1 show that
all solutions of carboxyl-terminated 1,4-PBs had higher
.eta..sub.sp than their tert-butyl ester-terminated (i.e.,
protected) counterparts, but the highest increase was observed in
the case of N=4 (FIG. 23). The lack of .eta..sub.sp data for
carboxyl-terminated 1,4-PB with N=8 is due to the poor solubility
of the polymer in both solvents. While .eta..sub.sp for all of the
non-associative .about.230K tert-butyl ester-terminated polymers
was the same, the deprotection of carboxyl groups on polymer chain
ends produced a threefold increase in specific viscosity in both
CDD and tetralin for N=4, whereas at N=1 and 2 only marginal
increases were observed after deprotection of carboxyl groups (FIG.
23). Thus, there appears to be a minimum number of carboxyl groups
on polymer chain ends to achieve the intermolecular association
suitable for viscosity modification (N>2) and a maximum number
imposed by the solubility limit (N<8). The effect of solvent
quality on .eta..sub.sp was also observed in FIG. 23. Increasing
the length of 1,4-PB backbone, for identical TA end groups (N=4)
increases the specific viscosity strongly (FIG. 23): In tetralin,
for the 76,000 g/mol polymer, deprotection of carboxyl groups only
increases the specific viscosity by 90%, whereas the increase is
more than 320% for the 430,000 g/mol polymer. For each polymer,
.eta..sub.sp of its 1 wt % tetralin solution was found nearly twice
as high as that of its 1 wt % 1-chlorododecane solution.
Example 17: Concentration Dependence of Specific Viscosity
[0402] While the values of .eta..sub.sp of three tert-butyl
ester-terminated polymers in both CDD and TL showed a nearly linear
dependence on polymer concentration, the CDD and TL solutions of
the three carboxyl-terminated polymers (76K, 230K and 430K di-TA
1,4-PBs) exhibited nonlinear increases of .eta..sub.sp with
concentration, and the extent of such non-linearity was found
positively correlated with the M.sub.w of polymer backbone (FIG.
24). In accord with the observation that associative polymers with
1 and 2 carboxyl groups at their ends have less effect on
viscosity, comparison of the three 230K carboxyl-terminated 1,4-PBs
with N=1, 2 and 4 shows that the non-linear increase of
.eta..sub.sp with polymer concentration was obvious only in the
case of N=4 (FIG. 25).
Example 18: Shear-Thinning Behavior of Solutions of
Carboxyl-Terminated Polymers
[0403] The onset and magnitude of shear-thinning can depend on the
molecular weight and concentration of polymer. Solutions of 76K
di-TA 1,4-PB showed negligible shear-thinning (up to 3000 s.sup.-1)
(in either CDD or TL, FIGS. 33 and 34, respectively). In the case
of 230K di-TA 1,4-PB, its CDD and TL solutions showed
shear-thinning at 1 wt %, with onsets in the range 10-100 s.sup.-1.
With decreasing concentration, the magnitude of shear thinning
decreased and the shear rate required to elicit it increased (e.g.,
relative to the 1 wt % solution, at 0.7 wt %, the extent of
shear-thinning observed in both CDD and TL was less significant and
the onset shifted to >100 s.sup.-1) (FIGS. 33 and 34). Similar
trends were observed for solutions of 430K di-TA 1,4-PBs, with
greater extent of shear-thinning and onset of shear-thinning at
lower shear rates compared to their 76K and 230K counterparts (in
both CDD and TL, FIGS. 33 and 34, respectively).
[0404] An interesting shear-thickening feature followed by further
shear-thinning was observed for 430K di-TA 1,4-PB at 1 wt % in CDD
and 0.7 wt % in TL (see FIGS. 26A and 26B). The shear-thickening
appeared at a higher shear rate in CDD than in TL (shear rates
between 250 and 1000 s.sup.-1 in FIG. 26, compared to 160 and 630
s.sup.-1 in FIG. 26B).
Example 19: .sup.1H NMR Study on Complementary End-Association in
Deuterated Chloroform
[0405] .sup.1H NMR spectroscopy has been widely used to study the
association of hydrogen-bonding-based hetero-complementary
associative motifs in non-polar deuterated solvents (e.g.,
CDCl.sub.3) because the resultant hydrogen bonds can cause
significant changes in electron environments surrounding protons
participating complementary associations; consequently, measurable
changes in chemical shifts of those protons can be observed as the
results of such complementary associations [26-32]. This technique
was adopted to investigate if the three pairs of
hetero-complementary associative groups (THY/DAAP, HR/CA, and
TA/TB) can perform complementary association in CDCl.sub.3 at room
temperature when attached to chain ends of 1,4-PB of
M.sub.w.about.10,000-50,000 g/mol, which was chosen to keep signals
of end-groups recognizable.
[0406] .sup.1H NMR Study of Hetero-Complementary End-Association.
.sup.1H NMR study of hetero-complementary end-association of
telechelic 1,4-PB chains was carried out at a total polymer
concentration of .about.1 wt % in deuterated chloroform
(CDCl.sub.3) at room temperature. .sup.1H NMR samples of individual
telechelic associative polymers were prepared by combining polymer
and CDCl.sub.3 at a polymer concentration.about.1 wt % in 20 mL
scintillation vials, which were placed on a Wrist-Action Shaker
(Burrell Scientific) for up to 16 h to allow the polymer to
completely dissolve. .sup.1H NMR samples of complementary polymer
pairs were prepared by mixing .about.1 wt % CDCl.sub.3 solutions of
their corresponding polymers in 20 mL scintillation vials in
desired end-group ratios, except for the 1:1 (w/w) mixture of 24K
di-TA/22K di-TB 1,4-PBs, of which the .sup.1H NMR sample was
prepared by combining the two polymers at a 1:1 weight ratio and
CDCl.sub.3 at a total polymer concentration.about.1 wt % in a 20 mL
scintillation vial that was placed on a Wrist-Action Shaker
(Burrell Scientific) for 16 h at room temperature.
[0407] The investigation of hetero-complementary end-association by
.sup.1H NMR spectroscopy was carried out by measuring the .sup.1H
NMR spectra of individual telechelic associative polymers and those
of complementary polymer pairs, followed by comparing signals of
protons participating hetero-complementary end-association in
.sup.1H NMR spectra of individual polymer solutions to those of the
same protons in the spectra of corresponding polymer mixtures. Due
to the inherent detection limit of .sup.1H NMR spectroscopy, either
changes in chemical shifts or the disappearance of the signals of
protons participating hetero-complementary association of polymer
end-groups were followed as the evidence of end-association,
depending on the sizes of polymer backbones. For telechelic
associative polymers of M.sub.w.ltoreq.50,000 g/mol, characteristic
shifts of signals of associative end-groups were followed; for
those of M.sub.w.gtoreq.200,000 g/mol, the focus was whether the
mixing of complementary partners caused the disappearance of the
signals of protons participating hetero-complementary association
of polymer end-groups.
[0408] .sup.1H NMR spectra were obtained using a Varian Inova 500
spectrometer (500 MHz); all spectra were recorded in CDCl.sub.3,
acetone-d.sub.6, and DMSO-d.sub.6 at ambient temperature. Chemical
shifts were reported in parts per million (ppm, .delta.) and were
referenced to residual solvent resonances. Polymer molecular weight
measurements were carried out in tetrahydrofuran (THF) at
35.degree. C. eluting at 0.9 mL/min (pump: Shimadzu LC-20AD
Prominence HPLC Pump) through four PLgel 10-.mu.m analytical
columns (Polymer Labs, 10.sup.6 to 10.sup.3 .ANG. in pore size)
connected in series to a DAWN EOS multi-angle laser light
scattering (MALLS) detector (Wyatt Technology, Ar laser,
.lamda.=690 nm) and a Waters 410 differential refractometer
detector (.lamda.=930 nm).
[0409] The results of each pair are described as follows:
[0410] THY (thymine)/DAAP (diacetamidopyridine): FIG. 27 shows the
expanded .sup.1H NMR spectra (500 MHz, CDCl.sub.3) of 10K di-THY
1,4-PB 5, 10K di-DAAP 1,4-PB 14, and the mixture of 5 and 14 in a
1:2 wt ratio. In the absence of its complementary unit, the signal
of the imide proton of THY end groups was observed at 8.05 ppm
(FIG. 27). Upon addition of .about.2 eq of DAAP end groups, a large
downfield shift to 11.05 ppm accompanied by signal broadening was
observed (FIG. 27). Similar shift was also observed for the signal
of the amide protons of DAAP end groups (from 7.58 to 8.42 ppm, in
FIG. 27, panels B and C). The observed association-induced shift
(.about.2.9 ppm) of the imide proton signal of THY end groups is in
good agreement with the literature [27, 28, 30], and it indicates
that THY and DAAP end groups could find and associate with each
other in CDCl.sub.3.
[0411] HR (Hamilton receptor)/CA (cyanuric acid): FIG. 28 shows the
expanded .sup.1H NMR spectra (500 MHz, CDCl.sub.3) of 50K di-CA
1,4-PB, 24K di-HR 1,4-PB, and the mixture of 50K di-CA 1,4-PB and
24K di-HR 1,4-PB in a 1:1.4 wt ratio. In the absence of its
complementary unit, the signal of the imide protons of the CA end
group was observed at 7.75 ppm (FIG. 28). A very large downfield
shift to 12.90 ppm accompanied by peak broadening was observed
(FIG. 28) as .about.2 eq of HR end groups were added. Similar to
the case of THY/DAAP pair, the observed association-induced shift
(.about.5.2 ppm) of the signal of the imide protons of CA units
indicates that CA and HR end groups could also find and associate
with each other in CDCl.sub.3. The magnitude of the observed shift
is in good agreement with the literature [33-38].
[0412] TA/TB: Due to the fact that 24K di-TA 1,4-PB is not soluble
in CDCl.sub.3, .sup.1H NMR study was only performed on 22K di-TB
1,4-PB and its 1:1 (w/w) mixture with 24K di-TA 1,4-PB and
monitored the association by tracking the shifts of the signals of
the tertiary amine end group (H.sub.1 and H.sub.2, see FIG. 29).
The results are shown in FIG. 29. It was found that the presence of
22K di-TB 1,4-PB assisted the dissolution of 24K di-TA 1,4-PB in
CDCl.sub.3 and thus rendered the .sup.1H NMR experiment possible.
The signals of H.sub.1 and H.sub.2 were observed at 2.28 and 3.60
ppm respectively in the absence of 24K di-TA 1,4-PB (FIG. 29). The
addition of 24K di-TA 1,4-PB resulted in shifts of both signals:
The signals of H.sub.1 and H.sub.2 shifted from 2.28 and 3.60 to
2.46 and 3.85 ppm, respectively. The observed shifts indicate the
association of TA and TB end groups.
[0413] In order to determine if the three pairs of complementary
associative groups were still effective when attached to chain ends
of 1,4-PBs of M.sub.w.about.200,000-300,000 g/mol, .sup.1H NMR
analysis of the corresponding polymers and the complementary pairs
was performed at .about.1 wt % in CDCl.sub.3 at room temperature.
It was found that in this case, signals of polymer end groups were
barely recognizable due to their low contents in the test samples.
In addition, association-induced signal broadening could cause
signals of protons involved in complementary association to appear
vanished. Nevertheless, evidence of end-association was observed in
all three pairs of telechelic associative polymers of
M.sub.w.about.200,000 g/mol. In the case of the THY/DAAP pair, the
signal of the imide proton of THY end group of 288K di-THY 1,4-PB
was observed at 8.05 ppm with a very low intensity (FIG. 30), and
it was found disappeared in the .sup.1H NMR spectrum of the 1:2
(w/w) mixture of 288K di-THY and 219K di-DAAP 1,4-PBs. The
disappearance of the signal indicates that THY and DAAP end groups
could find and bind with each other in CDCl.sub.3, even when
attached to chain ends of polymers of M.sub.w.about.200,000 g/mol.
Likewise, the signal of imide protons of the CA end groups of 200K
di-CA 1.4-PB, along with those of the amide protons of the HR end
groups of 240K di-HR 1,4-PB, were not observable in the .sup.1H NMR
spectrum of the 1:1 (w/w) mixture of 200K di-CA and 240K di-HR
1,4-PBs (FIG. 31). Signals of the TB end groups of 250K di-TB
1,4-PB were also found disappeared after the polymer was mixed with
230K di-TA 1,4-PB in a 1:1 wt ratio (FIG. 32). These results
suggest that all three complementary associative pairs can provide
sufficient strength of end-association for telechelic 1,4-PB chains
of M.sub.w.about.200,000 g/mol to form supramolecular aggregates
stable at least on the time scale of .sup.1H NMR spectroscopy.
Example 20: Shear Viscometric Study of Complementary
End-Association
[0414] Shear viscometry was used as a complementary measure of
.sup.1H NMR study to evaluate the strength of hetero-complementary
pairs. 1-Chlorododecane (CDD) was chosen as the solvent due to its
low interference with hydrogen bonding, low volatility at room
temperature, high solvency for 1,4-PB backbones, and being a pure
solvent. For all of the four hetero-complementary pairs (THY/DAAP,
HR/CA, DA/DB, and TA/TB), telechelic polymers of
M.sub.w.about.200,000 g/mol were used. In addition to CDD, dodecane
and Jet-A were also used in shear viscometric study of THY/DAAP and
HR/CA pairs, respectively. Except for di-DA and di-TA 1,4-PBs,
polymer solutions in 1-chlorododecane were prepared by combining
polymer and solvent at a weight fraction of polymer=1 wt % in clean
20 mL scintillation vials, which were placed on a Wrist-Action
Shaker (Burrell Scientific) at room temperature for up to 16 h to
allow complete dissolution of polymers. 1 wt % CDD solutions of
di-DA and di-TA 1,4-PBs of M.sub.w.about.200,000 g/mol were
prepared according to the procedure described in Examples 2-5. For
each hetero-complementary associative pair, 1 wt % solutions of
polymer mixture were prepared by mixing 1 wt % solutions of the
individual polymers in desired weight ratios in 20 mL scintillation
vials at room temperature. Shear viscosity of polymer solutions
were measured according to the procedure described herein (see,
e.g. Examples 16-17).
[0415] Steady-flow shear viscometry at 25.degree. C. was used in
parallel with .sup.1H NMR spectroscopy to investigate the ability
of OHB-based and CAHB-based hetero-complementary associative pairs
to afford supramolecular aggregates of telechelic 1,4-PBs of
M.sub.w.gtoreq.200,000 g/mol that are stable enough at low-moderate
shear rates to provide modulation of rheological properties. In
other words, it is expected that at the same concentrations, the
solution of complementary polymer pair would be more viscous than
those of individual components. To avoid possible complications
arising from the multi-component nature of fuels, 1-chlorododecane
(CDD) was chose as the model solvent, and prepared all polymer
solutions at 1 wt % in CDD. In both THY/DAAP and HR/CA
complementary polymer pairs, none of them showed the expected
enhancement in shear viscosity due to complementary end-association
(FIGS. 43 and 44). To find out if the comparatively polar CDD
(dielectric constant=4.2 at 25.degree. C.) interferes with THY/DAAP
and HR/CA complementary interactions, the experiments were repeated
in less polar solvents: Dodecane (dielectric constant=2.0 at
20.degree. C.) and Jet-A (dielectric constant=1.8 at 20.degree. C.)
were used for THY/DAAP pair and HR/CA pair, respectively. As shown
in FIGS. 43 and 44, the expected enhancement in shear viscosity was
still absent in both cases when less polar solvents were used.
[0416] Different results were observed in the case of TA/TB pair.
The 1:1 (w/w) mixture of 1 wt % CDD solutions of 230K di-TA and
250K di-TB 1,4-PBs was found considerably more viscous than both
solutions (FIG. 33), and the observed enhancement in viscosity
illustrated that the strength of TA/TB complementary
end-association was sufficient to drive the formation of
supramolecules stable at shear rates investigated in the present
study. As discussed in above, strong self-association of 230K di-TA
1,4-PB resulted in significant difference in shear viscosity
between the 1 wt % CDD solution of 230K di-TA 1,4-PB and that of
the non-associative pre-polymer 230K di-TE 1,4-PB (FIG. 33). It was
observed that the addition of equal amount (by weight) of 250K
di-TB 1,4-PB further enhanced the shear viscosity. What is also
worth noting is the shear-thinning behavior observed in the 1 wt %
CDD solution of 1:1 mixture of 230K di-TA and 250K di-TB 1,4-PBs,
which is a feature shared by aqueous solutions of water-soluble
telechelic associative polymers [39-42]. As for the 1 wt % CDD
solution of 250K di-TB 1,4-PB, even though GPC-LS analysis
confirmed no crosslinking of polymer backbone took place during
end-functionalization with tertiary amine groups, it was found that
it was more viscous than that of the non-associative 230K di-TE
1,4-PB. Aggregation of triazole units resulting from the
end-functionalization reaction (FIG. 45) may contribute to the
above difference in shear viscosity [43].
[0417] With the positive results of the pair of 230K di-TA/250K
di-TB 1,4-PBs, the viscometric study was extended further to the
complementary DA/DB association as an attempt to approach the limit
of the strength of carboxyl/tertiary amine association. FIG. 34
shows the results of 1 wt % CDD solutions of the corresponding
polymers (230K di-DE, 230K di-DA, and 250K di-DB 1,4-PBs) and the
1:1 (w/w) DA/DB mixture. Surprisingly, strong enhancement in shear
viscosity induced by complementary DA/DB association was still
observed in the 1:1 mixture. While only insignificant difference in
shear viscosity was observed between the 1 wt % CDD solution of
230K di-DA 1,4-PB and that of the non-associative 230K di-DE
1,4-PB, the considerable increase in viscosity due to DA/DB
complementary end-association reaffirmed the promising strength of
carboxyl/tertiary amine interaction.
[0418] The final part of the shear viscometric study of
carboxyl/tertiary amine pairs was to investigate if the TA/TB
complementary end-association was effective in Jet-A when the
M.sub.w of the 1,4-PB backbone increased to 430,000 g/mol, and the
results are shown in FIG. 35. Strong enhancement in shear viscosity
due to TA/TB complementary association was observed: At 1 wt %, the
1:1 mixture of 430K di-TA and 430K di-TB 1,4-PBs in Jet-A was found
significantly more viscous than the Jet-A solutions of the
individual polymers. These results indicate that when used in
dendritic configurations, carboxyl/tertiary amine pair is suitable
for building complementary pairs of telechelic associative polymers
as mist-control additives for fuels.
Example 21: A.1 Measurements of Polymer Molecular Weights
[0419] The determination of molecular weight and molecular weight
distribution is of central interest in polymer analysis, as the
molecular weight of a polymer directly relates to its physical
properties.[44] Take telechelic associative polymers as
mist-control additives for kerosene for example, their efficacy in
providing fire protection and resistance to shear degradation rely
on proper choice of backbone length, which falls in the range
M.sub.w=5.times.10.sup.5-10.sup.6 g/mol. Table 8, which shows
molecular weight measurement methods, summarizes common
characterization methods for determining different average
molecular weights (MWs) and molecular weight distributions (MWDs)
of polymers [25, 44, 45].
TABLE-US-00009 TABLE 8 Abso- Rela- Method lute tive M.sub.n M.sub.w
Range (g/mol) Proton NMR end-group x x M.sub.n < 2.5 .times.
10.sup.4 analysis Vapor pressure x x M.sub.n < 3 .times.
10.sup.4 osmometry Ebulliometry x x M.sub.n < 3 .times. 10.sup.4
Light Scattering (LS) x x 10.sup.4 < M.sub.w < 10.sup.7
Intrinsic Viscosity x M < 10.sup.6 GPC.sup.a with concen- x x x
10.sup.3 < M.sub.w < 10.sup.7 tration detectors GPC.sup.a
with concen- x x x 10.sup.4 < M.sub.w < 10.sup.7 tration and
LS detectors MALDI-TOF-MS.sup.b x x x M < 3 .times. 10.sup.4
.sup.aGPC, gel permeation chromatography. .sup.bMALDI-TOF-MS,
matrix-assisted laser desorption/ionization time-of-flight mass
spectroscopy
[0420] Among the methods in Table 8, GPC with concentration and LS
(light scattering) detectors (referred to as "GPC-LS" herein) was
chosen in the present study for determining MW and the MWD of
telechelic associative 1,4-PBs due to the following reasons: (1) it
allows measurements of absolute weight-average MWs and
corresponding MWDs; (2) it has a wide applicable range
(10.sup.4-10.sup.7 g/mol) which covers the M.sub.w range of
interest (5.times.10.sup.5-10.sup.6 g/mol) for mist-control
applications; (3) it is comparatively easy to implement. Although
MALDI-TOF-MS is capable of measuring absolute MWs and MWDs of
polymers with more accuracy than GPC-LS, it is not as useful in
analyzing polymers of MW>30,000 g/mol [46]; selection of matrix
compounds, sample preparation and interpretation of the mass
spectra become difficult in the case of synthetic polymers of
MW>30,000 g/mol and thus detract from the benefits associated
with the unrivalled accuracy provided by MALDI-TOF-MS [44, 45, 47].
Given that many associative polymers as herein described are
telechelic 1,4-PBs of MW>>30,000 g/mol, it is clear that
GPC-LS can be a better option to measure MWs than MALDI-TOF-MS in
the present study. The same rationale also applies to the other
competing method, proton NMR end-group analysis, which has been
widely used in determining number-average MWs (i.e., M.sub.n) of
synthetic polymers via comparing the integration values of signals
of backbone protons to those of the end-group protons [44, 48, 49].
The implementation of proton NMR end-group analysis can be
straightforward: the M.sub.n value of a polymer can be derived from
its .sup.1H NMR spectrum without any additional experimental work.
However, the determination of M.sub.n by proton NMR end-group
analysis for polymers of MW>25,000 g/mol loses its accuracy due
to a diminished resolution resulting from the inherent detection
limit of proton NMR spectroscopy, and the uncertainty in the
M.sub.n values becomes greater for polymers of higher MWs [44]. The
other issue of this method is that it lacks the ability to measure
molecular weight distributions (MWDs) of polymers. These
shortcomings render proton NMR end-group analysis a less effective
method to characterize high-MW (i.e., MW>100,000 g/mol)
telechelic 1,4-PBs as potential mist-control additives for
kerosene.
[0421] In the case that associative groups are attached onto the
chain ends of telechelic 1,4-PBs, measuring of MWs and MWDs of such
polymers by GPC-LS becomes challenging, since the associative chain
ends could possibly interact with the column packing, or drive the
formation of supramolecular aggregates in THF, leading to false
reading of MWs and MWDs. It was found that compared to the
non-associative 230K di-TE 1,4-PB, the apparent M.sub.w of 230K
di-TA 1,4-PB was found to be higher by 63% (see Table 9, which
shows molecular weight and PDI (polydispersity index) data of
tert-butyl ester- and carboxyl-terminated telechelic 1,4-PBs, and
FIG. 23).
TABLE-US-00010 TABLE 9 N = 1 N = 2 N = 4 N = 8 N = 4 Before TFA
M.sub.w 226 230 230 207 430 Hydrolysis (kg/mol).sup.a PDI.sup.b
1.43 1.53 1.50 1.43 1.49 After TFA M.sub.w 276 299 375 304 510
Hydrolysis (kg/mol).sup.a PDI 1.56 1.73 1.72 1.51 1.61 Increase in
22.12 30.00 63.04 46.86 18.60 M.sub.w (%) .sup.a,bdetermined by
GPC-LS
[0422] It was hypothesized that the apparent increase in M.sub.w
resulted from the aggregate of associative TA end groups in THF,
rather than crosslinking of 1,4-PB backbone during TFA hydrolysis
of tert-butyl ester groups. To test the hypothesis, 230K di-TA
1,4-PB was treated with LiAlH.sub.4 in THF so as to reduce the
highly associative carboxyl groups to less associative hydroxyl
groups. The GPC-LS result of the resultant hydroxyl-terminated 230K
telechelic 1,4-PB, as shown in FIG. 36, virtually overlaps with
that of 230K di-TE 1,4-PB, although the former seems slightly
broadened compared to the latter. Comparison of the three GPC-LS
traces in FIG. 36 verified the hypothesis: the apparent increase in
M.sub.w after TFA hydrolysis of 230K di-TE 1,4-PB was due to
aggregation of associative TA end groups, since the increase in
M.sub.w disappeared after the carboxyl groups on polymer chain ends
were reduced to hydroxyl groups. It also suggests that the mild
condition of TFA hydrolysis does not cause appreciable amount of
crosslinking of 1,4-PB backbone. As for the broadening of GPC-LS
trace of hydroxyl-terminated 230K telechelic 1,4-PB, it is thought
to result from interaction of hydroxyl-terminated chain ends with
column packing. The results in FIG. 36 also reveal the importance
of interpreting GPC-LS results of telechelic associative polymers
with scrutiny, since association of chain ends and chain-end/column
interaction can both result in false reading of MWs and MWDs. In
other words, using the non-associative forms of telechelic
associative polymers in GPC-LS analysis yields more accurate
information concerning the MWs and MWDs of polymer backbones on the
condition that the transformation of associative chain ends to
non-associative counterparts does not damage the backbones.
Example 22: Effect of COD Purity on the Proceeding of ROMP with
CTAs
[0423] It was found that the purity of VCH
(4-vinylcyclohexene)-free COD has a profound effect on the
synthesis of telechelic 1,4-1,4-PBs via ROMP of COD using Grubbs
II: peroxides and n-butanol (introduced during BH.sub.3.THF
treatment of COD according to the Macosko protocol) can also
adversely affect the metathetical activity of Grubbs II by reacting
with it and irreversibly transforming it into inactive species. In
response to the issues associated with peroxides and n-butanol, a
multi-stage process (Section 2.2.3) was developed to rigorously
purify COD.
[0424] In particular, in an exemplary purification procedure,
redistilled cis,cis-1,5-cyclooctadiene (COD, 72.3 g, 0.67 mol) was
syringe-transferred to a 250 ml Schlenk flask in an ice bath at
0.degree. C. under argon atmosphere. Under argon flow, 1M
borane-THF complex in THF (BH.sub.3.THF, 108 mL, 0.11 mol) was then
slowly added into the flask over a 10-min period. The flask was
taken out of the ice bath, and left to stir under argon atmosphere
at room temperature for 2 h. THF was evaporated under reduced
pressure at room temperature to an extent that the concentration of
residual THF in the mixture was below 300 ppm (verified by .sup.1H
NMR analysis). The monomer was vacuum distilled from the mixture at
40.degree. C., 100 mTorr into a 100 mL Schlenk flask (loaded with 9
g of MAGNESOL.RTM. xl and a magnetic stir bar) in a dry-ice tub.
The mixture was stirred under argon atmosphere at room temperature
overnight. The monomer was vacuum distilled again at 45.degree. C.
and 100 mTorr from the mixture into a 100 mL Schlenk flask (loaded
with 10 g of calcium hydride (CaH.sub.2) and a stir bar) in a
dry-ice tub in order to remove moisture introduced by MAGNESOL.RTM.
xl. After stirring at room temperature for 3 h under argon flow,
the monomer was once again vacuum distilled (45.degree. C., 100
mTorr) from the mixture into a 100 mL Schlenk flask in a dry-ice
tub. After warmed to ambient temperature, the flask was sealed with
a SUBA-SEAL.RTM. rubber septum while argon stream was flowing, and
placed in a freezer at -30.degree. C. for storage of purified COD
(40.0 g, 55.3% yield). The purified monomer was vacuum-distilled
again at 35.degree. C. prior to use.
[0425] To illustrate the influence of the purity of VCH-free COD on
the preparation of telechelic 1,4-PBs via ROMP of COD, the
synthesis of di-TE 1,4-PB via the two-stage ROMP of COD with
octa-functional tert-butyl ester-terminated bis-dendritic CTA
(compound 8 in FIG. 46B) was chosen as the benchmark reaction (FIG.
37). Two different batches of VCH-free COD were prepared: the first
(i.e., the control, COD I) was afforded via purification according
to only the Macosko protocol, whereas the second one (COD II) was
prepared according to the purification procedure described above.
The implementation of two-stage ROMP using both batches of COD was
the same as the purification procedure described above, in which
the total monomer:CTA ratio was 2000:1, and 100 eq of COD was used
in the first stage of ROMP; the load of Grubbs II was 1/30 eq of
the CTA. Here the following properties to quantitate the effect of
the purity of COD were chosen: (1) the period of time during which
the reaction mixture develops enough viscosity to stop the magnetic
stir bar from moving after the addition of 1900 eq of COD (t.sub.v)
(2) the overall conversion of COD (X.sub.f, measured by .sup.1H NMR
analysis of the aliquot of reaction mixture) (3) the cis/trans
ratio of the polymeric species in the aliquot (measure by .sup.1H
NMR analysis) (4) M.sub.w of the resultant polymer (measured by
GPC-LS). The results for COD I and COD II were summarized in Table
10, which shows the results of synthesis of di-TE 1,4-PB via ROMP
of batch 1 and batch 2 VCH-free COD.
TABLE-US-00011 TABLE 10 COD I COD II t.sub.v(min) 40.0 1.5 X.sub.f
(mol %) 85.0 97.6 cis/trans ratio 2.20 1.73 M.sub.w (kg/mol) 264
142 PDI 1.58 1.43
[0426] Table 10 shows that the second stage of ROMP of COD II
proceeded significantly faster (t.sub.v=1.5 min) compared to that
of COD I (t.sub.v=40 min); the conversion of COD II was nearly
quantitative (X.sub.f=97.6%), whereas the reaction stopped at
X.sub.f=85% in the case of COD I. In addition, .sup.1H NMR analysis
of aliquots taken in the end of polymerization reactions also
revealed that the use of COD II led to a lower cis/trans ratio
(1.73) compared to the case of COD I (2.20). The M.sub.w of the
resultant polymer of ROMP of COD II (142,000 g/mol), as revealed by
GPC-LS analysis, was found significantly lower than that of ROMP of
COD I (264,000 g/mol). When considered as a whole, these results
indicate that Grubbs II possesses a higher metathetical activity
(or a higher turnover number) when impurities in VCH-free COD that
can interfere with Grubbs II are removed. This explains the much
faster reaction rate of the second stage of ROMP of COD II.
Similarly, Grubbs II in the presence of COD II can perform more
cycles of metathesis reactions compared to in COD I, and thus a
nearly quantitative X.sub.f=97.6% was achieved in the case of COD
II. The low cis/trans ratio (1.73) and M.sub.w (142,000 g/mol)
resulting from ROMP of COD II suggest that a considerable fraction
of ruthenium complexes on polymer chain ends remained
metathetically active when COD II was mostly consumed, and as a
result they continued to react with available C.dbd.C bonds present
in the reaction mixture (in this case, C.dbd.C on polymer
backbones) till they reached their maximum turnover number. The
consumption of backbone by active ruthenium centers on chain ends
(i.e., back-biting) led to the decreases in cis/trans ratio and
M.sub.w.
[0427] In sum, the enhanced activity of Grubbs II observed above
validates the multi-stage purification procedure of COD described
above.
Example 23: Example of Controlling Drag Reduction
[0428] In some embodiments, the associative polymers described
herein can be used to provide a composition in which the property
controlled is drag reduction. In particular, using the methods
described herein, the composition can have a more than 10%
reduction in the pressure drop required to drive a given volumetric
flow rate through a given pipeline.
[0429] In particular, a skilled person can identify the non-polar
host to be transported in which the drag is desired to be
reduced.
[0430] The skilled person can then use published solubility
parameters to estimate the solubility parameter of the identified
non-polar host, or in the alternative, the skilled person can use
literature on polymer solubility in similar liquids, and use this
information to identify polymers that would be expected to dissolve
in the non-polar host, for use as backbones of the associative
polymers. The solubility can be confirmed by the skilled person by
using techniques identifiable to the skilled person, for example by
dissolving a sample of the polymer in the host and determining if
it is homogeneous (e.g., by performing light-scattering
measurements).
[0431] The skilled person can then use published dielectric
constants to estimate the dielectric constant of the host liquid,
and determine the kind of associative interaction of the FGs would
be most suitable. For example, if the dielectric constant is less
than or approximately 2, there are a wide range of suitable
associative groups, including ordinary hydrogen bonding moieties
(e.g. Hamilton receptor/cyanuric acid pairs,
thymine/diacetamidopyridine pairs, and other identifiable to a
skilled person) and charge transfer complexing moieties (e.g.
dinitrophenyl/carbazole pairs and other identifiable to a skilled
person). As the dielectric constant increases, the range of viable
associative moieties decreases. For example, in chlorododecane
(dielectric constant of 4.2 at 25.degree. C.), charge-assisted
hydrogen bonding moieties perform better than ordinary
hydrogen-bond moieties. If there are organic acids (such as,
Butyric acid, isobutyric acid, valeric acid, isovaleric acid,
Heptanoic acid, and others identifiable to a skilled person) or
organic bases (trimethylamine, diethylamine, diisopropylamine,
Triethylamine, Diisobutylamine, diisoamylamine, diphenylamine, and
others identifiable to a skilled person) present in the host
composition, ionic interactions or ligand-metal interactions (a
type of Bronsted/Lewis acid/base interaction) can be more suitable
than charge-assisted hydrogen bond association. Therefore, some
additional optimization can be performed as described below.
[0432] The additional optimization can be performed by preparing
several telechelic polymers with backbone degree of polymerization
of at least 200 and with candidate associative groups at their ends
(e.g. ordinary hydrogen bonding moieties and/or charge transfer
complexing moieties), and dissolving them in the host liquid using
polymer concentration approximately equal to the overlap
concentration for the backbone polymer and length used in the trial
polymers (e.g., by calculating c* as described herein). The
polymers that do not dissolve can be identified, and their
corresponding associative end groups can be designated as being
unsuitable, to thereby identify the suitable associative groups. If
the viscosity of the non-polar composition is not greater than it
would be for a solution of a non-associative polymer of the same
backbone, length and concentration, the associative end groups can
be modified by increasing the number of associative moieties in
each group (i.e., increase the strength of association using
polyvalent interactions).
[0433] Using one or more of the combinations of polymer backbone
structure and end-group structure identified above, the skilled
person can then estimate the backbone length that is compatible
with a desirable or acceptable polymer concentration in the host.
For example, if the backbone is determined to be polybutadiene, and
the associative polymer concentration needs to be kept down to 0.8%
or less (the "x" marked on the vertical axis of FIG. 40), then the
minimum polybutadiene backbone can be read off a graph of the
relationship between the overlap concentration and the
weight-average molecular weight (as shown by the horizontal line
from the "x" on the vertical axis to the corresponding point on the
c* vs M.sub.w relationship for polybutadiene and the vertical line
from that point down to the horizontal axis in FIG. 40), leading to
a value of M.sub.w of about 400,000 g/mol.
[0434] A skilled person can then use experiments to refine the
choice of backbone, backbone length, and FGs by preparing candidate
polymers with the most promising backbone, backbone length, and
FGs, then subjecting them to a limited set of experiments to
validate their performance in both reducing turbulent drag (e.g.,
measuring the flow rate of the non-polar composition though a
conduit, or measuring the change in pressure of the non-polar
composition flowing through a conduit) and, if desired, resisting
degradation due to turbulent flow (e.g. by measuring changes in
viscosity of the non-polar composition after transportation through
a conduit). If the required concentration is found by the skilled
person to be too high (e.g. the amount of polymer required would be
too costly), then the skilled person can prepare another polymer
with the same, but longer, backbone and repeat the process until
the polymer shows efficacy at an acceptably low concentration. This
exemplary procedure is expected to give a drag reduction in
turbulent pipe flow of at least 10%. If the extent of drag
reduction is less than 30%, the skilled person can improve drag
reduction up to 30% by increasing the strength of association, for
example by increasing the number of associative moieties per
associative group (e.g., using end groups with four carboxyl groups
rather than two) or by using a stronger type of association (e.g.,
using charge-assisted hydrogen bonding--that is, a hydrogen bond
formed between a hydrogen bond donor and hydrogen bond acceptor
where the hydrogen bond donor is more acidic than the conjugate
acid of the hydrogen bond acceptor by at least about 4 pKa
units-rather than ordinary hydrogen bonding--that is, a hydrogen
bond formed between a hydrogen bond donor and hydrogen bond
acceptor where the hydrogen bond donor is less acidic than the
conjugate acid of the hydrogen bond acceptor).
Example 24: Use of Associative Polymers in a Fuel in an Engine
while Maintaining Engine Performance
[0435] In this example, an exemplary self-associative polymers were
incorporated in fuel at a level that is appropriate for drag
reduction and/or mist control for improved fire safety. 430K di-TA
PB was selected as the test polymer along with diesel as the base
fuel; a polymer concentration of 0.1 wt % in diesel was
subsequently chosen. A concentrated 1 wt % stock solution of the
exemplary associative polymer was prepared by mixing the polymer
with diesel under oxygen-free condition at 120.degree. C. for 12
hours, and two identical 0.1 wt % diesel solutions of the polymer
with a volume of 1.3 liters were prepared by diluting the 1 wt %
stock solution with the same base fuel at room temperature. Test
samples comprised the two 0.1 wt % solutions and two 1.3-liter
bottles of unmodified base fuel as controls. A 3.75 kW diesel
generator connected to a Simplex Swift-e load bank and a Fluke 434
Series II Energy Analyzer was used as the test apparatus, and the
tests were performed at the Vehicle Emission Research Laboratory
(VERL) of the Center for Environmental Research & Technology
(CE-CERT), University of California at Riverside. A sequence of
generator load/operating time comprising the following stages was
used to carry out the tests: 2000 Watts (.about.53% of its rated
power)/9 min, 3000 Watts (.about.80% of the rated power)/9 min,
3500 Watts (.about.93% of the rated power)/6 min, 3000 Watts/9 min,
and 2000 Watts/9 min. Between samples the fuel supply to the engine
was switched to a reservoir filled with the reference fuel (the
same diesel fuel that was used to prepare the samples with
associative polymers herein described) to keep the generator
operating. The AC output from the generator was recorded
continuously by the Energy Analyzer, and the emissions were
analyzed using gas analysis of an isothermal stream of precisely
calibrated dilution of the exhaust gas; quantitative values for
carbon dioxide (CO.sub.2), carbon monoxide (CO), mono-nitrogen
oxide (NO.sub.x), methane (CH.sub.4) and total hydrocarbons (THC)
were continuously monitored. Samples were run in a blind randomized
sequence and the results were quantitatively analyzed prior to
unmasking the sample identification. The results show no decrease
in power output at any of the three loads to within the uncertainty
of the power measurement. The results showed no adverse effects on
engine emissions (Table 11). For the composition used in this
example, it was not possible to identify the time at which the fuel
supply to the engine was switched between the reference fuel, since
none of the measured quantities changed at or near the time the
valve was switched. The emissions of CO and THC were reduced (11),
while the power output was the same (to within the uncertainty of
the measurement) as for untreated diesel.
TABLE-US-00012 TABLE 11 % change Condition A #29.sup.a CO.sub.2
Sample-Diesel 2 kW 2.03 Sample-Diesel 3 kW -0.09 Sample-Diesel 3.5
kW 0.43 Sample-Diesel 3 kW 1.56 Sample-Diesel 2 kW 1.46 CO
Sample-Diesel 2 kW 5.63 Sample-Diesel 3 kW -4.34 Sample-Diesel 3.5
kW -10.20 Sample-Diesel 3 kW -1.93 Sample-Diesel 2 kW 8.87 THC
Sample-Diesel 2 kW -15.54 Sample-Diesel 3 kW -13.04 Sample-Diesel
3.5 kW -11.54 Sample-Diesel 3 kW -8.73 Sample-Diesel 2 kW -0.68
NO.sub.x Sample-Diesel 2 kW 4.30 Sample-Diesel 3 kW 2.81
Sample-Diesel 3.5 kW 3.76 Sample-Diesel 3 kW 4.13 Sample-Diesel 2
kW 5.96 .sup.aA#29 is diesel treated with 0.1 wt % di-TA PB
Example 25: Reduction of Emissions in Fuels Comprising Associative
Polymers
[0436] In this example, exemplary donor-acceptor polymers are
incorporated in fuel at a level that is appropriate for drag
reduction and/or mist control for improved fire safety, with the
additional benefit that emissions from the engine are reduced. A
1:1 (w/w) mixture of 630K di-DA PB and 540K di-DB PB was selected
as an exemplary donor-acceptor polymer pair along with diesel as
the base fuel; a total polymer concentration of 0.1 wt % in diesel
was subsequently chosen. A concentrated 1 wt % stock solution of
the donor-acceptor pair was prepared by mixing the pair with diesel
at room temperature for 12 hours and at 70.degree. C. for 7 hours,
and two identical 0.1 wt % diesel solutions of the pair with a
volume of 1.3 liters were prepared by diluting the 1 wt % stock
solution with the same base fuel at room temperature. Test samples
comprised the two 0.1 wt % solutions and two 1.3-liter bottles of
unmodified base fuel as controls. The Same apparatuses, procedures,
and characterizations described in Example 24 were used in this
example. Samples were run in a blind randomized sequence and the
results were quantitatively analyzed prior to unmasking the sample
identification. The results showed no decrease in power output at
any of the three loads to within the uncertainty of the power
measurement. For the composition used in this example, the
emissions of CO and THC were reduced (Table 12), while the power
output was the same (to within the uncertainty of the measurement)
as for untreated diesel.
TABLE-US-00013 TABLE 12 % change Condition AB #90.sup.a AB #8.sup.a
AB averaged CO.sub.2 Sample-Diesel 2 kW 0.68 0.95 0.81
Sample-Diesel 3 kW -1.74 1.40 -0.17 Sample-Diesel 3.5 kW 0.71 0.92
0.82 Sample-Diesel 3 kW 0.19 -0.43 -0.12 Sample-Diesel 2 kW 0.09
1.09 0.59 CO Sample-Diesel 2 kW -13.89 -10.99 -12.44 Sample-Diesel
3 kW -15.81 -12.52 -14.16 Sample-Diesel 3.5 kW -14.36 -16.31 -15.33
Sample-Diesel 3 kW -10.79 -14.91 -12.85 Sample-Diesel 2 kW -11.79
-12.49 -12.14 THC Sample-Diesel 2 kW -25.12 -23.83 -24.47
Sample-Diesel 3 kW -14.39 -16.65 -15.52 Sample-Diesel 3.5 kW -10.13
-12.63 -11.38 Sample-Diesel 3 kW -11.75 -12.50 -12.12 Sample-Diesel
2 kW -12.27 -13.37 -12.82 NO.sub.x Sample-Diesel 2 kW -1.29 0.77
-0.26 Sample-Diesel 3 kW -3.16 -0.35 -1.76 Sample-Diesel 3.5 kW
-2.17 -0.59 -1.38 Sample-Diesel 3 kW -1.95 -0.43 -1.19
Sample-Diesel 2 kW 0.77 2.70 1.73 .sup.aAB #90 is a first sample of
0.1 wt % 1:1 di-DA PB/di-DB PB; AB #90 is a second sample of 0.1 wt
% 1:1 di-DA PB/di-DB PB
[0437] Based on the observed reductions of THC and CO, a
corresponding increase in fuel efficiency occurred.
Example 26: Improvement of Fuel Efficiency with Self-Associative
Polymers
[0438] The emissions data discussed for Example 24 (0.1 wt % diesel
solution of 430K di-TA PB) show a reduction in THC and CO emissions
compared to the diesel reference sample, indicating a more
efficient burning of the fuel.
Example 27: Improvement of Fuel Efficiency with Donor-Acceptor
Associative Polymers
[0439] The emissions data discussed for example 25 (0.1 wt % diesel
solution of 630K di-DA PB/540K di-DB PB 1:1 mixture) show a
reduction in THC and CO emissions compared to the diesel reference
sample, indicating a more efficient burning of the fuel.
Example 28: Additional Improvement of Fuel Efficiency with
Donor-Acceptor Associative Polymers
[0440] The exhaust gas temperatures for untreated diesel and the
sample described in Example 25 (0.1 wt % diesel solution of 630K
di-DA PB/540K di-DB PB 1:1 mixture) were measured by a thermal
couple immediately after the exhaust was diluted with an isothermal
stream of carrier gas (hence, the temperature of the actual exhaust
gas was considerably higher that reported here after dilution). The
results revealed a 5.degree. C. reduction for the exhaust
corresponding to example 25, indicating a more efficient burning
and conversion of fuel energy to useful power in the engine for
this example.
Example 29: Materials
[0441] All chemical reagents were obtained at 99% purity from
Sigma-Aldrich, Alfa Aesar, or Mallinckrodt Chemicals. Magnesol.RTM.
XL was purchased from The Dallas Group of America, Inc. .sup.1H-NMR
spectra were obtained using a Varian Inova 500 spectrometer (500
MHz); all spectra were recorded in CDCl.sub.3. Chemical shifts were
reported in parts per million (ppm) and were referenced to residual
protio-solvent resonances. Deuterated solvents used for .sup.1H-NMR
and SANS experiments (CDCl.sub.3 and d.sub.12-cyclohexane) were
purchased from Cambridge Isotope Laboratories. Cylindrical quartz
"banjo" cells used in scattering experiments were purchased from
Hellma Analytics.
Example 30: Representative Procedure for Purification of
Cyclooctadiene (COD)
[0442] Trace impurities introduced when purifying COD to remove its
constitutional isomer 4-vinylcyclohexene using
borane-tetrahydrofuran complex (BH.sub.3.THF) were found to affect
the procedure to prepare long telechelic polycyclooctadienes
(PCODs).
[0443] Redistilled-grade COD (72.3 g, 0.67 mol) was
syringe-transferred to a 250 ml Schlenk flask in an ice bath under
argon. 1 M BH.sub.3.THF complex in THF (108 ml, 0.11 mol) was
slowly added into the flask over 10 min. The flask was taken out of
the ice bath, and left to stir under argon at room temperature for
2 h. THF was evaporated under reduced pressure at room temperature
to an extent that the concentration of residual THF in the mixture
was below 300 ppm (verified by .sup.1H NMR analysis). The monomer
was vacuum distilled from the mixture at 40.degree. C. into a 100
ml Schlenk flask (loaded with 9 g of Magnesol.RTM. XL and a stir
bar) in a dry-ice tub. The mixture was stirred under argon
atmosphere at room temperature overnight. The monomer was vacuum
distilled from the mixture into a 100 ml Schlenk flask (loaded with
10 g of calcium hydride (CaH.sub.2) and a stir bar) in a dry-ice
tub. After stirring at room temperature for 3 h under argon flow,
the monomer was vacuum distilled from the mixture into a 100 ml
Schlenk flask in a dry-ice tub. After being warmed to ambient
temperature, the flask was sealed with a Suba-Seal rubber septum
while argon was flowing through the flask, and placed in a freezer
at -30.degree. C. for storage of the rigorously purified COD (40.0
g, 55.3% yield). The rigorously purified monomer was vacuum
distilled again prior to use.
[0444] FIG. 60 shows .sup.1H NMR spectra of increasingly purified
COD in the range from 3.4 to 5.9 ppm. FIG. 60, Panel A, COD after
BH.sub.3.THF treatment and vacuum distillation (containing
.about.330 ppm of butanol based on integration). FIG. 60, Panel B,
Alternatively, COD further purified with magnesium
silicate/CaH.sub.2 treatments (to show removal of butanol and the
resulting purity of COD used as monomer).
Example 31: GPC-MALLS for Characterization of Polymers
[0445] MALLS, i.e. Multi-angle Laser Light Scattering, was used in
conjunction with GPC to determine the molecular weights and
polydispersity of the polymers. The system used a Wyatt DAWN EOS
multi-angle laser light scattering detector (.lamda.=690 nm) with a
Waters 410 differential refractometer (RI) (.lamda.=930 nm)
connected in series. Chromatographic separation by the size
exclusion principle (largest comes out first) was achieved by using
four Agilent PLgel columns (pore sizes 10.sup.3, 10.sup.4,
10.sup.5, and 10.sup.6 .ANG.) connected in series. Degassed THF was
used as the mobile phase with a temperature of 35.degree. C. and a
flow rate of 0.9 ml/min. The time for complete elution through the
system was 50 min, and MALLS and RI data were recorded at 5 Hz.
[0446] Samples were prepared by dissolving 5 mg of polymer in 1 ml
of THF and filtering the solution through 0.45 .mu.m PTFE membrane
syringe filters immediately before injection. An injection volume
of 20 .mu.l was used. The data were analyzed by Wyatt Astra
Software (version 5.3.4) using the Zimm fitting formula with
dn/dc=0.125 for PCOD in THF to obtain weight-average molecular
weight (M.sub.w) for each polymer reported. Polymers are described
in the Table 13.
TABLE-US-00014 TABLE 13 Characterization of polymers in this
application. M.sub.w.sup.a M.sub.n.sup.a M.sub.w.sup.b Polymer
(kg/mol) (kg/mol) PDI.sup.a (kg/mol) 45kNA 48.5 31.3 1.55 45kDA
44.7 28.6 1.56 45kDB 48.8 36.7 1.33 140kNA 138.5 89.8 1.54 140kDA
143.1 90.2 1.59 140kDB 148.0 100.0 1.48 300kNA 318.4 213.5 1.49
300kDA 304.3 201.3 1.51 300kDB 290.1 198.3 1.46 320 .+-. 20 670kNA
637.5 441.0 1.45 670kDA 671.4 445.5 1.51 670kDB 629.2 436.2 1.44
600 .+-. 50 76kNA 76.2 52.3 1.46 76kTA 91.2 57.0 1.60 230kNA 232.8
155.4 1.50 230kTA 374.5 218.7 1.71 430kNA 430.0 288.6 1.49 430kTA
510.0 316.8 1.61 (.sup.adetermined by GPC-MALLS in THF;
.sup.bdetermined by batch-mode MALLS in cyclohexane.)
Example 32: Rheology
[0447] Polymers were dissolved by shaking with tetralin,
cyclohexane or Jet-A. To confirm that the end-association among
telechelics is responsible for the changes in fluid properties,
additional controls were prepared by treating some associative
telechelic solutions (1.76 mg/ml) with 2.5 .mu.l/ml triethylamine
(TEA) to block their end association. Shear-flow rheology data were
obtained at 25.degree. C. with stress-controlled rheometer TA
AR1000, equipped with a cone-plate geometry (angle 1.degree.,
diameter 60 mm) for polymer solutions in tetralin and Jet-A, and a
strain-controlled rheometer TA ARES-RFS, equipped with a cone-plate
geometry (angle 2.degree., diameter 50 mm) and a solvent trap for
polymer solutions in cyclohexane, with shear rate ranging from 1000
s.sup.-1 to 10 s.sup.-1. For polymer solutions in tetralin, the
viscosities measured by AR1000 and ARES-RFS were checked to be
agreed with each other well. The specific viscosity values shown in
FIG. 48 were averaged over data points taken from the range that
doesn't have shear rate dependence (e.g., the range is 300 to 10
s.sup.-1 in FIG. 49A `DA/DB`). Three replicates with freshly
prepared solutions were measured to obtain the error bars (SD
values).
Example 33: Stead-Flow Shear Viscometry
[0448] Polymers were dissolved by shaking with solvents of interest
(tetralin and Jet-A). Steady shear viscosity was measured in a
cone-plate geometry (60 mm diameter aluminum, 1.degree. cone, 29 m
truncation) at 25.degree. C. using an AR1000 rheometer from TA
Instruments (temperature controlled at 25.degree. C.). Test
solutions were probed in the shear rate range 1-3000 s.sup.-1
logarithmically (5 shear rates per decade). All viscosity data were
reported in terms of specific viscosity (.eta..sub.sp,
.ident.(.eta..sub.solution-.eta..sub.solvent)/.eta..sub.solvent,
where .eta..sub.solvent=2.02 mPas for tetralin and 1.50 mPas for
Jet-A at 25.degree. C.) which reflects the contribution of the
polymer to the viscosity.[25]
Example 34: Shear Stability Test
[0449] A recirculation setup consisting of a Bosch 69100 In-line
Electric Fuel Pump and a MW122A 2AMP Regulated DC Power Supply (LKD
Ind.) at 12 V (shown in FIG. 66 Panel A) was used to subject
polymer solutions to a flow history that mimics, for example,
recirculation of fuel through an engine's heat transfer system.
Test samples were recirculated through the setup at room
temperature for 60 s (approximately 60 passes through the pump
using 50-60 mL of solution and a flow rate of 3 L/min). After
recirculation, samples were collected in 100 mL glass jars and
stored at -30.degree. C. for further tests. Between tests, the pump
was rinsed 4 times with approximately 200 mL of hexanes, followed
by drying in vacuo at 40.degree. C. overnight to prevent
cross-contamination among samples or dilution by hexanes. Shear
stability was evaluated by comparing shear viscosities of
recirculated samples to those of the corresponding unsheared
controls.
Example 35: Small-Angle Neutron Scattering (SANS)
[0450] d.sub.12-Cyclohexane solutions of polymers were prepared by
weighing out polymer on a Mettler precision balance (.+-.0.01 mg)
into new glass scintillation vials with PTFE lined caps and
subsequently adding the appropriate amount of solvent using a
precision syringe (.+-.1%). These were subsequently placed on a
wrist action shaker at room temperature overnight.
[0451] SANS data in the present application were obtained at the
National Institute of Standards and Technology (NIST) on beamline
NG-3, preliminary experiments (data not shown) were conducted at
Oak Ridge National Laboratory (ORNL) on beamline CG-2 at the High
Flux Isotope Reactor (HFIR). Samples were placed in Hellma quartz
cylindrical cells with 5 mm path length. Temperature was controlled
by a recirculating water bath at NIST and by Peltier at ORNL. All
scattering experiments were conducted at 25.degree. C.
Two-dimensional scattering patterns were taken for each sample
using three detector distances (1.3-13 m at NIST and 0.3-18.5 m at
ORNL). The overall scattering vector ranges were
0.003<q(.ANG..sup.-1)<0.4 at NIST and
0.002<q(.ANG..sup.-1)<0.8 at ORNL with the effective limits
for a given sample determined by the signal to noise ratio.
Example 36: Multi-Angle Laser Light Scattering MALLS ("Batch
Mode")
[0452] MALLS (not connected to GPC) was used to characterize the
supramolecular assembly behavior of complementary associative
telechelic polymers (DA/DB mixtures) in cyclohexane. Cyclohexane
solutions of polymers were prepared by weighing out polymer on a
Mettler precision balance (.+-.0.01 mg) into new glass
scintillation vials (20 ml) with metal foil lined caps and
subsequently adding the appropriate amount of solvent using a
precision syringe (.+-.1%). These were subsequently placed on a
wrist action shaker at room temperature overnight. All solutions
were filtered through 0.45 .mu.m PTFE filters into clean glass
scintillation vials (20 ml) and allowed to equilibrate for at least
24 hours prior to characterization. MALLS measurements were carried
out using a Wyatt DAWN EOS laser light scattering instrument in
"batch mode" with 18 detectors in the angular range from 22.5 to
1470 using a solid-state laser (.lamda.=690 nm).
[0453] Data were acquired at 35.degree. C. three times (rotating
the vial to average out heterogeneities) for at least 2 minutes and
analyzed using Wyatt Astra Software (version 5.3.4). The
associative supramolecules conformed to the Zimm fitting formula,
which was used to evaluate the apparent weight-average molecular
weight (app M.sub.w) and apparent radius of gyration (app R.sub.g)
for each polymer composition at each concentration, with dn/dc=0.11
for PCOD in cyclohexane.
Example 37: Modeling: A Theoretical Model of Ring-Chain
Equilibrium
[0454] Statistical mechanics were used to design polymers that defy
conventional wisdom by self-assembling "mega-supramolecules"
(.gtoreq.5,000 kg/mol) at low concentration (.ltoreq.0.3% wt).
Theoretical treatment of the distribution of individual
subunits--end-functional polymers--among cyclic and linear
supramolecules (ring-chain equilibrium) predicts that
mega-supramolecules can form at low total polymer
concentration--if, and only if, the backbones are long (>400
kg/mol) and end-association strength is optimal (16-18 kT wherein k
as used herein indicates Boltzmann constant). Viscometry and
scattering measurements of long telechelic polymers (LTPs,
M.sub.w.gtoreq.400 kg/mol) having polycyclooctadiene backbones and
acid or amine end groups verify formation of mega-supramolecules.
They control misting and reduce drag like ultra-long covalent
polymers. With individual building blocks short enough to avoid
hydrodynamic chain scission (400<M.sub.w[kg/mol].ltoreq.1,000)
and reversible linkages that protect covalent bonds, these
mega-supramolecules overcome the obstacles of shear degradation and
engine incompatibility.
[0455] Ultra-long polymers (M.sub.w.gtoreq.5,000 kg/mol) exhibit
dramatic effects on fluid dynamics even at low concentration (e.g.,
.ltoreq.100 ppm confers mist control ([50], [6]) and drag reduction
([51]). The key to both mist control and drag reduction is the
ability of polymers to store energy as they stretch, such that the
fluid as a whole resists elongation. The high potency of ultra-long
linear polymers is due to the onset of chain stretching at low
elongation rates and their high ultimate conformational elongation
([52]). For example, increasing M.sub.w from 50 kg/mol to 5,000
kg/mol (below, kg/mol values refer to weight-average molecular
weight, M.sub.w) decreases the critical elongation rate by more
than three orders of magnitude, and increases the ultimate
molecular elongation by two orders of magnitude.
[0456] Here a set of parameter values is identified for which the
equilibrium distribution of the supramolecular species is suitable
for mist-control applications. Based on prior literature on
ultra-long polymers (which themselves are not acceptable due to
shear degradation during routine handling of fuel and
incompatibility with engine systems), polyisobutylene chains having
weight-average molecular weight.about.5.times.10.sup.6 g/mol are
satisfactory mist-suppressing agents at concentrations as low as 50
ppm in kerosene [6]. Therefore, a theoretical model of ring-chain
equilibrium is used to identify choices of the molecular weight of
telechelic chains (MW.sub.p), the strength of end-association
(.epsilon.kT) and concentration (.PHI..sub.total) that would
provide 50 ppm of "mega-supramolecules" (linear supramolecules of
M.sub.w.gtoreq.5.times.10.sup.6 g/mol and cycles of
M.sub.w.gtoreq.10.times.10.sup.6 g/mol). Initial results provide
motivations to synthesize exceptionally long telechelics and guided
the selection of associative end groups: the model indicates that
chains of approximately 5.times.10.sup.5 g/mol to 1.times.10.sup.6
g/mol with ends that associate with strength 16 kT-18 kT at
approximately 800-1400 ppm concentration could provide the
necessary concentration of mega-supramolecules. Details of the
particular theoretical formulation were developed and described
herein.
Example 38: Parameter Space for Ring-Chain Equilibrium of Long,
End-Associative Telechelics
[0457] Results are presented for complementary pairs of telechelic
polymers (A - - - A, B - - - B) that have similar backbone lengths
(MW.sub.A=MW.sub.B=MW.sub.p) in stoichiometric solutions
(.PHI..sub.Atotal=.PHI..sub.Btotal=.PHI..sub.total/2). When the A
and B end-groups meet, they form a physical association with energy
E. In the resulting parameter space of {MW.sub.p, .epsilon.,
.PHI..sub.total}, the equilibrium distribution of supramolecules
are optimized for mist-control applications, within the constraints
on MW.sub.p (M.sub.w.ltoreq.1.times.10.sup.6 g/mol) and
.PHI..sub.total (<5,000 ppm) in the context of fuel
additives.
[0458] The challenge associated with using end-to-end association
at the low concentrations relevant to fuel is the tendency to form
small cyclic species that, in effect, consume most of the
telechelic building blocks without contributing to mist control. To
reduce the fraction of telechelic chains incorporated into cyclic
species, very long telechelics are used, which reduce the fraction
of polymer "wasted" in small rings because the loop closure
probability scales as N.sup.-3/2 for Gaussian chains and
N.sup.-1.66 for swollen chains (see Example 45). Based on prior
literature on shear degradation, MW.sub.p=1.times.10.sup.6 g/mol is
considered as an upper bound and it is compared to chains that are
half that length MW.sub.p=0.5.times.10.sup.6 g/mol to quantify
sensitivity to MW.sub.p. As a further step to mitigate formation of
small rings, complementary association of A - - - A and B - - - B
telechelics is used, for which the smallest ring is a dimer. This
reduces the amount of telechelic wasted in small cyclics due to two
effects: i) the entropy penalty for ring closure for the smallest
possible ring is much greater than the penalty for closing a ring
of size a single telechelic because the loop is twice as long as a
single telechelic; and ii) the odd rings (cycles of 1, 3, 5, . . .
telechelics) are eliminated, greatly reducing the fraction of
building blocks partitioned in cyclic species.
[0459] Another challenge in the context of fuel additives is the
need to maintain low viscosity. The longer a polymer is, the lower
the concentration .PHI.* at which the chains begin to overlap and
viscosity begins to increase strongly. Therefore, the total polymer
concentration .PHI..sub.total needs to be less than the overlap
concentration of the individual telechelic building blocks,
.PHI.*(MW.sub.p). Further, the model shows that a concentration of
.PHI..sub.total=1/4 .PHI.*(MW.sub.p) is low enough that all
supramolecules in the equilibrium distribution are below their
respective overlap concentrations. For the two chain lengths
selected above, results are presented for .PHI..sub.total=1/4
.PHI.*(MW.sub.p), which is 800 ppm for MW.sub.p=1.times.10.sup.6
g/mol, and 1400 ppm for MW.sub.p=0.5.times.10.sup.6 g/mol. In
addition, results are presented for 1.times.10.sup.6 g/mol at 1400
ppm, both to illustrate the change in the distribution of
supramolecular species with increasing concentration (from
.PHI..sub.total=800 ppm to 1400 ppm for MW.sub.p=1.times.10.sup.6
g/mol) and to illustrate the effect of the size of the telechelic
building blocks at matched total concentration (comparing both
chain lengths at .PHI..sub.total=1400 ppm). With the above choices
for MW.sub.p and .PHI..sub.total, the problem is reduced to a
single dimension, .epsilon., which is examined over its physically
relevant range: it is much greater than kT to drive association and
it is much less than 150 kT (approximate strength of a covalent
bond) so that the reversible links can function as tension relief
links that protect against chain scission in strong flows.
TABLE-US-00015 TABLE 14 Literature Values for Parameters in the
Model Polydiene backbone double non-1,4- .rho. b M_K 1,4-rich cis
trans units (b) [g/ml] C.infin. [nm] [g/mol] References
Polyisoprene .sup. 100% (a) 0 (a) 0 (a) 0.910 5.2 0.93 128.6 [1]
70% 23% 7% 0.900 4.7 0.84 119.6 [2] 19% 45% 36% 0.895 5.3 0.96
156.9 [1], [4] Polybutadiene 98% 1% 1% 0.900 4.6 0.83 90.5 [1], [3]
29% 53% 18% 0.895 5.6 1.01 119.8 [1], [5] 44% 59% 7% 0.895 5.5 0.99
112.5 [1], [5] Properties measured at temperature of 25.degree. C.
.rho. density in the melt state C.infin. characteristic ratio b
Kuhn step length M_K molar mass of a Kuhn segment Shaded cells:
most similar to the polycyclooctadiene in this study, which has 75%
cis units, 25% trans units and no 1,4-units. Notes: (a) natural
rubber (b) for polyisoprene, these are mainly 3,4-units and trace
amounts of 1,2-units; and for polybutadiene, these are
1,2-units
(c) shaded cells refers to cells in the top row of the
Polybutadiene portion in Table 14.
Example 39: Modeling: Computation and Experiment
[0460] Despite prior reports indicating that end association
becomes difficult as chain length increases ([53], [54], [55]), the
regime of long telechelic polymers (LTPs, FIG. 47A, right; see
Table 13 for list of polymers) at concentrations below 1% was
ventured into, theory was used to guide the selection of molecular
structures. To aid material design, a lattice model was used in
which the polymer molecular weight simply maps onto the
corresponding number of connected lattice sites, each site with a
volume equal to that of an effectively freely-jointed segment
("Kuhn segment")--a well-established property, tabulated for many
polymers (Table 14). Unsaturated hydrocarbon backbones were chosen
based on their solubility (remaining in solution down to the
freezing point of fuel) and strength (FIG. 76 see [8]). In addition
to the Kuhn segment volume, two additional attributes of the
polymer backbone enter into the entropy cost of ring closure: the
Kuhn segment length (how close ends are for a ring to close) and
the excluded volume parameter (how expanded the chain is in
solution). The end-association strength (i.e., energy penalty for
unpaired ends) enters through the chemical potential of the linear
species.
[0461] To guide the design of an experimental system, the
relationship of model parameters to polymers having unsaturated
hydrocarbon backbones--1,4-polyisoprene (PI), 1,4-polybutadiene
(PB) and polycyclooctadiene (PCOD)--in Jet-A solvent is considered.
The model is formulated with sites of volume a.sup.3 on a lattice
with coordination number c=6. The lattice size a3=v.sub.K, where
v.sub.K=MW.sub.K/(N.sub.A.rho.) is the volume of a Kuhn segment
(with N.sub.A denoting Avogadro's number and .rho., the polymer
density) for a specific polymer of interest. A chain of molecular
weight MW.sub..rho. maps onto M=MW.sub.p/MW.sub.K connected lattice
sites. To model a solution at volume fraction .PHI..sub.p, a system
of N.sub.p polymer molecules in a volume
V=(MN.sub.p+N.sub.s)a.sup.3 is treated, the number of solvent
lattice sites adjusted to give the specified concentration, i.e.,
N.sub.s=MN.sub.p(1-.PHI..sub.p)/.PHI..sub.p. To quantify the
entropic cost of loop closure (Example 47), numerical values are
needed for the small end-to-end distance x required to close a loop
and for the number of monomers in a thermal blob
g.sub.T.apprxeq.b.sup.6/v.sup.2. For simplicity x/b=1 is
chosen.
[0462] All three backbones of interest here, PI, PB and PCOD, can
be represented to good approximation by a single set of parameters,
because the differences among them are relatively small (Table 14).
For these unsaturated hydrocarbon backbones, variations in
molecular parameters result from differences in cis/trans ratio of
the backbone double bonds and the fraction of monomer insertions
that create short side chains (3,4- and 1,2-units in PI and PB). If
all six chain microstructures in Table 14 are considered, the
lattice size is a=0.61.+-.0.03 nm. Focus is placed on polymers that
have very few side chains (PCOD does not have any); if only
microstructures with .ltoreq.7% 3,4- and 1,2-units, the lattice
size shifts very slightly to a=0.59.+-.0.03 nm. Similarly, the
molecular weight of a Kuhn segment is MW.sub.K=121.+-.22 g/mol if
all six microstructures are included and shifts slightly to
MW.sub.K=113.+-.16 g/mol if microstructures with 18% or more 3,4-
and 1,2-units are excluded. The Kuhn step length is roughly 50%
greater than the lattice size a: if all six microstructures are
included b=0.93.+-.0.07 nm (with <7% 3,4- and 1,2-units,
b=0.90.+-.0.08 nm). The excluded volume parameter v was estimated
as v/b.sup.3.apprxeq.0.10 for PI in Jet-A, consistent with
g.sub.T.apprxeq.100. [15] Based on literature results in
cyclohexane, the expanded conformations of PI and PB are very
similar when they are dissolved in a good solvent that is similar
to Jet-A (R.sub.g [nm]=A(MW).sup.v, with A=0.0129 for PB and 0.0126
for PI, and with v=0.609 for PB and 0.610 for PI). Thus,
theoretical predictions with a single set of parameters are
expected to provide equally good guidance for molecular design with
PI, PB and PCOD backbones. Results are shown for MW.sub.K=113
g/mol, a=0.61 nm, b=0.90 nm, x/b=1 and g.sub.T=100
[0463] The model predicts the equilibrium distribution of
aggregates in terms of concentrations of supramolecular species
with various sizes as functions of polymer concentration, length of
the telechelic building blocks and binding energy. The model
provides a guideline to achieve the desired rheological benefits
(mist control and drag reduction).
[0464] To overcome the problem of chain collapse that occurs when
stickers are distributed along a chain, a model of ring-chain
equilibrium is used to test the hypothesis that clustering stickers
at the ends of polymer chains can be used to generate a sufficient
population of mega-supramolecules to exert mist control. It is
shown that linear chains displaying strongly associating,
complementary end-groups (A - - - A and B - - - B binary mixtures)
form linear and cyclic supramolecules that extend to
"mega-supramolecules" if the individual building blocks are long
enough. Specifically, >50 ppm of mega-supramolecules (ca.
5-10.times.10.sup.6 g/mol) is only achieved with telechelic chains
of length>5.times.10.sup.5 g/mol and a specific range of
association energy, 16.ltoreq..epsilon..ltoreq.18. These
calculation results help to inspire the development of synthetic
routes to the novel molecules.
[0465] Experimentally, poly(1,5-cyclooctadiene) is chosen as an
exemplary polymer backbone for testing, which corresponds to a
1,4-polybutadiene with 75% cis, 25% trans and 0% short side
branches. Thus, the required chain length for PCOD can be similar
to that predicted with parameters based on PI and PB as discussed
in Example 39 taking into account the fact that unlike the model,
real polymers are polydisperse. The telechelics synthesized using
ROMP/CTA have M.sub.w/M.sub.n=1.5.+-.0.1, so the guidance from
theory is applied by targeting polymers in range from
M.sub.w=5.times.10.sup.5 g/mol to M.sub.n=5.times.10.sup.5 g/mol
(M.sub.w=10.times.10.sup.5 g/mol). The remarkable polymers
described in the paper demonstrate the success of the described
theoretical model and the parameter estimation using prior
literature on 1,4-PI and 1,4-PB. Exemplary effects on the
distribution of the polymers of parameters such as concentration,
lengths of polymers and energy association (Ka) are reported in
Examples 39 to 41 below.
Example 40: Effect of Concentration
[0466] A comparison of model results for MW.sub.p=10.sup.6 g/mol
(labeled 1000k) at total polymer volume fraction .PHI..sub.total of
1400 ppm and 800 ppm was performed. The models were obtained with
the computation and experiments of Example 38.
[0467] The results illustrated in FIG. 51 demonstrate two important
effects of total polymer concentration. First, at fixed MW.sub.p
and .epsilon., increasing concentration improves the fraction of
the polymer involved in larger linear aggregates (compare upper
right and middle right in FIG. 51): at 1400 ppm the distribution of
linear supramolecules (open symbols) decays more gradually with
increasing M.sub.W, and the position of the peak in
.PHI..sub.linear vs. M.sub.W is greater at 1400 ppm than at 800 ppm
(most visibly for .epsilon.=18, right column of FIG. 51).
Example 41: Effect of Length of Telechelic Building Blocks
[0468] Effects of polymer lengths on the polymer distribution of
the poly(1,5-cyclooctadiene in a host composition was determined by
the modeling computation and experiments of Example 38.
[0469] Longer chains begin to overlap at a lower concentration than
shorter ones. To examine the effect of the length of the individual
building blocks (MW.sub.p) at similar degree of overlap, they are
compared at .PHI..sub.total=1/4 .PHI.* for their respective
.PHI.*(MW.sub.p): results for 5.times.10.sup.5 g/mol chains at 1400
ppm (bottom row, FIG. 51) and 1.times.10.sup.6 g/mol chains at 800
ppm (middle row). The shape of the .PHI..sub.linear VS. M.sub.W
does not change significantly with MW.sub.p (for all E). An effect
of MW.sub.p is that longer telechelics reduce the fraction of
polymer "wasted" in rings with small aggregation numbers, due to
the increased entropic cost of cyclization for larger loops.
Example 42: Effect of Energy of Association
[0470] Effects of energy of association on the polymer distribution
of the poly(1,5-cyclooctadiene in a host composition was determined
by modeling computation and experiments of Example 38.
[0471] The equilibrium distribution changes qualitatively as the
association energy increases (FIG. 51, from left to right): the
population of loops of all sizes increases (due to higher penalty
for dangling ends) and the breadth of the distribution of linear
species broadens and the peak in .PHI..sub.linear decreases. At
values of .epsilon..ltoreq.14, aggregates are few and the dominant
components are the telechelic building blocks themselves. At values
of .epsilon..gtoreq.20 (not shown), the dominant components are
cycles of low M.sub.W. Intermediate values of the energy of
association, corresponding to 16.ltoreq..epsilon..ltoreq.18,
provide a balance of interactions strong enough to drive formation
of large supramolecules and weak enough to accommodate a
significant population of linear superchains (with unpaired
ends).
Example 43: Mist-Control Applications
[0472] The model showed that optimal formation of
"mega-supramolecules" (linear supramolecules of
M.sub.W.gtoreq.5.times.10.sup.6 g/mol and cycles of
M.sub.W.gtoreq.10.times.10.sup.6 g/mol) correlates with maximizing
the equilibrium fraction of polymers involved in linear
supramolecules in the 5-10.times.10.sup.6 g/mol range.
[0473] Two key features of the distributions that satisfy this
objective are (i) favorable partitioning of the polymer into linear
rather than cyclic supramolecules, and (ii) a well-defined peak in
.PHI..sub.linear centered around .about.5.times.10.sup.6 g/mol.
[0474] As expected, partitioning of the polymer into linear
supramolecules is favored at higher values of MW.sub.p and
.PHI..sub.total but both of these quantities are constrained due to
the limitations of shear degradation (M.sub.W.ltoreq.10.sup.6
g/mol) and system compatibility for fuel (.PHI..sub.total<1/4
.PHI.*). Near these maximal values, the strong dependence of the
supramolecular distributions on the energy of interactions has
important implications for mist-control applications. For mixtures
of A - - - A and B - - - B molecules, model predictions indicate
that favorable results will be found in a relatively narrow range
of association energy, 16.ltoreq..epsilon..ltoreq.18.
Example 44: Model to Determine Lifetime of Equilibrium
Distribution
[0475] The model assumes that under conditions of practical
importance, equilibrium is restored as fast as it is disturbed.
Therefore, the time taken by a polymer to reach the equilibrium
partitioning of the polymer into aggregates of all sizes was
investigated
[0476] The average lifetime of a donor-acceptor physical bond is
estimated using .tau..sub.b.about..tau..sub.0 exp(E), where
.tau..sub.0.about..eta.b.sup.3/kT describes a typical motional time
for a monomer in solvent with shear viscosity .eta.. For solvents
like fuel, .eta..about.1 mPas, giving .tau..sub.0.about.10.sup.-10
s, so the lifetime is on the order of .tau..sub.b.about.1 ms for
.epsilon.=17. Therefore, if equilibrium can be reached with roughly
10.sup.3 bond-breaking and bond-forming events and for end-groups
with 16-18 kT energy of association, that time is on the order of 1
s.
Example 45: Theoretical Treatment of Equilibrium Distribution of
Cyclic and Linear Supramolecules
[0477] The inventory of all cyclic and linear supramolecules was
computed with the modeling of Example 43, as a function of
concentration, backbone length and end-association strength by
solving the system of equilibrium relationships in a population
balance model (FIG. 47B). The resulting predictions indicate that
an adequate concentration of mega-supramolecules (e.g., >50 ppm
of supramolecules with M.sub.w.gtoreq.5,000 kg/mol ([6])) form if
the concentration of LTPs is 1,400 ppm, their backbone has
approximately 6,000 Kuhn segments (M.sub.w=500 kg/mol for
polycyclooctadiene, PCOD) and their ends associate pairwise with an
energy of 16-18 kT (modeling, after Goldstein ([56]), FIGS. 51-56).
Furthermore, theory shows that the favorable window of chain
lengths and association strengths is relatively narrow. If the
backbone is too short (e.g., 200 kg/mol PCOD), the fraction of
material that is "lost" to the formation of small cyclics increases
and, consequently, the concentration of telechelics can be
increased. If the backbone is too long (e.g., 1,000 kg/mol PCOD),
the individual telechelics become susceptible to degradation in
strong flows (below). If the association energy is too low (e.g.,
14 kT), formation of supramolecules is inadequate. If the
association energy is too high (e.g., 20 kT), dangling ends are
overly penalized and too few linear species form.
[0478] While there are already many studies of the theory of
ring-chain equilibrium, of interest is formulating the problem so
that problem of equilibrium population as a function of the length,
concentration and association energy could be readily solved. In
the present construction, terms arising from microscopic
interactions, as well as terms arising from the center-of-mass and
configurational entropy (except loop closure) of polymer components
and solvent in solution are carried out explicitly. Whereas terms
arising from (i) the energy of association of the end-groups within
a polymer aggregate, and (ii) the entropic cost of loop closure for
cyclic supramolecular aggregates are absorbed into the standard
chemical potentials of the polymeric species.
[0479] As a first step in modeling the equilibrium distribution of
cyclic and linear supramolecules from telechelic polymers A - - - A
and B - - - B (FIG. 52), the case of association of telechelic
polymers A.sub.1 - - - A.sub.2 and B.sub.1 - - - B.sub.2 is started
with. Subsequently, it is shown that the predicted distributions
hold for A - - - A and B - - - B as well (Example 48). It is
assumed that the end-groups A.sub.1 and A.sub.2, and likewise B1
and B.sub.2, are distinguishable but of identical reactivity (as
though one end were isotopically labeled).
Example 46: Model Description: Equilibrium Using a Lattice
Model
[0480] This equilibrium is approximated using a lattice model
following Goldstein [56]. A solution of N.sub.s solvent molecules
and N.sub.Atotal and N.sub.Btotal telechelic A.sub.1 - - - A.sub.2
and B.sub.1 - - - B.sub.2 chains of M.sub.A and M.sub.B repeat
units, respectively, occupies a volume V that is partitioned into
lattice sites of volume a.sup.3, which is the volume of a solvent
molecule and also the volume of a monomer. There is negligible
volume change upon mixing, so
V=a.sup.3(N.sub.s+N.sub.AtotalM.sub.A+N.sub.BtotalM.sub.B)=.LAMBDA.a.sup.-
3, where .LAMBDA. is the total number of "sites." Subscripts i (or
j) refer to polymeric components. Component i is composed of
n.sub.i A.sub.1 - - - A.sub.2 building blocks and m.sub.i B.sub.1 -
- - B.sub.2 building blocks, and has
M.sub.i=n.sub.iM.sub.A+m.sub.iM.sub.B repeat units. The volume
fraction of solvent is .PHI..sub.s=N.sub.s/.LAMBDA. and that of
component i is .PHI..sub.i=N.sub.iM.sub.i/A. Unless otherwise
specified, sums .SIGMA..sub.i are over all polymer components in
solution, e.g., the sum of the volume fractions of all polymeric
species are equal the total polymer volume fraction
.PHI.=.SIGMA..sub.iM.sub.iN.sub.i/A=1-.PHI..sub.s.
[0481] The total free energy F of the solution is the sum of
entropic and enthalpic contributions, F.sub.S and F.sub.int, and of
contributions from the internal free energy of solvent and polymer
components:
F = F int + F S + N s .times. .mu. s 0 + j .times. N j .times. .mu.
j 0 ( 1 ) ##EQU00008##
where .mu..sub.j.sup.0 is the standard chemical potential of
polymeric component j. The first term is due to solvent-solvent,
polymer-solvent, and polymer-polymer interactions, which are
estimated by the random mixing approximation:
F.sub.int=.LAMBDA..delta.[(1-.PHI.).sup.2h.sub.ss+.PHI..sup.2h.sub.pp+2.-
PHI.(1-.PHI.)h.sub.ps] (2)
where .delta. is one-half the local coordination number, and
h.sub.ij are the microscopic interaction energies of the polymer
and solvent species. The second term is due to configurational and
center-of-mass entropy, S:
S = k .times. j .times. ln .times. .times. .OMEGA. .function. ( 0 ,
N j ) + .DELTA. .times. .times. S mix ( 3 ) ##EQU00009##
where .OMEGA.(0,N.sub.j) is the number of possible configurations
of N.sub.j molecules of polymer component j each having M.sub.j
repeat units, onto M.sub.jN.sub.j sites (i.e., pure component j
before mixing with other polymer species or solvent). Following the
notation of Hill [57] for the entropy of a melt of N.sub.i linear
polymer chains of length M.sub.i:
ln .times. .times. .OMEGA. .function. ( 0 , N i ) = - N i .times.
.times. ln .times. .times. N i + N i + M i .times. N i .times.
.times. ln .function. ( M i .times. N i ) - M i .times. N i + N i
.function. ( M i - 1 ) .times. .times. ln .times. .times. ( c - 1 M
i .times. N i ) ( 4 ) ##EQU00010##
where c is the coordination number. The entropy of mixing of the
solvent and all polymer components, .DELTA.S.sub.mix, is
approximated using the Flory-Huggins expression:
.DELTA. .times. .times. S mix = - k ( N s .times. .times. ln
.times. .times. .PHI. s + j .times. N j .times. .times. ln .times.
.times. .PHI. j ) . ( 5 ) ##EQU00011##
[0482] The entropic contribution to the free energy of the mixture
is therefore:
F S = .times. - T .times. .times. .DELTA. .times. .times. S mix -
kT .times. j .times. ln .times. .times. .OMEGA. .function. ( 0 , N
j ) = .times. kT .function. [ N s .times. ln .times. .times. ( N s
) + j .times. N j .times. .times. ln .times. .times. ( N j ) ] + kT
.times. j .times. N j .times. .times. ln .times. .times. ( M j ) -
.times. kT .times. j .times. ln .times. .times. .OMEGA. .function.
( 0 , N j ) ( 6 ) ##EQU00012##
where .PHI..sub.s and .PHI..sub.j are replaced by N.sub.s/.LAMBDA.
and N.sub.jM.sub.j/.LAMBDA. respectively.
[0483] The equilibrium distribution of species is readily analyzed
in terms of the chemical potentials of the solvent .mu..sub.s and
the polymeric species .mu..sub.i. For example, at equilibrium, the
chemical potential of a supramolecular component i made up of
n.sub.i A.sub.1 - - - A.sub.2 and m.sub.i B.sub.1 - - - B.sub.2
satisfy the equilibrium condition:
.mu..sub.i=n.sub.i.mu..sub.A+m.sub.i.mu..sub.B (7)
where .mu..sub.A and .mu..sub.B are the chemical potentials of
building blocks A.sub.1 - - - A.sub.2 and B.sub.1 - - - B.sub.2,
respectively. The chemical potential of polymer component i
involves both interactions (solvent-solvent, polymer-solvent and
polymer-polymer) and entropic contributions. The contribution to
the chemical potential of component i due to interactions is:
.mu. int , i = .differential. F int .differential. N i .times. N j
.noteq. i = - .omega. .times. .times. M i .times. .PHI. s 2 +
.omega. pp .times. M i ( 8 ) ##EQU00013##
where
.PHI.=(M.sub.iN.sub.i+.SIGMA..sub.j.noteq.iM.sub.jN.sub.j)/.LAMBDA.
with
.LAMBDA.=N.sub.s+M.sub.iN.sub.i+.SIGMA..sub.j.noteq.iM.sub.jN.sub.j
and .PHI..sub.s=1-.PHI. are used and, for convenience,
.omega..sub.mn=.delta.h.sub.mn and
.omega.=.omega..sub.pp+.omega..sub.ss-2.omega..sub.ps are
introduced. The entropic contribution to the chemical potential of
component i is:
.mu. S , i k .times. T = 1 k .times. T .times. .differential. F S
.differential. N i .times. | N j .noteq. i = ln .times. .times. (
.PHI. i M i ) + 1 - .PHI. i - M i [ .PHI. s + j .noteq. i .times.
.PHI. j M j ] + ln .times. .times. M i - 1 - M i .function. [ ln
.function. ( c - 1 ) - 1 ] - ln .times. .times. M i + ln .function.
( c - 1 ) ( 9 ) ##EQU00014##
[0484] Differentiation of Equation 6 and substitution of Equations
7 and 9 give the following expression for the chemical potential of
component i, valid for the single-chain building blocks and all
supramolecules:
.mu. i = .differential. F .differential. N i .times. | N j .noteq.
i = .mu. i 0 + k .times. T .times. { ln .times. .times. ( .PHI. i M
i ) - M i [ .PHI. s + j .times. .PHI. j M j ] + f i } - .omega.
.times. .times. M i .times. .PHI. s 2 + .omega. pp .times. M i ( 10
) ##EQU00015##
where f.sub.i=ln(c-1)+M.sub.i[1-ln(c-1)]. Substituting the
expressions for .mu..sub.i, .mu..sub.A, and .mu..sub.B from
Equation 10 into Equation 7 above, after rearrangement, the
following mass-action relation for component I is obtained:
.mu. i 0 + k .times. T .function. [ ln .times. .times. ( .PHI. i M
i ) + f i ] = n i .times. .mu. A 0 + m i .times. .mu. B 0 + kT
.function. [ n i .times. .times. ln .times. .times. ( .PHI. A M A )
+ m i .times. .times. ln .times. .times. ( .PHI. B M B ) + n i
.times. f A + m i .times. f B ] ( 11 ) ##EQU00016##
where .PHI..sub.A and .PHI..sub.B are the equilibrium volume
fractions of the free telechelics A.sub.1 - - - A.sub.2 and B.sub.1
- - - B.sub.2, respectively. It is convenient to rewrite Equation
11 as follows:
( .PHI. i n i .times. M A + m i .times. M B ) = ( .PHI. A M A ) n i
.times. ( .PHI. B M B ) m i .times. exp .function. ( .GAMMA. i ) ,
( 12 ) where .times. .times. .GAMMA. i = 1 k .times. T .times. ( n
i .times. .mu. A 0 + m i .times. .mu. B 0 - .mu. i 0 ) + ( n i + m
i - 1 ) .times. ln .function. ( c - 1 ) . ( 13 ) ##EQU00017##
[0485] The conservation equations are then:
.PHI. Atotal = j .times. .PHI. j .function. ( n j .times. M A n j
.times. M A + m j .times. M B ) = j .times. n j .times. M A
.function. ( .PHI. A M A ) n j .times. ( .PHI. B M B ) m j .times.
exp .function. ( .GAMMA. j ) .times. .times. .PHI. Btotal = j
.times. .PHI. j .function. ( m j .times. M B n j .times. M A + m j
.times. M B ) = j .times. m j .times. M B .function. ( .PHI. A M A
) n j .times. ( .PHI. B M B ) m j .times. exp .function. ( .GAMMA.
j ) . ( 14 ) ##EQU00018##
[0486] To this point, the formulation has treated terms arising
from microscopic interactions, as well as center-of-mass and
configurational entropy (except loop closure) of polymer components
and solvent. Next (i) the energy of association of the paired
end-groups within a supramolecule and (ii) the entropic cost of
loop closure for cyclic supramolecules are accounted for, which are
incorporated into the standard chemical potentials
.mu..sub.j.sup.0.
[0487] For this purpose, it is useful to identify "groups" of
polymer species, each assigned an index g, that are topologically
similar and have the same values of M.sub.j=M.sub.g,
n.sub.j=n.sub.g, m.sub.j=m.sub.g, and .GAMMA..sub.j=.GAMMA..sub.g.
In identifying "groups" of polymer species, A and B are used to
refer to A1 or A2 and B1 or B2, respectively (FIG. 53). In counting
number of distinct species in group g (.OMEGA..sub.g,) the two ends
of an A-telechelic or a B-telechelic are treated as
distinguishable. Thus, group g is composed of all the different
possible aggregates obtained by the assembly of the A1 - - - A2 and
B1 - - - B2 building blocks. For example, group g=3 has
.OMEGA..sub.g=4 distinct aggregates (FIG. 53): A1 - - - A2B1 - - -
B2, A1 - - - A2B2 - - - B1, A2 - - - A1B1 - - - B2, and A2 - - -
A1B2 - - - B1.
[0488] How many components belong to each group? For linear
aggregates there are two possibilities: (i) for n.sub.g+m.sub.g
even (i.e., n.sub.g=m.sub.g), no sequence read from left to right
will be the same as a sequence read from right to left, so the
number of ways to arrange the molecules is
.OMEGA..sub.g=2.sup.n.sup.g.sup.+m.sup.g; (ii) for n.sub.g+m.sub.g
odd, every sequence read from left to right will have a matching
sequence read from right to left, so the number of ways to arrange
the molecules is .OMEGA..sub.g=2.sup.n.sup.g.sup.+m.sup.g.
Supramolecular cycles always have n.sub.g=m.sub.g. The number of
ways to form such a loop is derived in Example 48 below; to good
approximation it is
.OMEGA..sub.cyc,g=2+(2.sup.2n.sup.g.sup.-1-2)/n.sub.g.
[0489] The fact that (by construction) all of the components j in
any particular group g have the same value of
.mu..sub.j.sup.0=.mu..sub.g.sup.0 allows the equilibrium condition
and the conservation equations to be rewritten in terms of
.PHI..sub.g, the cumulative volume fraction of all polymer
components in group g:
( .PHI. g n g .times. M g + m g .times. M g ) = .OMEGA. g
.function. ( .PHI. A M A ) n g .times. ( .PHI. B M B ) m g .times.
exp .function. ( .GAMMA. g ) ( 15 ) .PHI. Atotal = g .times. n g
.times. M A .times. .OMEGA. g .function. ( .PHI. A M A ) n g
.times. ( .PHI. B M B ) m g .times. exp .function. ( .GAMMA. g )
.times. .times. .PHI. Btotal = g .times. m g .times. M B .times.
.OMEGA. g .function. ( .PHI. A M A ) n g .times. ( .PHI. B M B ) m
g .times. exp .function. ( .GAMMA. g ) ( 16 ) ##EQU00019##
[0490] The standard chemical potentials .mu..sub.g.sup.0 include
the appropriate multiples of the standard chemical potentials of
the A - - - A and B - - - B building blocks and the appropriate
multiple of the association energy .epsilon.kT. For a cyclic group,
there is an additional term due to the entropy cost of ring
closure, .DELTA.S.sub.loop=-klnG.sub.cyc, where G.sub.cyc is the
probability density (treated in Example 47 below) for closure of a
group g ring:
.mu. g 0 = { n g .times. .mu. A 0 + m g .times. .mu. B 0 - .times.
.times. kT .function. ( n g + m g ) - kT .times. .times. ln .times.
.times. G cycl , g if .times. .times. cyclic n g .times. .mu. A 0 +
m g .times. .mu. B 0 - .times. .times. kT .function. ( n g + m g -
1 ) if .times. .times. linear , ( 17 ) ##EQU00020##
so that .GAMMA..sub.g in the equilibrium and conservation
relationships (Equations 15 and 16) is:
.GAMMA. g = { .function. ( n g + m i ) + ( n i + m i - 1 ) .times.
ln .function. ( c - 1 ) + ln .times. .times. G cycl , g if .times.
.times. cyclic .function. ( n g + m g - 1 ) + ( n g + m g - 1 )
.times. ln .function. ( c - 1 ) if .times. .times. linear . ( 18 )
##EQU00021##
Example 47: Entropic Cost of Loop Closure
[0491] The entropic cost of loop closure is determined by
calculating the probability of loop closure, as follows: For
Gaussian linear chains of N Kuhn monomers of length b, the
probability density function for the end-to-end vector r is
[15]:
G G .times. a .times. ussian .function. ( r , N ) = ( 3 2 .times.
.pi. .times. N .times. b 2 ) 3 2 .times. exp .times. { - 3 .times.
r 2 2 .times. N .times. b 2 } . ( 19 ) ##EQU00022##
[0492] The argument within the exponential
-3r.sup.2/(2Nb.sup.2).apprxeq.0 for
.parallel.r.parallel.<<<r.sup.2>.sup.1/2, so the
probability that the chain ends be within a small distance x of
each other, where x/b.about.O(1), is:
G cyc , Gaussian = ( 3 2 .times. .pi. .times. N .times. b 2 ) 3 2
.times. .intg. 0 2 .times. .pi. .times. d .times. .times. .PHI.
.times. .intg. 0 .pi. .times. d .times. .times. .theta.sin .times.
.times. .theta. .times. .intg. 0 x / b .times. dr r 2 .times. exp
.function. ( 0 ) = 4 .times. .pi. .function. ( 3 2 .times. .pi.
.times. N .times. b 2 ) 3 2 .times. .intg. 0 x / b .times. dr r 2
.times. exp .function. ( 0 ) = ( 6 .pi. .times. .times. N 3 ) 1 2
.times. ( x b ) 3 . ( 20 ) ##EQU00023##
[0493] For real chains, excluded volume interactions of the
monomers at chain ends reduce the probability density function
G(r,N) by the factor
G real .function. ( r , N ) G Gaussian .function. ( r , N ) .times.
.about. .times. ( r r 2 ) .gamma. .times. .times. for .times.
.times. r r 2 1 ( 21 ) ##EQU00024##
where the exponent .gamma..apprxeq.0.28 [15], so that the
probability of cyclization becomes
G cyc , real .apprxeq. 4 .times. .pi. .function. ( 3 2 .times. .pi.
.times. N .times. b 2 ) 3 2 .times. ( 1 bN .nu. ) .gamma. .times.
.intg. 0 x / b .times. dr r 2 + g .times. exp .function. ( 0 )
.times. ~ .times. N - 3 / 2 - .gamma..nu. ( 22 ) ##EQU00025##
where the fractal exponent vis 0.588 in good solvent. The loop
closure probability thus scales as N.sup.-3/2 for Gaussian chains
and N.sup.-1.66 for swollen chains. The entropic cost of loop
closure is simply .DELTA.S.sub.loop=-klnG.sub.cyc.
[0494] In dilute or semi-dilute solutions, all chain segments
smaller than the thermal blob g.sub.T.apprxeq.b.sup.6/v.sup.2
(where v is the excluded volume parameter) have Gaussian statistics
because excluded volume interactions are weaker than the thermal
energy. At the concentrations of interest, the total polymer volume
fraction .PHI.=.SIGMA..sub.j.PHI..sub.j is low enough to ignore
polymer-polymer overlap, so the following expression is appropriate
for the entropic cost of loop closure
.DELTA.S.sub.loop=-klnG.sub.cyc for any cyclic aggregate j:
G cyc , j .apprxeq. ( 6 .pi. .times. .times. g T 3 ) 1 2 .times. (
x b ) 3 .times. ( M j g T ) - 1.66 . ( 23 ) ##EQU00026##
[0495] That is, all chain segments larger than g.sub.T are fully
swollen.
Example 48: Number of Ways to Form Loops
[0496] To determine the number of different loops that can be
formed by linking n A - - - A and n B - - - B telechelic chains
end-to-end via association of A and B end-groups (FIG. 53 left),
telechelics are started to be treated with distinguishable ends
(i.e., n A.sub.1 - - - A.sub.2 molecules that are indistinguishable
from each other, and likewise n B.sub.1 - - - B.sub.2 molecules).
This way of treatment maps onto the combinatorial problem of
counting necklaces formed using beads of different colors, in which
two necklaces are considered equivalent if one can be rotated to
give the other. By viewing each supramolecular loop in terms of
adjacent pairs of telechelics (with one A.sub.1 - - - A.sub.2 and
one B.sub.1 - - - B.sub.2 molecule per pair), they correspond to
necklaces made up of n "beads" of 4 "colors" (FIG. 54). For
example, A1A2B1B2=black, A1A2B2B1=white, A2A1B1B2=blue, and
A2A1B2B1=green can be chosen. The formula for the number of
different necklaces is [58]:
m .function. ( n ) = 1 n .times. d n .times. [ .phi. .function. ( d
) 4 n / d ] ( 24 ) ##EQU00027##
where the sum is over all numbers d that divide n, and .phi.(d) is
the Euler phi function.
[0497] In reality, the above formula overcounts the number of ways
to form supramolecular loops by a factor of 2. The number of
distinct cyclic supramolecules s(n) in the set obtained from n
A.sub.1 - - - A.sub.2 and n B.sub.1 - - - B.sub.2 telechelic
chains, {loops.sub.n}, can be seen to be half the number of
distinct necklaces of n beads of four colors {necklaces.sub.n}
because any supramolecular loop "reads" as a distinct necklace
clockwise vs. counter-clockwise (FIG. 55). While each necklace in
{necklaces.sub.n} uniquely maps onto a supramolecular loop in
{loops.sub.n}, every loop in {loops.sub.n} maps back to two
different necklaces, which belong to {necklaces.sub.n}. The
elements of {necklaces.sub.n} can be arranged pairwise, revealing
that there are twice as many elements in {necklaces.sub.n} as in
{loops.sub.n}. Therefore, the number of distinct supramolecular
loops s(n) is:
s .function. ( n ) = 1 2 .times. n .times. d | n .times. [ .phi.
.function. ( d ) 4 n / d ] ( 25 ) ##EQU00028##
[0498] To see that the result obtained by treating the end groups
as distinguishable gives the correct result for the actual case in
which A-ends are indistinguishable and likewise for B-ends, the
reversible association reactions are considered in FIG. 56. The
reverse reaction rates are all identical. However, the forward
reaction for case a (monotelechelic chains) is clearly one-fourth
that of case b (telechelics with indistinguishable end-groups). In
case c, there are four identical intramolecular scission reactions
that give the starting products, so the forward reaction in case c
can be 4-fold faster than that of the forward reaction in case a.
Thus, the difference in the number of ways to form dimers
(.OMEGA..sub.c=4 compared to .OMEGA..sub.a=1) can be used to
evaluate the increased contact probability of the end-groups to
form the product. If the end-groups A, A.sub.1, and A.sub.2 have
precisely the same reactivity, and likewise the end-groups B,
B.sub.1, and B.sub.2, there cannot be any difference in the
equilibrium partitioning of the molecules in cases b and c. This
argument is generalized to conclude that the solution to the
equilibrium problem presented in FIG. 52, where end-groups are
indistinguishable, is the solution which is developed for
telechelics A.sub.1 - - - A.sub.2 and B.sub.1 - - - B.sub.2, where
end-groups are distinguishable. A less careful modeling of the
association of telechelic polymers A - - - A and B - - - B might
miscalculate the cumulative equilibrium volume fraction of polymer
aggregates that fall within any group g by omitting the factor
.OMEGA..sub.g in Equation 15.
Example 49: Computation of Volume Fraction at Equilibrium
[0499] The following procedure was used to calculate the volume
fraction of all polymer components (i.e., single-chain starting
materials and aggregates of all sizes) at equilibrium, for polymer
solutions of A.sub.1 - - - A.sub.2 and B.sub.1 - - - B.sub.2
telechelics of specified molecular weights at specified initial
concentrations .PHI..sub.Atotal and .PHI..sub.Btotal, (polymer
components were grouped as shown in FIG. 53).
[0500] First, a number of groups T.sub.groups is chosen to include
in the analysis (even though there is an infinite number of
possible polymer components, it is expected that above a certain
size, polymer aggregates will have negligible equilibrium volume
fraction and can therefore be ignored).
[0501] Calculate n.sub.g, m.sub.g, M.sub.g, .OMEGA..sub.g,
G.sub.cyc,g (if appropriate), and .GAMMA..sub.g for polymer group
g, for g=1 . . . T.sub.groups.
[0502] Solve the conservation equations, Equations 16, for (.PHI.A,
.PHI..sub.B).
[0503] Calculate .PHI..sub.g for g=1 . . . T.sub.groups using
Equation 15.
[0504] Repeat with a new value of T.sub.groups twice that of the
previous one until changes in the calculated values of .PHI..sub.g
from one value of T.sub.groups to the next are negligible.
Example 50: Selection of End-Groups
[0505] FIG. 57, Panel A shows the chemical structures and molar
masses of the end-associative polymers (excepting isophthalic
acid/tertiary amine functionalized ones that are shown in FIG.
47C). FIG. 57, Panel B shows the specific viscosities of telechelic
polymers at 8.7 mg/ml total polymer in 1-chlorododecane. Based on
the literature on complementary polyvalent hydrogen-bonding pairs,
it is shown that a 1:1 THY/DAAP solution had a viscosity equal to
the average of the viscosities of the individual components'
solutions. It is also shown that when the 1:1 HR/CA showed a
viscosity equal to the average of the individual components. Only
the DA/DB pair shows enhancement in viscosity relative to the
individual telechelic polymers. FIG. 57, Panel C illustrates the
secondary electrostatic interactions (SEIs) in THY/DAAP and HR/CA
pair.
[0506] The data suggest that, despite the simplicity of carboxylic
acid and tertiary amine structures, the DA/DB pair provides
stronger end-association than the hexadentate HR/CA pair. This
difference is primarily attributed to the 3- to 4-fold greater
strength of charge-assisted hydrogen bonds (as is the case of
DA/DB) relative to ordinary hydrogen bonds (in both THY/DAAP and
HR/CA). Therefore, in non-polar solvent the sum of the two
charge-assisted hydrogen-bonds in a DA/DB pair is likely stronger
than the sum of the six ordinary hydrogen bonds in the HR/CA pair.
In addition, the DA/DB pair does not suffer from the adverse effect
of repulsive secondary electrostatic interactions (SEIs) that occur
when the both partners have H-bond donors and H-bond acceptors: in
the HR/CA pair, the polarities of the six hydrogen-bonds alternate
in direction, thus decreasing the overall strength of HR/CA
association. It is estimated that for THY/DAAP (association
constant in deuterated chloroform at 25.degree. C.=10.sup.3
M.sup.-1) [28], three primary hydrogen bonds contribute -24 kJ/mol
and four repulsive SEIs contribute +12 kJ/mol (net ca. 5 kT); and
for HR/CA, six hydrogen bonds contribute -47 kJ/mol and eight
repulsive SEIs contribute +23 kJ/mol (net ca. 10 kT, FIG. 57, Panel
C). The literature value of the association constant for a
polymer-bound HR/CA pair in deuterated chloroform at 25.degree. C.
is 1.5.times.10.sup.4 M.sup.-1 (7), corresponding to an
end-association strength of 9.6 kT, in good agreement with the
value of 10 kT estimated from SEI analysis. As described herein,
the strength of the DA/DB pair is estimated to be 16-18 kT. The
difference in estimated strength between DA/DB and HR/CA is
consistent with the disclosed experimental results in FIG. 57,
Panel B. Together, SEI analysis and shear viscometry reveal that
HR/CA does not, in fact, have an association constant in non-polar
solvents that is high enough to drive long telechelic polymers to
form mega-supramolecules at concentrations of interest in the scope
of the present work.
Example 51: .sup.1H NMR Study of Incorporation of Chain Transfer
Agent (CTA) into Polymer
[0507] To install functional groups at both chain ends with high
fidelity (>95%, FIGS. 58-59), a two-step ring-opening metathesis
polymerization (ROMP) protocol (FIG. 47C) ([59], [60]) in the
presence of a chain transfer agent (CTA) is used. Polymers
conforming to the theory are synthesized using carefully purified
cis,cis-1,5-cyclooctadiene (COD, FIG. 60 ([60], [61])) and CTAs
bearing functional end groups (ratio of COD:CTA>3,000:1,
adjusted to give the desired molecular weight). End groups with
discrete numbers of hydrogen bonds (di-functional ends, denoted
DA/DB and tetra-functional ends, denoted TA) (FIG. 47C) can be
installed after polymerization by conversion of ester- or
chloride-ended polymers (which serve as non-associative controls,
NA), with degrees of conversion>95% (FIGS. 61A-62C). To test
predicted effects of backbone length, corresponding telechelics
with shorter backbones (e.g., FIG. 48A, M.sub.w.about.45, 140, 300
kg/mol, see Table 13) were prepared.
[0508] FIGS. 58 and 59 show incorporation of CTA into polymer
during the first stage of two-stage ROMP of COD, and chain
extension to long telechelics in the second stage. FIG. 58 .sup.1H
NMR of characteristic peaks for di(di-tert-butyl-isophthalate) CTA
(structure of end-group shown in FIGS. 61A and 61B), unreacted CTA
(proton 1) and CTA incorporated into macromer (proton 2), at three
time points; the integrations of the peaks were used to calculate
the percentage of unreacted CTA, shown in FIG. 59A. FIG. 59A,
Kinetic curves show that the peaks characteristic of the
unincorporated CTA are already difficult to quantify in the sample
taken after 40 min, and it is not evident for the sample taken at 1
hour (given the magnitude of the noise in the spectra, the amount
of unincorporated CTA is less than 3%). Dashed curve is calculated
based the data point at 10 min assuming exponential decay of
unreacted CTA. FIG. 59B, In an example with di-chloro PCOD, the
M.sub.n calculated by NMR is in good agreement with that measured
by GPC, considering the inherent uncertainty in NMR integration and
the inherent uncertainty in GPC measurement (5-10%). FIG. 59C, GPC
traces show no indication of macro CTA (42 kg/mol) in the
chain-extended telechelics (structure shown in FIG. 59C, 497
kg/mol) produced in the second step.
Example 52: Conversion of Non-Associative (NA) End-Groups to
Associative End-Groups
[0509] While theoretical predictions identify a class of polymers
promising as mist-control additives for kerosene, telechelics of
the length required (M.sub.w>400 kg/mol, M.sub.w/M.sub.n ca.
1.5), in reality, are unprecedented. In order to test the
predictions regarding such telechelic polymers, a two-step
ring-opening metathesis polymerization (ROMP) protocol in the
presence of a chain transfer agent (CTA) is adopted, as reports
indicate it could produce relatively long telechelics with M.sub.w
up to ca. 260 kg/mol (FIG. 45, Panels A-B and FIG. 47C).[59, 62]
Cyclooctadiene (COD) is selected as the monomer because it has an
adequate ring strain to drive ROMP and provides a backbone that has
both strength and solubility in hydrocarbons.[8, 63] Once carefully
purified COD is used, telechelics of the required length
(M.sub.w>400 kg/mol, up to 1,000 kg/mol if desired) and end
functionality (>95%) are accessible.
[0510] Associative groups of interest can be installed at both ends
of each polymer with high fidelity using custom CTAs, a built-in
benefit of the ROMP chemistry. In hydrocarbons, end-group
association by charge-assisted hydrogen bonding (such as carboxylic
acid/tertiary amine interaction) is particularly effective for
building supramolecules.[64] Hence, in this study well-defined
end-groups with discrete numbers of hydrogen bonds are synthesized:
isophthalic acid and di(tertiary amine) (denoted DA/DB for
diacid/dibase), and di(isophthalic acid) and tetra(tertiary amine)
(TA/TB) (FIG. 45, Panels A-B and FIG. 47C). Acid and amine
end-groups are installed after polymerization by conversion of
ester- or chloride-ended polymers (which serve as matched
non-associative negative controls, NA).
[0511] FIGS. 61A-61B show FIG. 61A, Structures of non-associative
(NA) end-groups and the conversion from N.sub.A to associative
end-groups: FIG. 61B, isophthalic acid. FIG. 45, Panel A shows
tertiary amine (products shown in FIG. 47). Isophthalic acid end
groups are obtained by deprotection of the tBu groups in the
tBu-ester-ended non-associative precursor. Tertiary amine
end-groups are obtained via conversion of chloride end-groups to
azide end-groups, followed by an alkyne/azide cycloaddition.
Example 53: .sup.1H NMR Study of Degree of Conversion of the
End-Groups
[0512] Conversion of tBu-ester to carboxylic acid as end-groups on
polycyclooctadiene is monitored by the peak for tBu group in the
.sup.1H NMR spectra. FIGS. 62A and 62B show .sup.1H NMR spectra of
tBu-ester ended (DE) and isophthalic acid ended (DA)
polycyclooctadiene (M.sub.w=630 kg/mol) to show high degree of
conversion of the end-groups. FIG. 62A the peaks for protons on the
phenyl ring (protons 1 and 2) shift due to the removal of tBu.
Comparing the integration of peak for proton 2 (.about.7.82 ppm)
with that of the baseline at .about.7.7 ppm (where the peak for
proton 2 in DE is, see FIG. 62A top) in the spectrum of DA (FIG.
62A bottom) shows a <5% (1 comparing to 0.04) potential
unconverted end-groups due to baseline noise. FIG. 62B the peak for
tBu group disappears in the spectrum for DA, indicating removal of
the tBu group.
Example 54: .sup.1H NMR Study of Azide Conversion to Tertiary
Amine
[0513] Similarly, conversion of azide (obtained via conversion of
chloride end groups) to tertiary amine (obtained via an
alkyne/azide cycloaddition, see FIG. 45, Panel B) as end-groups on
polycyclooctadiene is monitored by the proton peaks for triazole
and phenyl rings in the .sup.1H NMR spectra. FIG. 62C .sup.1H NMR
spectra of azide ended (DN.sub.3) and tertiary amine ended (DB)
polycyclooctadiene (M.sub.w=540 kg/mol) to show high degree of
conversion of the end-groups. In the spectrum for DB (bottom), the
presence of a peak at 7.4 ppm indicates the formation of triazole
rings (proton 5), absent in DN.sub.3's spectrum (top). The peak for
protons on the phenyl ring (at positions 1 and 2) shifts from 6.85
ppm before (top) to 6.75 ppm after the cycloaddition reaction
(bottom): integration of the peak for protons at 1 and 2
(.about.6.75 ppm, relative integral integral=3) in the spectrum of
DB (bottom) and of the baseline at .about.6.85 ppm (no detectable
1,2 of DN.sub.3, relative integral=0.09) places an upper bound of
<5% unconverted end-groups.
Example 55: Formation of Supramolecules and Effect of Excess
Tertiary Amine
[0514] FIG. 63 shows formation of supramolecules in equimolar
solutions of .alpha.,.omega.-di(isophthalic acid)
polycyclooctadiene, .alpha.,.omega.-di(di(tertiary amine))
polycyclooctadiene (DA/DB), with non-associated controls (NA, see
FIG. 61A top; and solutions treated with an excess of a
small-molecule tertiary amine, triethylamine, TEA at 10 .mu.l/ml).
FIG. 63, Panel A, Effect of chain length (k refers to kg/mol) on
specific viscosity of telechelics in tetralin and Jet-A (2 mg/ml)
at 25.degree. C. FIG. 63, Panel B, Effect of TEA (2.5 .mu.l/ml) on
the viscosities of associative telechelic polymers DA/DB. FIG. 63,
Panel C, Left: Static light scattering shows that association
between DA and DB chains (circle: 670k series; triangle: 300k
series) in cyclohexane (CH) at 0.22 mg/ml (0.028%) produces
supramolecules (filled), which separate into individual building
blocks (x) when an excess of a small-molecule tertiary amine is
added (open symbols, 10 .mu.l/ml of triethylamine, TEA). Curves
show predictions of the model (see Examples 37-49)). Right: Zimm
plot of the same static light scattering data shown in Left part.
Lines indicate the fitting to the Zimm equation and dashed lines
indicate the extrapolation that was used to evaluate the intercept
at zero concentration, zero angle; the slope of the line and the
value of the intercept are used to evaluate the apparent M.sub.w
and apparent R.sub.g, details below. FIG. 63, Panel D, Resulting
values of apparent M.sub.w and R.sub.g for the five polymer
solutions in FIG. 63, Panel C.
[0515] The effect of chain length on specific viscosity of
telechelics in tetralin and Jet-A (FIG. 63, Panel A) is similar to
that in cyclohexane (FIG. 48A). The specific viscosity of
telechelics in Jet-A is generally lower than that in tetralin or
cyclohexane. This effect is observed even for the non-associative
polymers (NA), indicating that the backbone adopts a more compact
conformation in Jet-A. This effect is related to the composition of
Jet-A as a mixture of many hydrocarbons with number of carbon atoms
between 6 and 16, including some components that are good solvents
for PCOD and some that are theta solvents for PCOD.
[0516] The model calculations FIG. 63, Panel C show the effect of
doubling the backbone length for complementary telechelics with
association energy 16 kT, backbone lengths corresponding to a PCOD
of 1,000 kg/mol (x) or 500 kg/mol (+) at 1,400 ppm concentration in
a good solvent on the scattering pattern computed from the
distribution of supramolecules (solid, supramolecules up to 9
telechelics; dashed, corresponding perfectly monodisperse
non-associative telechelics). To compare with the experimental
data, a single vertical shift was allowed to be applied to all four
curves and a single horizontal shift. The distributions of
supramolecules are shown in FIG. 64.
[0517] The Zimm fitting was performed using Wyatt Astra Software
(version 5.3.4): illustrations for the 300k DA/DB and 300k DB are
shown, with the linear regression through the data (black solid
line) extrapolated to zero-concentration (horizontal light gray
dashed line) and to zero angle (oblique gray dashed line). The
y-intercept of the zero-angle zero-concentration extrapolation
gives the apparent M.sub.w, while its slope is used to compute the
apparent R.sub.g.
Example 56: Interplay of Telechelic Length and Concentration
[0518] Mega-supramolecules are formed at low concentration that
behave like ultra-long polymers, exhibiting expanded
("self-avoiding") conformation at rest and capable of high
elongation under flow (FIG. 47A, right). This is in contrast to the
collapsed, inextensible supramolecules formed by long chains with
associative groups distributed along their backbone (FIG. 47A,
left) ([65], [66]). To mimic ultra-long polymers, association can
occur at chain ends and be predominantly pairwise. In contrast to
multimeric association ([53], [55]) that leads to flower-like
micelles at low concentration (FIG. 47A, middle), recent studies
have shown that pairwise association is readily achieved for short
chains with M.sub.w.ltoreq.50 kg/mol using hydrogen bonding ([54],
[67], [68], [69], [70], [71], [72], [73]). At low concentration,
these have no significant rheological effects, consistent with the
theory of ring-chain equilibrium ([74], [75], [76], [77], [78]):
small rings are the predominant species at low concentration (FIG.
47A, middle). It was realized that using very long chains as the
building blocks would disfavor rings, because the entropy cost of
closing a ring increases strongly with chain length.
[0519] FIG. 64 shows modeling of interplay of telechelic length and
concentration in a stoichiometric mixture of complementary
end-associative telechelics in the regime of long telechelics
(corresponding to .gtoreq.0.5 Mg/mol for high-1,4-polyisoprene,
high-1,4-polybutadiene or polycyclooctadiene) and low concentration
(.ltoreq.0.14% wt/wt), facilitating comparison among the three
different cases (FIG. 51, center column), in terms of both the
number of telechelics in each supramolecular species and the
molecular weight of each supramolecular species. Symmetric cases
are considered (donor and acceptor telechelics have the same
length). End association energy between donor and acceptor
end-groups is 16 kT. The concentration of each distinct species is
shown for supramolecules composed of up to 12 telechelics; the
symbol in a square outline represents the sum of all supramolecules
containing 13 or more telechelics (square around x is for the case
1.0 Mg/mol chains at 1,400 ppm concentration; the square around +
is for the other case in each graph). FIG. 64, Panel A, Effect of
telechelic length on the distribution of the number of telechelics
in a supramolecule, given as the concentration in ppm wt/wt of each
species, cyclic (circles) or linear (x or +), at a fixed total
concentration of 1400 ppm. FIG. 64, Panel B, The same distributions
as in A, presented in terms of the molar mass of the
supramolecules; the weight-average molar mass of the supramolecules
is given to the left of the legend. FIG. 64, Panel C, Effect of
concentration on the distribution of supramolecules for telechelics
of 1M g/mol (hence, the number of telechelics in a given
supramolecule is also its molar mass in Mg/mol) Note the results
for the 1 Mg/mol telechelics at 0.14% concentration is given in all
three graphs to facilitate comparisons (see Examples 37-49).
[0520] In the regime of long telecheclics at low concentration, the
equilibrium distribution of rings is dominated by rings composed of
2 telechelics (one donor+one acceptor) or 4 telechelics (in a
donor/acceptor system, rings can only close if the number of
telechelics is even). The fraction of telechlics "lost" to these
rings is cut in half by doubling the length of the telechelics from
0.5M to 1.0 Mg/mol, increasing the formation of linear
supramolecules FIG. 64, Panel A. Increasing the length of the
backbone also increases the size of the supramolecules at each
number of telechelics per supramolecules (compare FIG. 64, Panel B
to FIG. 64, Panel A); consequently, increasing the telechelic
length strongly increases the population of "mega-supramolecules"
(the sum of the concentrations of all species having molecular
weight greater than 5 Mg/mol increases from 200 ppm for 0.5 Mg/mol
telechelics to 400 ppm for 1.0 Mg/mol). Dilution, here from 1,400
ppm to 800 ppm wt/wt, favors the formation of "small"
supramolecules composed of 4 or fewer telechelics at the expense of
mega-supramolecules (here, the sum of all species>5 Mg/mol falls
from 400 ppm to 230 ppm). Note that "small" species assembled from
3-4 telechelics were already the dominant ones at higher
concentration, so dilution has relatively mild effects on the
weight average molecular weight (numbers shown to the left of the
legend in FIG. 64, Panel C). For further details on the model,
please see modeling.
Example 57: Shear Viscometry Study of LTPs with Donor-Acceptor Type
End-Groups
[0521] Shear viscometry study of donor-acceptor type LTPs in
kerosene fuel (Jet-A in this study) proves that the present design
of associative end-groups based on charge-assisted hydrogen bonding
(DA/DB and TA/TB in FIG. 22) is successful. FIG. 72, Panel A shows
the results of 1 wt % Jet-A solutions of 430 kg/mol NA-, TA- and
TB-PCODs, and the 1:1 (w/w) mixture of the 1 wt % solutions of TA-
and TB-PCODs at 25.degree. C. It can be seen that self-association
of TA remains effective in Jet-A, but it is not as remarkable as
TA/TB association, which gives an increase in specific viscosity by
270%. These results provide motivation to further study DA/DB
end-association, which is comprised of only 2 charge-assisted
hydrogen bonds (TA/TB has 4), as an attempt to approach the limit
of the strength of carboxylic acid/tertiary amine association.
Fixed at 1 wt % in Jet-A, the results of 200 kg/mol NA-, DA- and
DB-PCODs, and the 1:1 (w/w) DA/DB mixture are shown in FIG. 72,
Panel B. Comparing the result of the 1:1 DA/DB mixture to that of
the control NA, it is found that complementary DA/DB association is
also effective in Jet-A, and it leads to an increase in specific
viscosity by 150%, which indicates the formation of supramolecules
via DA/DB end-association. FIG. 72, Panel C shows that at an Mw of
600 kg/mol, DA/DB association still holds, leading to an even
higher enhancement of specific viscosity (nearly 200%) relative to
the control solution NA. These findings are contrary to what prior
literature teaches us: end-association becomes difficult when
telechelics have long backbones (>100 kg/mol).[54, 55] Taking
advantage of the superior strength of charge-assisted hydrogen
bonding (.about.4 times stronger than ordinary hydrogen
bonding),[79] it is able to be realized simple but yet effective
pairs of end-groups capable of driving unprecedentedly long chains
to form mega-supramolecules in Jet-A.
Example 58: .sup.1H NMR Study of Charge Assisted-Hydrogen Bonds
[0522] Therefore, charge-assisted hydrogen bonds (CAHB, [64]) that
are typically 3 times stronger than ordinary hydrogen bonds (each
CAHB provides ca. 8-9 kT binding energy) are turned to. Simply
placing two tertiary amines at each end of the "di-base" chains
(DB) and two carboxylic acids at each end of the "di-acid" chains
(DA) (FIG. 47C) provides an association strength of 16-18 kT
([64]), as recommended by the theoretical results.
[0523] FIG. 65 shows .sup.1H NMR spectra of isophthalic acid ended
(DA) and di(tertiary amine) ended (DB) polycyclooctadienes
(M.sub.w=45 kg/mol) and 1:1 molar mixture of DA/DB in deuterated
chloroform (CDCl.sub.3) indicating that carboxylic acid-amine
hydrogen bonds dominate over carboxylic acid-carboxylic acid
hydrogen bonds. FIG. 65, Panel A, .sup.1H NMR peaks due to
hydrogens on carbons adjacent to nitrogens of tertiary amine groups
of DB (methyl protons 2; methylene protons 1) shift downfield when
they form charge-assisted hydrogen bonds with carboxylic acid
groups of DA (cf. upper to lower spectra: 2 shifts from 2.27 to
2.68 ppm; and 1 shifts from 3.59 to 4.13 ppm). FIG. 65, Panel B,
.sup.1H NMR peaks due to hydrogens on the phenyl ring of DA shift
upfield upon formation of charge-assisted hydrogen bonds between
carboxylic acids and tertiary amines (cf. upper to lower spectra: 1
shifts from 7.96 to 7.84 ppm; and 2 shifts from 8.46 to 8.32 ppm).
In the present case, the hydrogen of the carboxylic acid itself is
not observable due to extreme broadening resulting from rapid
exchange with trace H.sub.2O in the solvent. The formation of
acid-amine charge-assisted hydrogen bonds entirely consumes the
available tertiary amine (FIG. 65, Panel A, lower spectrum, no
detectable peak at 3.59 ppm indicates less than 3% of
non-associated amine) and eliminates acid-acid hydrogen bonds (FIG.
65, Panel B, lower spectrum, no detectable peak at 8.46 ppm
indicates less than 3% of acid-acid association). The absence of
acid-acid pairing is consistent with literature values of the
association constants for carboxylic acid self-association (400
M.sup.-1) and for charge assisted-hydrogen bonds that form between
tertiary amine and carboxylic acid in chloroform (5.times.10.sup.4
M.sup.-1, [80]).
Example 59: Characterization of Mega-Supramolecule
[0524] The formation of mega-supramolecules is evident from
solution viscosity and multi-angle laser light scattering (MALLS)
measurements. Shear viscosities show that the present longer
telechelics do associate into supramolecules (e.g., at 2 mg/ml in
cyclohexane, 300k DA/DB gives a shear viscosity comparable to 670k
NA, FIG. 48A; this holds for tetralin and Jet-A, as well, FIG. 48B
and FIG. 63, Panel A). Even for telechelics with M.sub.w of 670
kg/mol--for which the concentration of end groups is less than 10
.mu.M (one thousandth of previously studied
concentrations)([54])--the ends manifestly associate: the viscosity
of the 670k DA/DB solution is twice that of the non-associative
control (FIG. 48A) and multi-million molecular weight
supramolecules are confirmed by MALLS (FIG. 48C and FIG. 63, Panels
C-D). At concentrations as low as 0.22 mg/ml (0.028% wt), 670
kg/mol LTPs form supramolecules with an apparent M.sub.w of 2,200
kg/mol (FIG. 48C), in accord with the model prediction that M.sub.w
corresponds to approximately a three-chain assembly for these
conditions, because rings and chains from dimer to tetramer
dominate (FIG. 64; and for 300k DA/DB, FIG. 63, Panels C-D). Based
on the present model, more than 1/3 of the telechelics are in
species with molecular weight greater than the M.sub.w of the
supramolecules. Due to the greater strength of CAHB, acid-base
pairing dominates over acid-acid pairing (measured by .sup.1H-NMR,
FIG. 65). Small angle neutron scattering (SANS) confirms that
complementary end-associative polymers avoid the problem of chain
collapse. The conformation on length scales up to the radius of
gyration (R.sub.g) of the individual chains is just as open for
end-associative chains as it is for the corresponding
non-associative chains: at q>2.pi./R.sub.g.apprxeq.0.03 1/.ANG.
their scattering patterns coincide (FIG. 48D). Together, MALLS, NMR
and SANS reveal the molecular basis of the rheological behavior
(FIG. 48A-B)--complementary end association into
mega-supramolecules with expanded conformations.
Example 60: Phase Behavior of Associative LTPs in Jet-A
[0525] Solubility in kerosene over a wide range of operating
temperature (-30 to +70.degree. C.) is a key requirement for
polymers as mist-control additives. One of the major issues with
FM-9 polymer contributing to the termination of the AMK program is
that it phase-separates from kerosene even at ambient temperature,
making fuel handling difficult. To test if the selection of polymer
backbone and end-group structures confers good low-temperature
solubility in Jet-A, Jet-A solutions of associative LTPs are
stored, which are homogeneous at room temperature, in a -30.degree.
C. freezer for prolonged periods of time. It is found that even
after months of storage at -30.degree. C., all solutions remain
homogenous, and no cloudiness due to phase separation of polymer is
observed in any sample. Two representative examples are shown in
FIG. 15, Panel A and FIG. 73: 0.5 wt % Jet-A solution of 264 kg/mol
TA-PCOD after storage at -30.degree. C. for 18 months (FIG. 15,
Panel A left) and 0.3 wt % Jet-A solution of 1:1 (w/w) mixture of
430 kg/mol TA- and TB-PCODs (FIG. 73). Clearly the results suggest
the present design of LTPs may overcome the barriers to adopting
prior polymers for improving transportation safety and
security.
[0526] The outstanding solubility of associative LTPs in Jet-A may
result from two unique aspects of the molecular design: an
unsaturated backbone (see FIG. 45, Panels A-B and FIG. 47C) and a
very low content of polar groups. The multitude of carbon-carbon
double bonds in the backbone provides the host Jet-A with a means
to interact with the backbone, leading to the observed good
low-temperature solubility without the need of any surfactant or
stabilizer. As also shown in FIG. 45, Panels A-B and FIG. 47C, LTPs
that show strong end-association in Jet-A have very little
(.ltoreq.4) polar groups on each chain end. Take 430 kg/mol TA-PCOD
for example, it contains approximately one oxygen atom per 1,000
carbon atoms. As a result, the occurrence of end-association does
not create polar domains that are large enough to cause phase
separation. On the contrary, FM-9 polymer, which is the
mist-control polymer that received the most intensive study to date
and has a high content of carboxylic acid group (.about.5 mol %)
randomly grafted along its backbone, demonstrates a strong tendency
to phase separate during storage at ambient temperature. A package
of "carrier fluid" comprised of polar compounds that are
detrimental to engine operation, including water, glycerol,
ethylene glycol, and formic or acetic acid, is needed to keep FM-9
barely soluble in Jet-A at ambient temperature.[7, 81] At
sub-ambient temperatures, even the use of carrier fluid cannot
prevent FM-9 from precipitating from Jet-A. In the context of
solution behavior, the sharp contrast between solution associative
LTPs and FM-9 emphasizes the value of the molecular design shown in
FIG. 22 that is based on fundamental science.
Example 61: "Shear Degradation" Test and Home-Built Apparatus
[0527] Unfortunately, ultra-long backbones undergo chain scission
during routine handling because hydrodynamic tension builds up
along the backbone to a level that breaks covalent bonds; this
"shear degradation" continues until the chains shorten to a point
that their valuable effects are lost (M.sub.w<1,000 kg/mol)
([51]). Assembly of end-associative polymers creates supramolecules
that can potentially break and re-associate reversibly, but
formation of such mega-supramolecules (M.sub.w.gtoreq.5,000 kg/mol)
at low concentration has never been realized for two reasons:
end-to-end association, at low concentration, predominantly leads
to rings of a small number of chains ([74]) and the size of the
building blocks is limited because end association is disfavored
when they are longer than 100 kg/mol ([53]-[55]).
[0528] In the absence of theory, it was not known whether or not
individual chains with lengths below the threshold for shear
degradation (1,200 kg/mol for PCOD, FIG. 66) and end-association
strengths much weaker than a covalent bond (150 kT) could form
mega-supramolecules. Theory provide a rationale to test telechelics
with the predicted end-association strength (16-18 kT) and chain
lengths, which do form mega-supramolecules even at low
concentration. They cohere well enough to confer benefits typically
associated with ultra-long polymers--including mist control and
drag reduction. These mega-supramolecules reversibly dissociate
under flow conditions that would break covalent bonds, allowing the
individual LTPs to survive pumping and filtering, and allowing
treated fuel to burn cleanly and efficiently in unmodified diesel
engines.
[0529] FIG. 66, Panel A shows Home-built apparatus for "shear
degradation" test. Ultra-long covalent polymers undergo chain
scission in intense flows, such as turbulent pipeline flow and,
especially, passage through pumps. This phenomenon is called "shear
degradation." To subject polymer solutions to conditions that
approach the asymptotic limit of shear degradation (i.e., the
backbone length is reduced to the point that further chain scission
is very slow), a relatively small volume of sample (50 ml) is
recirculated through a turbine fuel pump at room temperature for 60
s (approximately 60 passes through the pump using a flow rate of 3
L/min) using a Bosch 69100 In-line Electric Fuel Pump at 12 V. To
prevent cross-contamination, the pump was rinsed 4 times with
approximately 200 mL of hexanes, followed by drying under reduced
pressure at 40.degree. C. overnight. After recirculation, `sheared`
samples were collected in 100 mL glass jars and stored at
-30.degree. C. FIG. 66, Panel B, An initially 4,200 kg/mol PIB at a
concentration of 0.35% in Jet-A shows the decrease in specific
viscosity indicative of shear degradation with increasing number of
passes through the pump. Notice that over 80% of the asymptotic
degradation is induced by approximately 60 passes, leading to the
selection of the conditions described above. FIG. 66, Panel C, GPC
validation of "shear degradation" test using PIB and confirmation
that associative polymers resist degradation. Polyisobutylene
having an initial M.sub.w=4,200 kg/mol (Before) is dissolved in
Jet-A at a concentration of 0.35% wt and recirculated through the
fuel pump as described in FIG. 66, Panel A for 60 s (approximately
50 passages through the pump) and the resulting solution analyzed
by GPC (After). The shift to lower molecular weight (M.sub.w=2,300
kg/mol) confirms that the recirculation treatment does indeed
induce shear degradation in accord with the literature on
multi-million molecular weight polymers in dilute solution. The
length at which the before and after traces cross is the chain
length for which the rate of degradation matched the rate of
production (due to scission of much longer chains).
[0530] A stoichiometric solution of telechelic polycyclooctadienes
bearing either isophthalic acid groups at each end (DA, initial
M.sub.w=670k g/mol) or two tertiary amine groups at each end (DB,
initial M.sub.w=630k g/mol) in Jet-A at concentration of 0.3% wt
was also analyzed by GPC in as-prepared form (Before; detected
M.sub.w=747 kg/mol)) and after 60 s recirculation in apparatus
(After; detected M.sub.w=718 kg/mol). A small decrease in the
population of the longest chains (fastest elution time;
M.sub.w.gtoreq.1,200 kg/mol) may occur. This is considered
insignificant as it is near the detection limit of the instrument;
relative to the GPC trace of the as prepared DA/DB solution, the
GPC trace "after" the recirculation treatment may also show a
minute increase in the population of chains on the right side of
the peak. The latter change is too small to be confidently measured
with the GPC instrument. Note that the possible degradation of the
DA and DB telechelics occurs only where the individual polymers are
so long that they would be vulnerable to shear degradation. Thus,
"stress relief" by reversible dissociation appears to protect all
telechelics<1,200 kg/mol from hydrodynamic chain scission.
Example 62: Shear Stability of LTPs in Jet-A
[0531] Fuel is transported through pipes in highly turbulent flow,
passes through pumps, and needs to be passed through filters in
many engines, including aviation turbine engines and large diesel
engines. It can be circulated repeatedly through heat exchangers
that prevent the engine from overheating. In order to ensure that
fire protection is retained up to the moment it is needed,
degradation prior to fueling or during filtering and circulation
during operation of the engine can be minimized. Therefore,
resistance to flow-induced chain scission (often called "shear
degradation") is among the most crucial requirements for
mist-control additives for fuels. For linear polymers dissolved in
.theta.- and good solvents, the correlation between shear viscosity
and average molecular weight of polymer (MW) is well-described by
the following scaling relationship [25]:
.eta..sub.s.varies.(MW).sup.a
where .eta..sub.s is the shear viscosity and a is the Mark-Houwink
constant (0.5 for .theta.-solvents; 0.76 for good solvents). If a
polymer in solution shear-degrades, such a microscopic phenomenon
will be well-reflected by a macroscopic decrease in solution
viscosity. Hence, shear viscometry once again provides a reliable,
simple and straightforward method to evaluate shear degradation of
polymers in solution after exposure to high shear-force
environments, such as repeated passage through a fuel pump.
Accordingly the setup shown in FIG. 66, Panel A, is used to
recirculate the following Jet-A solutions for 60 s (roughly 60
passes) respectively: 4,200 kg/mol polyisobutylene (PIB, a very
effective mist-control polymer but very vulnerable to shear
degradation) at 0.35 wt %, 430 kg/mol TA-PCOD at 0.3 wt %, and 1:1
mixture of 600 kg/mol DA- and DB-PCODs at 0.3 wt %. Shear
viscometry is performed on each solution before and after
recirculation, and the results are shown in FIG. 74.
[0532] After 60 s of recirculation, the viscosity of the 4,200
kg/mol PIB solution decreases by 40% (FIG. 74 left; compare the
"unsheared" to "sheared"), indicating that the polymer is degraded
by shear force applied during the test. The results of 4,200 kg/mol
PIB not only confirm that PIBs of such a high molecular weight are
not shear stable, but also provide a validation that the setup
shown in FIG. 66, Panel A can be used to find out if associative
LTPs deliver the promised shear resistance. As shown in FIG. 74
(middle and right), none of the two solutions of LTPs show
detectable decrease in shear viscosity, meaning that even at an
M.sub.w of 600 kg/mol, associative LTPs are still resistant to
shear degradation.
[0533] The quest for mist-control polymers that survive passage
through pumps, filters, and turbulent pipe flow has remained a
major unsolved problem despite decades of research. Typical flow
conditions involved in routine fuel handling and transportation are
severe enough to degrade ultra-high molecular weight PIBs and even
FM-9, rendering them ineffective.[81, 82] The literature suggests
that in dilute (i.e., .about.0.1 wt %) solution, there is a
threshold backbone length (M.sub..infin.) below which shear
degradation of polymers does not occur when they are exposed to
strong shear, and M.sub..infin. values for polystyrene and PIB are
1,000 kg/mol and 250 kg/mol, respectively. [83-85] For the very
reason, even though hard work has been performed to achieve LTPs
much longer with respect to prior telechelics, the M.sub.w is
deliberately kept below 1,000 kg/mol in order to avoid irreversible
chain scission by shear force. With end-association strengths that
are substantially weaker than covalent bonds, supramolecules of
LTPs are equipped with "relief valves" that respond to turbulent
flow by reversibly dissociating, leading to a new class of potent
rheology modifiers that are resistant to shear degradation.
Example 63: Fuel Treatment with DA/DB for Engine Tests
[0534] The current study focuses on mega-supramolecules soluble in
low-polarity fluids, especially in liquid fuels. Transportation
relies on such liquids, presenting the risk of explosive combustion
in the event of impact, such as in the 1977 Tenerife airport
disaster--an otherwise-survivable runway collision that claimed 583
lives in the post-crash fireball. Subsequent tests of ultra-long,
associative polymers (e.g., ICI's "FM-9,">3,000 kg/mol
copolymer, 5 mol % carboxyl units) in fuel increased the drop
diameter in post-impact mist ([50], [7]), resulting in a relatively
cool, short-lived fire. However, these polymers interfered with
engine operation ([86]), and their ultra-long backbone--essential
for mist control--degraded upon pumping ([51]).
[0535] Unlike ultra-long polyisobutylene (4.2M PIB, 4,200 kg/mol)
(FIG. 49A), LTPs survive repeated passage through a fuel pump (FIG.
49B and FIG. 66) and allow fuel to be filtered easily. The acid
number, density and flash point of the fuel are not affected by
mega-supramolecules (FIG. 80). Initial tests in diesel engines
indicate that fuel treated with LTPs can be used without engine
modification (FIG. 67): in a long-haul diesel engine (360HP Detroit
Diesel), power and efficiency are not measurably affected (FIG.
67B). Interestingly LTPs provide a 12% reduction in diesel soot
formation (FIG. 49C).
[0536] FIG. 67, Panel A shows that the Federal Test Protocol (FTP)
for engine tests is a specified transient of RPM and torque
designed to include segments characteristic of two major
metropolitan areas in the US. The FTP cycle consists of four phases
(300 seconds each): (1) New York Non-Freeway (NYNF, light urban
traffic with frequent stops and starts), (2) Los Angeles
Non-Freeway (LANF, typical of crowded urban traffic with few
stops), (3) Los Angeles Freeway (LAFY, simulating crowded
expressway traffic in LA), and (4) a repetition of the first NYNF
phase. Initial engine test is performed in double-blind mode,
averaging three repetitions of the FTP cycle with all measurements
calibrated between each FTP cycle. The test was performed in diesel
engines rather than aviation jets due to lack of access to an
aviation jet engine test facility. FIG. 67, Panel B, Work and fuel
efficiency data using an unmodified long-haul diesel engine at the
University of California Riverside's Center for Environmental
Research and Technology (CE-CERT). Control: untreated diesel.
Treated: diesel with 0.14% w/v 670 kg/mol DA/DB. BSFC: "brake
specific fuel consumption" (fuel burned per work done against
dynamometer, a parameter for fuel efficiency). Bhp-hr:
brake-horsepower-hr (0.746 kWhr). Gal/bhp-hr: gallons per bhp-hr
(5.19 liters/kWhr).
Example 64: Long-Haul Engine Test
[0537] In the days of the AMK program, all testing aircrafts were
required to be modified with polymer degraders installed before
engines because of the disastrous effects of FM-9 on engine
operation, and this very issue eventually contributed to the
termination of the program.sup.5. The failures of the AMK program
learnt, the significance to have the associative LTPs is fully
aware of, no matter they are used as mist-control or drag-reducing
additives, be compatible with unmodified engines. A full-scale test
in a gas-turbine engine would be the ideal way to evaluate the
compatibility of LTPs with jet-engine operation; however it
requires approximately 100 barrels of treated jet fuel for each
composition and a corresponding total quantity of associative LTPs
on the order of tens of kilograms that is beyond the synthesis
capability of a university research group. The following facts
provide a rational basis to use a long-haul diesel engine to test
diesel treated with LTPs as a preliminary and affordable means to
assess the impacts of LTPs on engine operations: (1) A typical test
of fuels in a diesel engine requires a quantity on the order of 1
barrel. (2) Diesel fuel is considerably easier to acquire in large
quantity compared to jet fuel. (3) The U.S. Military uses jet fuel
to power its fleets of diesel-engine vehicles, which suggests the
significance of the interplay between the effects of LTPs and
diesel-engine operation.
[0538] Initial tests in diesel engines indicate that diesel fuel
treated with these associative LTPs can be used without any engine
modification. Untreated diesel is compared to the same fuel treated
with 0.14% w/v 1:1 mixture of 600 kg/mol DA- and DB-PCODs using a
long-haul diesel engine (360HP Detroit Diesel) and heavy-duty
dynamometer (GE 600HP) at the University of California Riverside's
Center for Environmental Research and Technology (CE-CERT). The
test is performed in double-blind mode, averaging three repetitions
of the Federal Test Protocol cycle with all measurements calibrated
between each FTP cycle. Power and efficiency are not measurably
affected (FIG. 67, Panel B); the most significant effect of the
LTPs is a reduction in production of diesel soot by 12% (FIG. 49C).
Further testing will be conducted to generate better understandings
of the influences of LTPs on the operation, efficiency and emission
of diesel engines powered by diesel, diesel engines powered by jet
fuel, and gas-turbine engines powered by jet fuel.
[0539] Measurements were performed at UC Riverside College of
Engineering-Center for Environmental Research and Technology's
(CE-CERT's) heavy-duty engine dynamometer laboratory. This engine
dynamometer test laboratory is equipped with a 600-hp General
Electric DC electric engine dynamometer. Testing was performed
using a Detroit Diesel 360HP engine and the FTP (Federal Test
Procedure) heavy-duty transient cycle for emission testing of
heavy-duty on-road engines in the United States [40 CFR 86.1333].
The FTP transient includes "motoring" segments that take into
account a variety of heavy-duty truck and bus driving patterns in
American cities, including traffic in and around the cities on
roads and expressways. The FTP cycle consists of four phases (300 s
each): (1) New York Non Freeway (NYNF, light urban traffic with
frequent stops and starts), (2) Los Angeles Non Freeway (LANF,
typical of crowded urban traffic with few stops), (3) Los Angeles
Freeway (LAFY, simulating crowded expressway traffic in LA), and
(4) a repetition of the first NYNF phase. The average load factor
of the FTP is roughly 20-25% of the maximum engine power available
at a given engine speed. The equivalent average vehicle speed is
about 30 km/h and the equivalent distance traveled is 10.3 km for a
running time of 1200 s. Fuel was prepared the day before the test.
Cans with 3 gallons each of control and treated concentrates were
provided and identified simply as RED and BLUE to minimize bias
during the test and data analysis. The mixture of DA- and DB-PCODs
was dissolved at 1.5% in the concentrate. CERT prepared two barrels
of identical fuel (25 gal in each barrel). On the day before the
test, CERT staff added RED can to one barrel and BLUE can to the
other. Mixing was promoted by placing the barrel on a roller and
turning it for approximately 1 hour. The fuel was allowed to stand
overnight and was used without further mixing during the actual
tests. For all tests, standard emissions measurements of
non-methane hydrocarbons (NMHC), total hydrocarbons (THC), carbon
monoxide (CO), NOx, particulate matter (PM), and carbon dioxide
(CO2) were performed, along with fuel consumption via carbon
balance. The emissions measurements were made using the standard
analyzers in CE-CERT's heavy-duty Mobile Emissions Laboratory
(MEL).
Example 65: Impact/Flame Propagation Comparison Tests for TA and
PIB
[0540] Similarly, high-speed impact experiments (FIG. 69, Panel A)
show that, unlike ultralong PIB, LTPs retain their efficacy in mist
control after repeated passage through a fuel pump. For untreated
Jet-A fuel, the impact conditions generate a fine mist through
which flames rapidly propagate into a hot fireball within 60 ms.
Polymer-treated fuel samples are tested in two forms: as prepared
("unsheared") and after approximately 60 passes through a fuel pump
("sheared") (FIG. 66). Ultra-long PIB (4,200 kg/mol, 0.35% wt) is
known to confer mist control that prevents flame propagation (FIG.
50A, top left; [6]); however, "sheared" PIB loses efficacy (FIG.
50A, top right). LTPs (TA, properties shown in FIG. 70, Panel A)
provide mist control both before and after severe shearing (FIG.
50A bottom), confirming their resistance to shear degradation (FIG.
70, Panel B). The qualitative effects seen in still images at 60 ms
(FIG. 50) are quantified by computing the average brightness of
each frame (3,000 images in 300 ms), which shows that both
"unsheared" and "sheared" TA-treated fuels control misting (FIG.
69, Panel C). Moreover, the test also proves that chain length of
the telechelics plays a crucial role in mist control (FIG. 50B),
consistent with the hypothesis that mega-supramolecules are the
active species conferring the observed effect.
[0541] FIG. 69, Panel A shows apparatus for impact/flame
propagation experiments. An aluminum canister (outer diameter=23
mm, height=100 mm) was used as a miniature fuel tank to hold
.about.30 mL of a test sample. The cap was tightly sealed with
superglue and electrical tape. A stainless steel cylinder
(diameter=24 mm, length=50 mm) was used as a projectile to impact
the sample canister and disperse the fuel. To the left of this
image: Compressed air at 6.89.times.10.sup.5 Pa was used to propel
the projectile through a 1.66 m-long barrel (inner diameter=25.4
mm), resulting in a muzzle speed of 63 m/s measured by time of
flight between two flush-mounted sensors in the barrel. An array of
three continuously burning propane torches was placed in the path
of the ejected fuel. To prevent the torches from being extinguished
by the burst of air from the gun, a shield was placed between the
torch tip and the gun. The impact, misting, subsequent ignition and
flame propagation were captured using a high-speed camera (Photron
SA1.1, frame rate 10 kHz). Image acquisition was triggered by a
laser-motion detector attached to the end of muzzle.
[0542] FIG. 69, Panel B shows frame at 60.4 ms for untreated Jet-A.
The rectangular box is the area within which pixels were analyzed
for brightness.
[0543] FIG. 69, Panel C shows average brightness of the pixels in
the rectangle box of FIG. 69, Panel B as a function of time during
the first 300 ms after impact for five compositions (untreated
Jet-A, 0.35% wt 4.2M PIB unsheared, 0.35% wt 4.2M PIB sheared, 0.3%
wt 430 kg/mol TA unsheared and 0.3% wt 430k TA sheared). The
brightness of each pixel was scaled from 0 to 250. The average
brightness of the pixels in the rectangular box (shown in part FIG.
69, Panel B) was calculated for each frame (every 0.1 ms).
Untreated Jet-A generated a large fireball (almost all pixels in
the red rectangle were saturated) that was relatively long lasting
(intense flame from 40 ms to 60 ms, followed by a prolonged time in
which separated flames continued to burn until all fuel was
consumed). As-prepared 4.2M PIB suppressed flame propagation, but
lost its efficacy after the shear treatment described in FIG. 66.
430 kg/mol TA was effective in mist-control before and after
shear.
Example 66: Impact/Flame Propagation Test
[0544] Associative LTPs are proven to be highly effective in mist
control, preventing flame propagation in post-impact jet fuel mist.
The apparatus shown in FIG. 69, Panel A is used to emulate the
impact-induced atomization and subsequent ignition of kerosene
released from ruptured fuel tanks in crash scenarios of ground
vehicles/aircraft. A steel projectile is shot at 63 m/s at a sealed
aluminum tube containing the fuel sample to generate mist, while
three propane torches are burning along the path of the ejected
fluid. The process of impact, misting, ignition and flame
propagation is captured using high-speed imaging.
[0545] Efficacy of high molecular-weight end-associative polymers
as mist-control additives for fuels was studied via high-speed
imaging during an impact/flame progagation test. The apparatus
(FIG. 69, Panel A) emulates the atomization and subsequent ignition
of fuels released from ruptured fuel tanks in crash scenarios of
ground vehicles/aircraft. An aluminum canister (outer diameter=23
mm, height=140 mm) pre-loaded with a cylindrical aluminum filler
(diameter=22 mm, height=40 mm) was used as a miniature fuel tank to
hold .about.30 mL of a test sample. The cap was tightly sealed with
superglue and 2-3 wraps of electrical tape to keep it in place
during the impact. A solid stainless steel cylinder (diameter=24
mm, length=50 mm) was used as a projectile to impact the canister
and disperse the fuel. Compressed air at 6.89.times.105 Pa was used
to propel the projectile through a 1.66 m-long barrel (inner
diameter=25.4 mm), resulting in a muzzle speed of 63 m/s. An array
of three continuously burning propane torches was placed in the
path of the ejected fuel to serve as ignition sources. The onset of
impact, formation of mist, and the following ignition events and
propagation of flame were captured at a frame rate of 10 kHz using
a high-speed camera (Photron SA1.1). Image acquisition was
triggered by a laser-motion detector attached to the end of
muzzle.
[0546] For untreated Jet-A, the impact conditions generate a fine
mist: at 30 ms after the impact, a cloud of very fine mist of Jet-A
is observed (FIG. 75, Panel A), and at 60 ms after impact flames
rapidly propagate through the fine mist into a hot fireball (FIG.
75, Panel B). The flame propagated to engulf the entire cloud of
fuel mist within a further 60 ms. Polymer-treated Jet-A samples are
tested in two forms: as prepared ("unsheared") and after being
passed through a fuel pump approximately 60 times ("sheared") using
the setup shown in FIG. 66, Panel A. The ultra-long 4,200 kg/mol
PIB at 0.35 wt % in Jet-A is used as a positive control that is
known to confer mist control which prevents flame propagation. As
shown in FIG. 76(left), much larger droplets interconnected by
fluid filaments are observed at 30 and 60 ms after impact. As
ejected fluid flies over the propane torches, localized ignition
events are observed, but they soon self-extinguish. The "sheared"
sample of the 0.35 wt % Jet-A solution of 4,200 kg/mol PIB,
however, shows a significantly different pattern of ejection of
fluid after impact (FIG. 76 right): fine droplets formed and
interconnecting filaments are no longer observed. Ignition events
observed at 30 ms after impact quickly propagate and engulf the
fuel cloud in fireball (FIG. 76 right, t=60 ms), indicating the
polymer loses its efficacy due to shear degradation. The results
confirm that the method is capable of creating a post-impact fuel
mist that propagates fire from any ignition event, correctly
captures the fire protection that is known to be conferred by 4,200
kg/mol PIB at 0.35 wt % and the loss of fire protection that is
known to occur after fuel is passed through pumps, filters or
turbulent pipe flow.
[0547] Having validated the setup, it is used to test the efficacy
of associative LTPs as mist-control additives for Jet-A. Here 430
kg/mol TA-PCOD is selected as a representative example. The results
in FIG. 77 prove that associative LTPs provide mist control both
before and after severe shearing, confirming their resistance to
shear degradation. It is found that in the test of the unsheared
solution of 430 kg/mol TA-PCOD, supramolecules suppress mist
formation of Jet-A: ignition events self-extinguish and, as a
result, no propagating fireballs are observed. When the sheared
solution is tested, the post-impact ignition events propagate to a
very limited extent (FIG. 77 right, t=60 ms), and they do not
evolve into a propagating fireball at all, evidencing that the
mist-control ability of the polymer remains after going through
severe shearing. Moreover, the test also proves that chain length
of associative LTPs plays a crucial role in mist control,
consistent with the hypothesis that mega-supramolecules are the
active species conferring the observed effect. Unsheared 0.5 wt %
Jet-A solutions of TA-PCODs at Mw=76, 230, 300 and 430 kg/mol are
tested, and complete suppression of fire propagation is only
observed in the case of the longest TA polymer (FIG. 50B).
[0548] The results shown in FIG. 77 clearly indicate that
associative LTPs do avoid the problem of chain collapse resulting
from randomly placing associative groups along polymer
backbone.[65, 87] If not, propagating fireballs would have been
observed in tests of 430 kg/mol TA-PCOD solutions. In accord with
theoretical predictions that very long backbones reduce cyclic
association and favor intermolecular association even at low
concentration, the results show that increasing the length of long
telechelic associative polymers favors formation elastic
supramolecules at low concentrations and confers mist control.[88]
Hence, overcoming synthetic obstacles to long (>300 kg/mol)
telechelic associative polymers is proved to be significant, for it
provides access to the unexplored regime of very long LTPs (>400
kg/mol) that can control misting of kerosene like ultra-high
molecular weight PIBs and survive turbulent flows that can destroy
ultra-high molecular weight PIBs.
[0549] In the 70's and 80's, the prevailing concept for improving
fire safety of fuels was that it could be achieved through the
addition of then-known anti-misting polymers into fuels to
completely eliminate the impact-induced atomization of fuels and
the subsequent fire/explosion hazards.[6, 7, 81, 89, 90] However,
more recent studies indicate that simply shifting the drop size
distribution to higher values can prevent flame propagation through
a fuel mist. For example, the critical values of Sauter mean
diameter of droplets of military fuel JP-8 in a droplet/air
(aerosol) mixture to propagate a flame from an ignition source is
approximately 52 .mu.m; at lower droplet sizes than this critical
values the aerosol becomes entirely engulfed in flame.[91] Thus,
complete elimination of mist formation is not necessary. This idea
is in good agreement with the data shown in FIGS. 75-77. Even
though fire resistance are observed in both unsheared solutions of
4,200 kg/mol PIB and 430 kg/mol TA-PCOD, impact on the latter
results in a cloud of finer droplets compared to the former. The
observed fire protection conferred by 430 kg/mol TA-PCOD clearly
indicates that it does not require complete elimination of misting
to achieve fire-safe fuels; instead, the goal can be achieved via
proper control of misting.
[0550] Motivated by the hope to prevent the use of civilian
aircrafts as weapons of mass destruction, long telechelic polymers
(LTPs) were explored and it was demonstrated that their length is
key to LTPs' potent rheological effects. It is found that by
carefully selecting associative end-groups that associate with a
strength much greater than thermal energy (kT), yet much weaker
than a covalent bond (ca. 150 kT), LTPs form mega-supramolecules
even at low concentration. These supramolecules provide benefits
typically associated with ultra-long polymers--including mist
control and drag reduction, and they reversibly dissociate under
flow conditions that would break covalent bonds, allowing the
individual LTPs to survive pumping and filtering and allowing
treated fuel to burn cleanly and efficiently in unmodified diesel
engines. After a 30-year gap in polymer research to improve fire
safety and stewardship of fuel, LTPs represent an "existence proof"
that polymers can indeed control misting and reduce pumping costs
without losing efficacy due to shear degradation, or harming fuel
economy or emissions.
Example 67: Effect of TA on Specific Viscosity of Tetralin
[0551] FIG. 70 shows characterization of
.alpha.,.omega.-di(di(isophthalic acid)) (TA) polycyclooctadiene
used in Impact test. FIG. 70, Panel A, Effect of chain length on
specific viscosity of TA in tetralin at 10 mg/ml. FIG. 70, Panel B,
Specific viscosity of 2.4 mg/ml 430 kg/mol TA in Jet-A at
25.degree. C., sheared vs unsheared. The 430 kg/mol
.alpha.,.omega.-di(di(isophthalic acid)) polycyclooctadiene (TA),
which is used in the impact test, is self-associative (and might
not be pairwise). Although its physics may differ from that of
complementary pairs, its rheological properties are similar FIG.
70, Panel A, it has similar resistance to shear degradation FIG.
70, Panel B as the .alpha.,.omega.-di(isophthalic acid)
polycyclooctadiene and .alpha.,.omega.-di(di(tertiary amine))
polycyclooctadiene 1:1 molar ratio mixture (.about.670 kg/mol
DA/DB).
Example 68: Safer and Cleaner Fuel by End-Association of Long
Telechelic Polymers
[0552] Liquid fuels, such as gasoline, diesel and kerosene, are the
world's dominant power source, representing 34% of global energy
consumption. Transportation relies on such liquids, presenting the
risk of explosive combustion in the event of impact, such as the
1977 Tenerife airport disaster--an otherwise-survivable runway
collision that claimed 583 lives in the post-crash fireball. The UK
and the U.S. responded with a multi-agency effort to develop
polymeric fuel additives for "mist control." Ultra-long,
associative polymers (e.g., ICI's "FM-9,">3,000 kg/mol
copolymer, 5 mol % carboxylic acid units) increased the drop
diameter in post-impact mist, resulting in a relatively cool,
short-lived mist fire. However, the polymers interfered with engine
operation, and their ultra-long backbone--essential for mist
control--degraded upon pumping. They were abandoned in 1986. 15
years later, the post-impact fuel fireball involved in the collapse
of the World Trade Center provided motivations to revisit polymers
for mist control.
[0553] Building on recent advances in supramolecular assembly as a
route to emergent functional materials, particularly assembly of
complex polymer architectures, an unexplored class of polymers that
is both effective and compatible with fuel systems was discovered.
Here, it is shown that long (>400 kg/mol) end-associative
polymers form "mega-supramolecules" that control post-impact mist
without adversely affecting power, efficiency or emissions of
unmodified diesel engines. They also reduce turbulent drag, hence,
conserving energy used to distribute fuel. The length and
end-association strength of the present polymers were designed
using statistical mechanical considerations. In comparison with
ultra-long polymers for mist control, the present polymers are an
order of magnitude shorter; therefore, they are able to resist
shear degradation. In contrast to prior randomly-functionalized
associative polymers, these end-associative polymers also avoid
chain collapse. It is found that simple
carboxylic-acid/tertiary-amine end-association is effective, and
the unprecedented length of these telechelic polymers is essential
for their potent rheological effects.
[0554] Kerosene fuels have been a major source of fire hazard and
vulnerability when they are released in an uncontrolled manner. It
is estimated that 40% of the fatalities in so-called "survivable
aircraft crashes," which make up approximately 70% of accidents
that occur on takeoff and landing, are due to fire caused by
combustion of aviation fuel.[92] Similarly, the violent and
catastrophic combustion of leaked fuel after the direct or indirect
ballistic penetration of a vehicle's fuel tank or fuel line by
shrapnel in IED attacks has inflicted heavy casualties on US
military over the last decade. In impact scenarios, fuel is
atomized by mechanical energy involved into fine mist, and such
mist burns explosively when ignited. The resultant fire can rapidly
propagate away from the ignition source, involve more fuel, and
trigger deadly pool fires that are very violent and difficult to
contain. Such fire often accompanies tank explosions, leaving no
chance for firefighters to intervene, as demonstrated in the
collapse of the World Trade Center[93].
[0555] Increasing the droplet size in post-impact mist of kerosene
(i.e., "mist control") has been identified as the most promising
way to mitigate impact-induced kerosene fires.[94]'[95]
"Mist-control kerosene" is indeed a fuel that "burns but doesn't
burn--" after ignition from an incendiary threat, it
self-extinguishes and slows the spread of fire so that
fire-extinguishing systems can intervene, and personnel can have
time to escape.[82] Ultra-high molecular weight (on the
order.about.10,000 kg/mol) polymers have potent effects on the
breakup of liquid jets and drops even at very low concentration (on
the order of 100 ppm),[96] since they are long enough to exhibit
elasticity and sustain tensile stress.[97-100] However, using such
polymers to provide mist control for kerosene has been found
practically difficult due to their vulnerability to shear
degradation in fuel transportation and dispensing processes.[101]
Once they are degraded, they lose their efficacy permanently.
Beginning in the late 1970's, efforts had been made to adopt the
concept of "associative polymers" in hope of providing mist-control
effectiveness of ultra-high molecular weight polymers while
circumventing their loss of efficacy due to shear degradation.
Specifically, these associative polymers are comprised of
shear-stable polymer chains (molecular weight<1,000 kg/mol) with
associative groups randomly placed on the backbone, capable of
aggregating into larger clusters (which might be effective in mist
control) via hydrogen bonding and responding to turbulent flow via
reversible dissociation.[102] A good example is ICI's FM-9 polymer
(>3,000 kg/mol copolymer, 5 mol % carboxylic acid units) used in
the engineering-oriented UK-U.S. joint Anti-Misting Kerosene (AMK)
program.[81, 82] Despite demonstration of efficacy, FM-9 interfered
with engine operation and fuel handling, and it was not immune to
shear degradation upon pumping. Eventually research in this area
was largely abandoned in 1986.
[0556] With a view towards improving fire safety of jet fuels,
polymers for mist control of kerosene are disclosed herein.
Fundamental relationship between molecular designs of mist-control
polymers and corresponding solution behaviors are described. It was
found that the design of associative polymers prevailing in the
80's suffers a fatal flaw: it leads to self-assembly of chains into
collapsed, inextensible structures that are of little use in mist
control.[65, 87] Using statistical mechanical analysis of
ring-chain equilibrium, it is found that exceptionally long
telechelic polymers (LTPs, FIG. 22) are needed to assemble large
supramolecules effective in mist control and other applications
that rely on large polymer coils, such as drag reduction.[88] The
theory provides a guideline on polymer backbone length based on two
trade-offs: the chain is typically be long enough that
mega-supramolecules form, yet short enough to avoid chain scission
(<1,000 kg/mol) during pumping and turbulent flow. Specifically,
it is expected that an adequate concentration (>50 ppm) of
>5,000 kg/mol supramolecules forms when the individual
telechelics are 500 kg/mol, if donor-acceptor type associations are
used with end-association energy approximately 16-18 kT, and the
total polymer concentration is 1,400 ppm. These criteria point to
an unprecedented class of polymers that did not exist before.
[0557] In the present disclosure, the recent advance in development
of LTPs for mist control of kerosene are described, including the
breakthrough in polymer and supramolecular chemistry and the
properties and performance of these polymers as fuel additives.
Example 69: Identification of Associative Polymers to Control Drag
Reduction in Aviation Fuel
[0558] The following approach can be used to identify associative
polymers for drag reduction in aviation fuel, in particular in to
achieve a 10% increase in pipeline capacity through the existing
pipelines serving an airport.
[0559] Candidate polymer backbones can be identified for a certain
fuel composition to be used as a host composition in the sense of
the present disclosure. For example a skilled person can refer to
literature to identify polyisobutylene (PIB) as a candidate known
to be widely used in fuel additives and be able remains in solution
down to low temperatures (e.g. -30.degree. C.). Additional
candidates (e.g. polycyclooctadiene) can be found based on
literature or experiments to be performed to identify the
solubility and stability of the polymer in a fuel composition of
choice.
[0560] Prioritization (rank order) of the candidate backbones can
be achieved by the following steps [0561] Step 1. For each
candidate backbone, identify the threshold molecular weight for the
onset of shear degradation. This provides a good estimate for the
maximum span of associative polymers herein described, whether
linear or branched, suitable for their application. [0562] Step 2.
For each candidate backbone, determine (e.g. by measuring) the
overlap concentration that corresponds to the maximum span of the
associative polymers suitable for their application, determined in
Step 1. If a backbone shorter than the maximum is used, it will
increase the value of the overlap concentration. So the overlap
concentration determined in this step is the lowest overlap
concentration relevant to their application. [0563] Step 3. For
each candidate polymer backbone, determine the end group
concentration that corresponds to the overlap concentration
determined in Step 2. [0564] Step 4. For each candidate polymer
backbone, estimate the range of the association constants worthy of
testing. Specifically, using the molar concentration of end groups
from Step 3, determine the value of the association constant that
would provide a pairing of the end groups equal to or greater than
75% (e.g. 99%) according to the binding constant calculated in
accordance with the present disclosure. If the polymer will be
tested at concentrations below c*, the association constant
estimated using c* provides a lower estimate of the association
constant that will give the desired effects. If polymers will be
used at higher concentration than c*, the association constant
estimated using c* will provide desired effects.
[0565] Results of application of the above approach to the
exemplary PIB and PCOD indicated above is summarized in the
following Table 15 below
[0566] Results of application of the above approach to the
exemplary PIB and PCOD indicated above is summarized in the
following Table 15 below
TABLE-US-00016 TABLE 15 Threshold Overlap Association constant
Candidate M.sub.w [g/mol] R.sub.g [nm] cnc. [g/L] End group range
of interest backbone for shear for threshold at threshold conc. [M]
For 75% For 99% structure degradation Mw M.sub.w & R.sub.g at
c* end assn. end assn. PIB 300,000 25 7.7 2.6 .times. 10.sup.-5 2
.times. 10.sup.5 1.2 .times. 10.sup.8 PCOD 700,000 73 2 2.3 .times.
10.sup.-6 5 .times. 10.sup.6 .sup. 3 .times. 10.sup.9
[0567] A skilled person can also perform experiments to identify
the threshold molecular weight for their application. For example,
an apparatus can be constructed that subjects the fluid to the
number of passes through a pump, the exposure to turbulent pipe
flow and passage through filters that is pertinent to the
application of interest to them. Alternatively, the skilled person
can perform a literature search to obtain an estimate of the value
of the threshold molecular weight for each backbone of interest.
For illustration, exemplary estimates for PIB and PCOD obtained
from laboratory experiments are provided in the second column of
Table 15 above.
[0568] The threshold molecular weight if the architecture are
linear, given in the second column of table 15 (the longest
span--see e.g. FIGS. 81A-81H--for the application of interest), can
be used to determine (e.g. by calculation or measurement) the
corresponding radius of gyration, shown in the third column of the
table. The radius of gyration R.sub.g calculated for a linear chain
corresponding to the longest span provides a good estimate of the
radius of gyration for the other polymer architectures of the
present disclosure. The skilled person can either perform
experiments to measure R.sub.g for the backbones of interest and
obtain the value of R.sub.g that corresponds to the threshold
molecular weight in the second column of table 15. Alternatively,
the skilled person can refer to the literature and their knowledge
of the solution condition relevant to the candidate backbones.
[0569] In the present example, fuel is a good solvent for both of
the backbones being considered. The values shown in the third
column of Table 15 were calculated for good solvent conditions
using equations provided for polybutadiene and polyisobutylene as
equations (6) and (26) in "Molecular Weight Dependence of
Hydrodynamic and Thermodynamic Properties for Well-Defined Linear
Polymers in Solution" (1994) by Fetters et al. [14].
[0570] The threshold molecular weight and the corresponding radius
of gyration can be used to calculate the minimum overlap
concentration that can be achieved with each candidate backbone,
limited by their individual threshold for shear degradation under
the condition of the user's application. As noted above, the
R.sub.g calculated from the longest span provides a good estimate
of the radius of gyration for the other polymer architectures of
the present disclosure. In the exemplary case of PIB and PCOD, the
Mw used to calculate the concentration in the fourth column of the
table assumes that the polymers are linear. A skilled person would
know how to determine Mw for other architectures from the size of
the longest span and the specific architecture of interest.
[0571] The end group concentration for the threshold molecular
weight at the overlap concentration can be determined (e.g. by
calculation or measurement). In this example, the case of a linear
associative molecule is used and complementary association (A+B
pairwise association) is assumed: each polymer has two ends; half
of the polymers carry the A functional group and half carry the B
functional group. Thus, the molar concentration of A ends equals
the molar concentration of B ends equals the molar concentration of
chains, given in the fifth column of the table. The skilled person
can adjust this as appropriate to the associative molecules of
interest to them, which might have more than two functional groups
if branched structures are considered (see e.g. FIGS. 81A-81H) and
might be self-associative or involve more than two complementary
functional groups.
[0572] In the example given in table 15, the relevant range of
association constants is calculated assuming pairwise,
complementary association, as described in the preceding paragraph.
Thus, the values given in the sixth and seventh columns of the
table are equal to (0.75 [end])/{(0.25 [end]).sup.2} for the 75%
case and (0.99 [end])/{(0.01 [end]).sup.2} for the 99% case, where
[end] denotes the end group concentration value given in the fifth
column. The skilled person would be able to adjust the calculation
as appropriate to other scenarios, also described above.
[0573] A skilled person can now prioritize the experiments to be
performed to develop the formulation that meets the required 10%
reduction in pipeline drag. For example, if the concentration needs
to be kept below 3 g/L, then the skilled person may exclude PIB
from further consideration. Initial experiments may focus on linear
PCOD with Mw and PDI such that less than 1% of chains are longer
than 700 kg/mol. Experiments can focus on end group structures that
give association constant greater than 4.9.times.10.sup.6. The
reduction of pipeline drag can then be measured for a small number
of concentrations, perhaps c*, c*/2 and c*/4, to characterize
trends in performance as a function of concentration. If the
effects are not adequate, a stronger association constant can be
tested. If the resistance to shear degradation is not adequate, a
branched architecture can be tested. The skilled person can use a
relatively modest number of experiments to develop a polymer and
formulation that meets the requirement for 10% reduction in
pipeline drag.
Example 70: Associative Polymers to Control Droplet Breakout During
Fibers' Preparation
[0574] A skilled person seeks to prepare fibers using
electrospinning of a nonpolar monomer, ethylhexylmethacrylate. The
liquid undergoes electrospray into fine droplets rather than
electrospinning. The skilled person adds 0.1% of 700k DA/DB to the
monomer. The problem of droplet breakup is eliminated, enabling
spinning of the desired fiber. When the fiber diameter is drawn
down to 80 nm, photopolymerization is used to solidify the
fiber.
Example 71: Associative Polymers to Control Size and Uniformity of
Drug Particles
[0575] A pharmaceutical company uses atomization of hydrophobic
drug in a non-polar solvent followed by evaporation of the nonpolar
solvent to produce particles of the drug. The size and uniformity
of the drug particles can be used to optimize their time release
when administered to the patient. A skilled person seeks to
eliminate satellite droplets. The skilled person chooses as the
backbone of the associative polymer herein described a hydrophobic
polymer accepted for use in drug formulations and soluble in the
drug solution used for atomization. The skilled person identifies
10 g/L concentration as the acceptable amount of polymer in the
drug solution used for atomization. Therefore, they choose a
polymer molecular weight that gives the polymer a radius of
gyration of 22 nm. They consider functional groups in relation to
the composition of the atomization solution to select functional
groups that will associate with association constant k>10.sup.5
when used in that solution. The polymer is introduced to the
solution at a concentration of 10 g/L and the formation of
satellite drops is reduced.
Example 72: Associative Polymers to Increase Volume of a Fluid
Supplied in a Pipeline
[0576] A fuel pipeline is operating at its maximum capacity. A
skilled person wants to increase the volume of fuel supplied
through the pipeline. The pipeline is operating at its maximum
pressure, so the increase in throughput cannot be accomplished by
increasing the pressure. The flow in the pipeline is turbulent (the
Reynolds number is greater than 5,000, e.g. 25,000). Therefore,
frictional losses in the pipeline are described using the familiar
friction coefficient C.sub.f. defined as
C f = Wall .times. .times. Shear .times. .times. Stress Dynamic
.times. .times. Pressure = 2 .times. D .times. .times. .DELTA.
.times. .times. p 4 .times. L .times. .times. .rho. .times. .times.
u m 2 ( 26 ) ##EQU00029##
where D is the inner diameter of the pipe, .DELTA.p/L is the
frictional pressure loss over a distance L along the pipeline,
.rho. is the density of the fuel, u_m=Q/A, where Q is the
volumetric flow rate and A=.pi. D.sup.2/4 is the cross sectional
area of the pipe. Often the frictional pressure loss is expressed
as "head loss" hf=.DELTA.p/(.rho.g):
h f = 4 .times. C f .times. Lu m 2 2 .times. gD = 4 .times. C f
.times. LQ 2 2 .times. gDA 2 = 32 .times. C f .times. LQ 2 g
.times. .times. .pi. 2 .times. D 5 = RQ 2 .times. .times. R .times.
.times. is .times. .times. the .times. .times. .times. fluid
.times. .times. resistance ( 27 ) ##EQU00030##
[0577] Laboratory experiments were performed at a Reynold's number
of Re=14,000 using 9 m long and 12 m long tubes. Compared to
untreated fuel, the fluid resistance due to flow through the tube
was reduced from hf/Q.sup.2=1.1.times.10.sup.11 s.sup.2/m.sup.5
(untreated fuel) to hf/Q.sup.2=6.8.times.10.sup.10 s.sup.2/m.sup.55
when treated with 0.1% of a 1:1 mixture of 700k DA and 700k DB.
[0578] In the pipeline, the Reynold's number is much greater,
approximately 100,000. In accord with prior literature indicating
that the fractional drag reduction increases with Re over this
range, when the polymer was used in the pipeline, the increase in
throughput was more than 25%.
Example 73: Associative Polymers to Provide Grafting Sites on a
Fiber Surface
[0579] In an exemplary application, a hydrophobic polydrug is only
available in molecular weights that are too short to enable fiber
spinning. In addition, a covalently grafted layer is needed on the
surface to inhibit non-specific protein adsorption. A product
development team seeks a single additive that can be used at low
concentration to provide grafting sites on the fiber surface.
Therefore, the team chooses a branched polymer with the following
average structure.
[0580] On average the polymers have four nodes. On average they
have four associative functional groups, FGas. In addition, on
average, each molecule has one FGd. On average they have nine
-[chain]- segments each approximately 100 kg/mol, such that the
average molecular weight of the polymer is approximately 1,000
kg/mol. When 0.3% of the above is added to the solution, the
associative polymer facilitates fiber spinning and provides FGd
groups at the fiber surface. The FGd groups displayed on the
surface of the fiber are later used as chemical groups for grafting
PEG or zwitterionic polymer chains to the fiber surface.
[0581] The examples set forth above are provided to give those of
ordinary skill in the art a complete disclosure and description of
how to make and use the embodiments of the associative polymers,
materials, compositions, systems and methods of the disclosure, and
are not intended to limit the scope of what the inventors regard as
their disclosure. All patents and publications mentioned in the
specification are indicative of the levels of skill of those
skilled in the art to which the disclosure pertains.
[0582] The entire disclosure of each document cited (including
patents, patent applications, journal articles, abstracts,
laboratory manuals, books, or other disclosures) in the Background,
Summary, Detailed Description, and Examples is hereby incorporated
herein by reference. All references cited in this disclosure are
incorporated by reference to the same extent as if each reference
had been incorporated by reference in its entirety individually.
However, if any inconsistency arises between a cited reference and
the present disclosure, the present disclosure takes
precedence.
[0583] The terms and expressions which have been employed herein
are used as terms of description and not of limitation, and there
is no intention in the use of such terms and expressions of
excluding any equivalents of the features shown and described or
portions thereof, but it is recognized that various modifications
are possible within the scope of the disclosure claimed Thus, it
should be understood that although the disclosure has been
specifically disclosed by preferred embodiments, exemplary
embodiments and optional features, modification and variation of
the concepts herein disclosed can be resorted to by those skilled
in the art, and that such modifications and variations are
considered to be within the scope of this disclosure as defined by
the appended claims.
[0584] It is also to be understood that the terminology used herein
is for the purpose of describing particular embodiments only, and
is not intended to be limiting. As used in this specification and
the appended claims, the singular forms "a," "an," and "the"
include plural referents unless the content clearly dictates
otherwise. The term "plurality" includes two or more referents
unless the content clearly dictates otherwise. Unless defined
otherwise, all technical and scientific terms used herein have the
same meaning as commonly understood by one of ordinary skill in the
art to which the disclosure pertains.
[0585] Unless otherwise indicated, the term "alkyl" as used herein
refers to a linear, branched, or cyclic saturated hydrocarbon group
typically although not necessarily containing 1 to about 15 carbon
atoms, or 1 to about 6 carbon atoms, such as methyl, ethyl,
n-propyl, isopropyl, n-butyl, isobutyl, t-butyl, octyl, decyl, and
the like, as well as cycloalkyl groups such as cyclopentyl,
cyclohexyl and the like. Generally, although again not necessarily,
alkyl groups herein contain 1 to about 15 carbon atoms. The term
"cycloalkyl" intends a cyclic alkyl group, typically having 4 to 8,
or 5 to 7, carbon atoms. The term "substituted alkyl" refers to
alkyl substituted with one or more substituent groups, and the
terms "heteroatom-containing alkyl" and "heteroalkyl" refer to
alkyl in which at least one carbon atom is replaced with a
heteroatom. If not otherwise indicated, the terms "alkyl" and
"lower alkyl" include linear, branched, cyclic, unsubstituted,
substituted, and/or heteroatom-containing alkyl and lower alkyl,
respectively.
[0586] Unless otherwise indicated, the term "hydrocarbyl" as used
herein refers to any univalent radical, derived from a hydrocarbon,
such as, for example, methyl or phenyl. The term "hydrocarbylene"
refers to divalent groups formed by removing two hydrogen atoms
from a hydrocarbon, the free valencies of which may or may not be
engaged in a double bond, typically but not necessarily containing
1 to 20 carbon atoms, in particular 1 to 12 carbon atoms and more
particularly 1 to 6 carbon atoms which includes but is not limited
to linear cyclic, branched, saturated and unsaturated species, such
as alkylene, alkenylene alkynylene and divalent aryl groups, e.g.,
1,3-phenylene, --CH.sub.2CH.sub.2CH.sub.2-propane-1,3-diyl,
--CH.sub.2-methylene, --CH.dbd.CH--CH.dbd.CH--. The term
"hydrocarbyl" as used herein refers to univalent groups formed by
removing a hydrogen atom from a hydrocarbon, typically but not
necessarily containing 1 to 20 carbon atoms, in particular 1 to 12
carbon atoms and more particularly 1 to 6 carbon atoms, including
but not limited to linear cyclic, branched, saturated and
unsaturated species, such as univalent alkyl, alkenyl, alkynyl and
aryl groups e.g. ethyl and phenyl groups.
[0587] Unless otherwise indicated, the term "heteroatom-containing"
as in a "heteroatom-containing alky group" refers to a alkyl group
in which one or more carbon atoms is replaced with an atom other
than carbon, e.g., nitrogen, oxygen, sulfur, phosphorus or silicon,
typically nitrogen, oxygen or sulfur. Similarly, the term
"heteroalkyl" refers to an alkyl substituent that is
heteroatom-containing, the term "heterocyclic" refers to a cyclic
substituent that is heteroatom-containing, the terms "heteroaryl"
and "heteroaromatic" respectively refer to "aryl" and "aromatic"
substituents that are heteroatom-containing, and the like. It
should be noted that a "heterocyclic" group or compound may or may
not be aromatic, and further that "heterocycles" may be monocyclic,
bicyclic, or polycyclic as described above with respect to the term
"aryl." Examples of heteroalkyl groups include alkoxyaryl,
alkylsulfanyl-substituted alkyl, N-alkylated amino alkyl, and the
like. Examples of heteroaryl substituents include pyrrolyl,
pyrrolidinyl, pyridinyl, quinolinyl, indolyl, pyrimidinyl,
imidazolyl, 1,2,4-triazolyl, tetrazolyl, and others known to a
skilled person, and examples of heteroatom-containing alicyclic
groups are pyrrolidino, morpholino, piperazino, piperidino, and
other known to a skilled person.
[0588] Unless otherwise indicated, the term "alkoxy" as used herein
intends an alkyl group bound through a single, terminal ether
linkage; that is, an "alkoxy" group may be represented as --O-alkyl
where alkyl is as defined above. A "lower alkoxy" group intends an
alkoxy group containing 1 to 6 carbon atoms. Analogously,
"alkenyloxy" and "lower alkenyloxy" respectively refer to an
alkenyl and lower alkenyl group bound through a single, terminal
ether linkage, and "alkynyloxy" and "lower alkynyloxy" respectively
refer to an alkynyl and lower alkynyl group bound through a single,
terminal ether linkage.
[0589] Unless otherwise indicated, the term "alkylamino" as used
herein intends an alkyl group bound through a single terminal amine
linkage; that is, an "alkylamino" may be represented as --NH-alkyl
where alkyl is as defined above. A "lower alkylamino" intends an
alkylamino group containing 1 to 6 carbon atoms. The term
"dialkylamino" as used herein intends two identical or different
bound through a common amine linkage; that is, a "dialkylamino" may
be represented as --N(alkyl).sub.2 where alkyl is as defined above.
A "lower dialkylamino" intends an alkylamino wherein each alkyl
group contains 1 to 6 carbon atoms. Analogously, "alkenylamino",
"lower alkenylamino", "alkynylamino", and "lower alkynylamino"
respectively refer to an alkenyl, lower alkenyl, alkynyl and lower
alkynyl bound through a single terminal amine linkage; and
"dialkenylamino", "lower dialkenylamino", "dialkynylamino", "lower
dialkynylamino" respectively refer to two identical alkenyl, lower
alkenyl, alkynyl and lower alkynyl bound through a common amine
linkage. Similarly, "alkenylalkynylamino", "alkenylalkylamino", and
"alkynylalkylamino" respectively refer to alkenyl and alkynyl,
alkenyl and alkyl, and alkynyl and alkyl groups bound through a
common amine linkage.
[0590] Unless otherwise indicated, the term "aryl" as used herein,
and unless otherwise specified, refers to an aromatic substituent
containing a single aromatic ring or multiple aromatic rings that
are fused together, directly linked, or indirectly linked (such
that the different aromatic rings are bound to a common group such
as a methylene or ethylene moiety). Aryl groups can contain 5 to 24
carbon atoms, or aryl groups contain 5 to 14 carbon atoms.
Exemplary aryl groups contain one aromatic ring or two fused or
linked aromatic rings, e.g., phenyl, naphthyl, biphenyl,
diphenylether, diphenylamine, benzophenone, and the like.
"Substituted aryl" refers to an aryl moiety substituted with one or
more substituent groups, and the terms "heteroatom-containing aryl"
and "heteroaryl" refer to aryl substituents in which at least one
carbon atom is replaced with a heteroatom, as will be described in
further detail infra.
[0591] Unless otherwise indicated, the term "arene", as used
herein, refers to an aromatic ring or multiple aromatic rings that
are fused together. Exemplary arenes include, for example, benzene,
naphthalene, anthracene, and the like. The term "heteroarene", as
used herein, refers to an arene in which one or more of the carbon
atoms has been replaced by a heteroatom (e.g. O, N, or S).
Exemplary heteroarenes include, for example, indole, benzimidazole,
thiophene, benzthiazole, and the like. The terms "substituted
arene" and "substituted heteroarene", as used herein, refer to
arene and heteroarene molecules in which one or more of the carbons
and/or heteroatoms are substituted with substituent groups.
[0592] Unless otherwise indicated, the terms "cyclic", "cyclo-",
and "ring" refer to alicyclic or aromatic groups that may or may
not be substituted and/or heteroatom containing, and that may be
monocyclic, bicyclic, or polycyclic. The term "alicyclic" is used
in the conventional sense to refer to an aliphatic cyclic moiety,
as opposed to an aromatic cyclic moiety, and may be monocyclic,
bicyclic or polycyclic.
[0593] Unless otherwise indicated, the terms "halo", "halogen", and
"halide" are used in the conventional sense to refer to a chloro,
bromo, fluoro or iodo substituent or ligand.
[0594] Unless otherwise indicated, the term "substituted" as in
"substituted alkyl," "substituted aryl," and the like, is meant
that in the, alkyl, aryl, or other moiety, at least one hydrogen
atom bound to a carbon (or other) atom is replaced with one or more
non-hydrogen substituents.
[0595] Examples of such substituents can include, without
limitation: functional groups such as halo, hydroxyl, sulfhydryl,
C1-C24 alkoxy, C2-C24 alkenyloxy, C2-C24 alkynyloxy, C5-C24
aryloxy, C6-C24 aralkyloxy, C6-C24 alkaryloxy, acyl (including
C2-C24 alkylcarbonyl (--CO-alkyl) and C6-C24 arylcarbonyl
(--CO-aryl)), acyloxy (--O-acyl, including C2-C24 alkylcarbonyloxy
(--O--CO-alkyl) and C6-C24 arylcarbonyloxy (--O--CO-aryl)), C2-C24
alkoxycarbonyl (--(CO)--O-alkyl), C6-C24 aryloxycarbonyl
(--(CO)--O-aryl), halocarbonyl (--CO)--X where X is halo), C2-C24
alkylcarbonato (--O--(CO)--O-alkyl), C6-C24 arylcarbonato
(--O--(CO)--O-aryl), carboxy (--COOH), carboxylato (COO--),
carbamoyl (--(CO)--NH.sub.2), mono-(C1-C24 alkyl)-substituted
carbamoyl (--(CO)--NH(C1-C24 alkyl)), di-(C1-C24 alkyl)-substituted
carbamoyl (--(CO)--N(C1-C24 alkyl).sub.2), mono-(C5-C24
aryl)-substituted carbamoyl (--(CO)--NH-aryl), di-(C5-C24
aryl)-substituted carbamoyl (--(CO)--N(C5-C24 aryl).sub.2),
di-N--(C1-C24 alkyl), N--(C5-C24 aryl)-substituted carbamoyl,
thiocarbamoyl (--(CS)--NH2), mono-(C1-C24 alkyl)-substituted
thiocarbamoyl (--(CO)--NH(C1-C24 alkyl)), di-(C1-C24
alkyl)-substituted thiocarbamoyl (--(CO)--N(C1-C24 alkyl).sub.2),
mono-(C5-C24 aryl)-substituted thiocarbamoyl (--(CO)--NH-aryl),
di-(C5-C24 aryl)-substituted thiocarbamoyl (--(CO)--N(C5-C24
aryl).sub.2), di-N--(C1-C24 alkyl), N--(C5-C24 aryl)-substituted
thiocarbamoyl, carbamido (--NH--(CO)--NH.sub.2), cyano(-C.ident.N),
cyanato (--O--C.ident.N), thiocyanato (--S--C.ident.N), formyl
(--(CO)--H), thioformyl ((CS)--H), amino (--NH2), mono-(C1-C24
alkyl)-substituted amino, di-(C1-C24 alkyl)-substituted amino,
mono-(C5-C24 aryl)-substituted amino, di-(C5-C24 aryl)-substituted
amino, C2-C24 alkylamido (--NH--(CO)-alkyl), C6-C24 arylamido
(--NH--(CO)-aryl), imino (--CR.dbd.NH where R=hydrogen, C1-C24
alkyl, C5-C24 aryl, C6-C24 alkaryl, C6-C24 aralkyl, and others
known to a skilled person), C2-C20 alkylimino (CR.dbd.N(alkyl),
where R=hydrogen, C1-C24 alkyl, C5-C24 aryl, C6-C24 alkaryl, C6-C24
aralkyl, and others known to a skilled person), arylimino
(--CR.dbd.N(aryl), where R=hydrogen, C1-C20 alkyl, C5-C24 aryl,
C6-C24 alkaryl, C6-C24 aralkyl, and others known to a skilled
person), nitro (--NO2), nitroso (--NO), sulfo (--SO2-OH), sulfonato
(--SO2-O--), C1-C24 alkylsulfanyl (--S-alkyl; also termed
"alkylthio"), C5-C24 arylsulfanyl (--S-aryl; also termed
"arylthio"), C1-C24 alkylsulfinyl (--(SO)-alkyl), C5-C24
arylsulfinyl (--(SO)-aryl), C1-C24 alkylsulfonyl (--SO2-alkyl),
C5-C24 arylsulfonyl (--SO2-aryl), boryl (--BH2), borono
(--B(OH).sub.2), boronato (--B(OR).sub.2 where R is alkyl or other
hydrocarbyl), phosphono (--P(O)(OH).sub.2), phosphonato
(--P(O)(O.sup.-).sub.2), phosphinato (--P(O)(O.sup.-)), phospho
(--PO.sub.2), phosphino (--PH.sub.2), silyl (--SiR.sub.3 wherein R
is hydrogen or hydrocarbyl), and silyloxy (--O-silyl); and the
hydrocarbyl moieties C1-C24 alkyl (e.g. C1-C12 alkyl and C1-C6
alkyl), C2-C24 alkenyl (e.g. C2-C12 alkenyl and C2-C6 alkenyl),
C2-C24 alkynyl (e.g. C2-C12 alkynyl and C2-C6 alkynyl), C5-C24 aryl
(e.g. C5-C14 aryl), C6-C24 alkaryl (e.g. C6-C16 alkaryl), and
C6-C24 aralkyl (e.g. C6-C16 aralkyl).
[0596] Unless otherwise indicated, the term "acyl" refers to
substituents having the formula --(CO)-alkyl, --(CO)-aryl, or
--(CO)-aralkyl, and the term "acyloxy" refers to substituents
having the formula --O(CO)-alkyl, --O(CO)-aryl, or --O(CO)-aralkyl,
wherein "alkyl," "aryl, and "aralkyl" are as defined above.
[0597] Unless otherwise indicated, the term "alkaryl" refers to an
aryl group with an alkyl substituent, and the term "aralkyl" refers
to an alkyl group with an aryl substituent, wherein "aryl" and
"alkyl" are as defined above. In some embodiments, alkaryl and
aralkyl groups contain 6 to 24 carbon atoms, and particularly
alkaryl and aralkyl groups contain 6 to 16 carbon atoms. Alkaryl
groups include, for example, p-methylphenyl, 2,4-dimethylphenyl,
p-cyclohexylphenyl, 2,7-dimethylnaphthyl, 7-cyclooctylnaphthyl,
3-ethyl-cyclopenta-1,4-diene, and the like. Examples of aralkyl
groups include, without limitation, benzyl, 2-phenyl-ethyl,
3-phenyl-propyl, 4-phenyl-butyl, 5-phenyl-pentyl,
4-phenylcyclohexyl, 4-benzylcyclohexyl, 4-phenylcyclohexylmethyl,
4-benzylcyclohexylmethyl, and the like. The terms "alkaryloxy" and
"aralkyloxy" refer to substituents of the formula --OR wherein R is
alkaryl or aralkyl, respectively, as just defined.
[0598] When a Markush group or other grouping is used herein, all
individual members of the group and all combinations and possible
subcombinations of the group are intended to be individually
included in the disclosure. Every combination of components or
materials described or exemplified herein can be used to practice
the disclosure, unless otherwise stated. One of ordinary skill in
the art will appreciate that methods, device elements, and
materials other than those specifically exemplified can be employed
in the practice of the disclosure without resort to undue
experimentation. All art-known functional equivalents, of any such
methods, device elements, and materials are intended to be included
in this disclosure. Whenever a range is given in the specification,
for example, a temperature range, a frequency range, a time range,
or a composition range, all intermediate ranges and all subranges,
as well as, all individual values included in the ranges given are
intended to be included in the disclosure. Any one or more
individual members of a range or group disclosed herein can be
excluded from a claim of this disclosure. The disclosure
illustratively described herein suitably can be practiced in the
absence of any element or elements, limitation or limitations which
is not specifically disclosed herein.
[0599] A number of embodiments of the disclosure have been
described. The specific embodiments provided herein are examples of
useful embodiments of the disclosure and it will be apparent to one
skilled in the art that the disclosure can be carried out using a
large number of variations of the devices, device components,
methods steps set forth in the present description. As will be
obvious to one of skill in the art, methods and devices useful for
the present methods can include a large number of optional
composition and processing elements and steps.
[0600] In particular, it will be understood that various
modifications may be made without departing from the spirit and
scope of the present disclosure. Accordingly, other embodiments are
within the scope of the following claims.
REFERENCES
[0601] 1. Fetters, L., D. Lohse, and R. Colby, Chain dimensions and
entanglement spacings, in Physical Properties of Polymers Handbook.
2007, Springer. p. 447-454. [0602] 2. Krishnamoorti, R., et al.,
Melt-state polymer chain dimensions as a function of temperature.
Journal of Polymer Science Part B: Polymer Physics, 2002. 40(16):
p. 1768-1776. [0603] 3. Brandrup, J. and E. Immergut, Polymer
handbook, 3rd. 1989: John Wiley and Sons. [0604] 4. Gotro, J. and
W. W. Graessley, Model hydrocarbon polymers: rheological properties
of linear polyisoprenes and hydrogenated polyisoprenes.
Macromolecules, 1984. 17(12): p. 2767-2775. [0605] 5. Colby, R. H.,
L. J. Fetters, and W. W. Graessley, The melt viscosity-molecular
weight relationship for linear polymers. Macromolecules, 1987.
20(9): p. 2226-2237. [0606] 6. Chao, K. K., et al., Antimisting
Action of Polymeric Additives in Jet Fuels. Aiche Journal, 1984.
30(1): p. 111-120. [0607] 7. Peng, S. T. J. and R. F. Landel,
Rheological Behavior of Fm-9 Solutions and Correlation with
Flammability Test-Results and Interpretations. Journal of
Non-Newtonian Fluid Mechanics, 1983. 12(1): p. 95-111. [0608] 8.
Nyden, M. R., et al., Applications of reactive molecular dynamics
to the study of the thermal decomposition of polymers and nanoscale
structures. Materials Science and Engineering a-Structural
Materials Properties Microstructure and Processing, 2004. 365(1-2):
p. 114-121. [0609] 9. Brandrup, J., et al., Polymer handbook. Vol.
1999. 1999: Wiley New York. [0610] 10. Maurer-Chronakis, K.,
Synthesis of cyanuric acid and Hamilton receptor functionalized
tetraphenylporphyrins: investigation on the chiroptical and
photophysical properties of their self-assembled superstructures
with depsipeptide and fullerene dendrimers, 2010, Erlangen,
Nurnberg, Univ. [0611] 11. Larock, R. C., Comprehensive organic
transformations: a guide to functional group preparations, 2nd Ed.
1999: Wiley-vch New York. [0612] 12. Ying, Q. and B. Chu, Overlap
concentration of macromolecules in solution. Macromolecules, 1987.
20(2): p. 362-366. [0613] 13. Colby, R. H. and M. Rubinstein,
Two-parameter scaling for polymers in .theta. solvents.
Macromolecules, 1990. 23(10): p. 2753-2757. [0614] 14. Fetters, L.,
et al., Molecular Weight Dependence of Hydrodynamic and
Thermodynamic Properties for Well-Defined Linear Polymers in
Solution. Journal of physical and chemical reference data, 1994.
23(4): p. 619-640. [0615] 15. Rubinstein, M. and R. H. Colby,
Polymer physics. 2003: OUP Oxford. 53-176. [0616] 16. Ke, F.-y.,
X.-l. Mo, and D.-h. Liang, Effect of Overlap Concentration and
Persistence Length on DNA Separation in Polymer Solutions by
Electrophoresis. Chinese Journal of Polymer Science, 2009. 27(5):
p. 601-610. [0617] 17. Thordarson, P., Determining association
constants from titration experiments in supramolecular chemistry.
Chem Soc Rev, 2011. 40(3): p. 1305-23. [0618] 18. Grubbs, R.,
Handbook of Metathesis, vol. 3. 2003: Wiley-VCH, Weinheim. [0619]
19. Tasdelen, M. A., M. U. Kahveci, and Y. Yagci, Telechelic
polymers by living and controlled/living polymerization methods.
Progress in Polymer Science, 2011. 36(4): p. 455-567. [0620] 20.
Goethals, E., Telechelic polymers: Synthesis and applications.
1989: CRC Press (Boca Raton, Fla.). [0621] 21. Wuts, P. G. and T.
W. Greene, Greene's protective groups in organic synthesis. 2006:
John Wiley & Sons. [0622] 22. Nese, A., et al., Synthesis of
Poly (vinyl acetate) Molecular Brushes by a Combination of Atom
Transfer Radical Polymerization (ATRP) and Reversible
Addition--Fragmentation Chain Transfer (RAFT) Polymerization.
Macromolecules, 2010. 43(9): p. 4016-4019. [0623] 23. Park, T. and
S. C. Zimmerman, A supramolecular multi-block copolymer with a high
propensity for alternation. J Am Chem Soc, 2006. 128(43): p.
13986-7. [0624] 24. Polymer Solutions: Solvents and Solubility
Parameters. Jan. 25, 2012]; Available from:
http://www.sigmaaldrich.com/etc/medialib/docs/Aldrich/General_Information-
/polymer_solutions.Par.0001.File.tmp/polymer_solutions.pdf. [0625]
25. Rubinstein, M. and R. H. Colby, Polymer physics. 2003, Oxford;
New York: Oxford University Press. xi, 440 p. [0626] 26. Chang, S.
K. and A. D. Hamilton, Molecular Recognition of Biologically
Interesting Substrates--Synthesis of an Artificial Receptor for
Barbiturates Employing 6 Hydrogen-Bonds. Journal of the American
Chemical Society, 1988. 110(4): p. 1318-1319. [0627] 27. Beijer, F.
H., et al., Hydrogen-bonded complexes of diaminopyridines and
diaminotriazines: Opposite effect of acylation on complex
stabilities (vol 61, pg 6374, 1996). Journal of Organic Chemistry,
1996. 61(26): p. 9636-9636. [0628] 28. Higley, M. N., et al., A
modular approach toward block copolymers. Chemistry--a European
Journal, 2005. 11(10): p. 2946-2953. [0629] 29. Burd, C. and M.
Weck, Self-sorting in polymers. Macromolecules, 2005. 38(17): p.
7225-7230. [0630] 30. Stubbs, L. P. and M. Week, Towards a
universal polymer backbone: Design and synthesis of polymeric
scaffolds containing terminal hydrogen-bonding recognition motifs
at each repeating unit. Chemistry--a European Journal, 2003. 9(4):
p. 992-999. [0631] 31. Cheng, C. C., et al., New self-assembled
supramolecular polymers formed by self- complementary sextuple
hydrogen bond motifs. Rsc Advances, 2012. 2(26): p. 9952-9957.
[0632] 32. Park, T., S. C. Zimmerman, and S. Nakashima, A highly
stable quadruply hydrogen-bonded heterocomplex useful for
supramolecular polymer blends. Journal of the American Chemical
Society, 2005. 127(18): p. 6520-6521. [0633] 33. Altintas, O., et
al., Bioinspired dual self-folding of single polymer chains via
reversible hydrogen bonding. Polymer Chemistry, 2012. 3(3): p.
640-651. [0634] 34. Altintas, O., U. Tunca, and C. Barner Kowollik,
Star and miktoarm star block (co)polymers via self-assembly of ATRP
generated polymer segments featuring Hamilton wedge and cyanuric
acid binding motifs. Polymer Chemistry, 2011. 2(5): p. 1146-1155.
[0635] 35. Yang, S. K., A. V. Ambade, and M. Weck, Supramolecular
ABC Triblock Copolymers via One-Pot, Orthogonal Self-Assembly.
Journal of the American Chemical Society, 2010. 132(5): p.
1637-1645. [0636] 36. Burd, C. and M. Weck, Solvent influence on
the orthogonality of noncovalently functionalized terpolymers.
Journal of Polymer Science Part a-Polymer Chemistry, 2008. 46(6):
p. 1936-1944. [0637] 37. Kolomiets, E., et al., Structure and
properties of supramolecular polymers generated from
heterocomplementary monomers linked through sextuple
hydrogen-bonding arrays. Macromolecules, 2006. 39(3): p. 1173-1181.
[0638] 38. Berl, V., et al., Supramolecular polymers generated from
heterocomplementary monomers linked through multiple
hydrogen-bonding arrays--Formation, characterization, and
properties. Chemistry--a European Journal, 2002. 8(5): p.
1227-1244. [0639] 39. Hietala, S., et al., Rheological Properties
of Associative Star Polymers in Aqueous Solutions: Effect of
Hydrophobe Length and Polymer Topology. Macromolecules, 2009.
42(5): p. 1726-1732. [0640] 40. Stavrouli, N., T. Aubry, and C.
Tsitsilianis, Rheological properties of ABA telechelic
polyelectrolyte and ABA polyampholyte reversible hydrogels: A
comparative study. Polymer, 2008. 49(5): p. 1249-1256. [0641] 41.
Suzuki, S., et al., Nonlinear Rheology of Telechelic Associative
Polymer Networks: Shear Thickening and Thinning Behavior of
Hydrophobically Modified Ethoxylated Urethane (HEUR) in Aqueous
Solution. Macromolecules, 2012. 45(2): p. 888-898. [0642] 42.
Chassenieux, C., T. Nicolai, and L. Benyahia, Rheology of
associative polymer solutions. Current Opinion in Colloid &
Interface Science, 2011. 16(1): p. 18-26. [0643] 43. Li, H. K., et
al., Metal-free click polymerization of propiolates and azides:
facile synthesis of functional poly(aroxycarbonyltriazole)s.
Polymer Chemistry, 2012. 3(4): p. 1075-1083. [0644] 44. Izunobi, J.
U. and C. L. Higginbotham, Polymer Molecular Weight Analysis by H-1
NMR Spectroscopy. Journal of Chemical Education, 2011. 88(8): p.
1098-1104. [0645] 45. Nielen, M. W. F., Maldi time-of-flight mass
spectrometry of synthetic polymers. Mass Spectrometry Reviews,
1999. 18(5): p. 309-344. [0646] 46. Meyers, R. A., Encyclopedia of
analytical chemistry: applications, theory, and instrumentation.
2000, Chichester; New York: Wiley. [0647] 47. Yalcin, T., D. C.
Schriemer, and L. Li, Matrix-assisted laser desorption ionization
time-of- flight mass spectrometry for the analysis of polydienes.
Journal of the American Society for Mass Spectrometry, 1997. 8(12):
p. 1220-1229. [0648] 48. Pitet, L. M. and M. A. Hillmyer,
Carboxy-Telechelic Polyolefins by ROMP Using Maleic Acid as a Chain
Transfer Agent. Macromolecules, 2011. 44(7): p. 2378-2381. [0649]
49. Morita, T., et al., A ring-opening metathesis polymerization
(ROMP) approach to carboxyl- and amino-terminated telechelic
poly(butadiene)s. Macromolecules, 2000. 33(17): p. 6621-6623.
[0650] 50. McKinley, G. H. and T. Sridhar, Filament-stretching
rheometry of complex fluids. Annual Review of Fluid Mechanics,
2002. 34(1): p. 375-415. [0651] 51. Paterson, R. W. and F.
Abernathy, Turbulent flow drag reduction and degradation with
dilute polymer solutions. Journal of Fluid Mechanics, 1970. 43(04):
p. 689-710. [0652] 52. Larson, R. G., The structure and rheology of
complex fluids. 1999: Oxford university press New York. 132-142.
[0653] 53. Tant, M. R., Ionomers: synthesis, structure, properties
and applications. 1997: Blackie Academic and Professional, London.
Chap. 4. [0654] 54. Yang, S. K., A. V. Ambade, and M. Weck,
Main-chain supramolecular block copolymers. Chemical Society
Reviews, 2011. 40(1): p. 129-137. [0655] 55. Winnik, M. A. and A.
Yekta, Associative polymers in aqueous solution. Current Opinion in
Colloid & Interface Science, 1997. 2(4): p. 424-436. [0656] 56.
Goldstein, R. E., Model for phase equilibria in micellar solutions
of nonionic surfactants. The Journal of chemical physics, 1986.
84(6): p. 3367-3378. [0657] 57. Hill, T., An Introduction to
Statistical Thermodynamics. NY: Dover, 1986: p. 402-404. [0658] 58.
van Lint, J. H. and R. M. Wilson, A course in combinatorics. 2001:
Cambridge university press. 522-525. [0659] 59. Hillmyer, M. A., S.
T. Nguyen, and R. H. Grubbs, Utility of a ruthenium metathesis
catalyst for the preparation of end-functionalized polybutadiene.
Macromolecules, 1997. 30(4): p. 718-721. [0660] 60. Ji, S., T. R.
Hoye, and C. W. Macosko, Controlled synthesis of high molecular
weight telechelic polybutadienes by ring-opening metathesis
polymerization. Macromolecules, 2004. 37(15): p. 5485-5489. [0661]
61. Nickel, A., et al., A highly efficient olefin metathesis
process for the synthesis of terminal alkenes from fatty acid
esters. Topics in Catalysis, 2012. 55(7-10): p. 518-523. [0662] 62.
Ji, S. X., T. R. Hoye, and C. W. Macosko, Controlled synthesis of
high molecular weight telechelic polybutadienes by ring-opening
metathesis polymerization. Macromolecules, 2004. 37(15): p.
5485-5489. [0663] 63. Lerum, M. F. Z. and W. Chen,
Surface-Initiated Ring-Opening Metathesis Polymerization in the
Vapor Phase: An Efficient Method for Grafting Cyclic Olefins with
Low Strain Energies. Langmuir, 2011. 27(9): p. 5403-5409. [0664]
64. Gilli, G. and P. Gilli, The nature of the hydrogen bond:
outline of a comprehensive hydrogen bond theory. IUCr monographs on
crystallography. 2009, Oxford; New York: Oxford University Press.
147-192. [0665] 65. David, R. L. A., et al., Effects of Pairwise,
Self-Associating Functional Side Groups on Polymer Solubility,
Solution Viscosity, and Mist Control. Macromolecules, 2009. 42(4):
p. 1380-1391. [0666] 66. Pedley, A., et al., Thermodynamics of the
aggregation phenomenon in associating polymer solutions.
Macromolecules, 1990. 23(9): p. 2494-2500. [0667] 67. Lehn, J.-M.,
Toward self-organization and complex matter. science, 2002.
295(5564): p. 2400-2403. [0668] 68. Aida, T., E. Meijer, and S.
Stupp, Functional supramolecular polymers. science, 2012.
335(6070): p. 813-817. [0669] 69. Boal, A. K., et al.,
Self-assembly of nanoparticles into structured spherical and
network aggregates. Nature, 2000. 404(6779): p. 746-748. [0670] 70.
Tayi, A. S., et al., Room-temperature ferroelectricity in
supramolecular networks of charge- transfer complexes. Nature,
2012. 488(7412): p. 485-489. [0671] 71. Ikkala, O. and G. ten
Brinke, Functional materials based on self-assembly of polymeric
supramolecules. science, 2002. 295(5564): p. 2407-2409. [0672] 72.
Li, S.-L., et al., Advanced supramolecular polymers constructed by
orthogonal self- assembly. Chem Soc Rev, 2012. 41(18): p.
5950-5968. [0673] 73. Sijbesma, R. P., et al., Reversible polymers
formed from self-complementary monomers using quadruple hydrogen
bonding. science, 1997. 278(5343): p. 1601-1604. [0674] 74.
Jacobson, H. and W. H. Stockmayer, Intramolecular reaction in
polycondensations. I. The theory of linear systems. The Journal of
chemical physics, 1950. 18(12): p. 1600-1606. [0675] 75. Chen,
Z.-R., et al., Modeling ring-chain equilibria in ring-opening
polymerization of cycloolefins. Macromolecules, 1995. 28(7): p.
2147-2154. [0676] 76. Freed, K. F., Influence of small rings on the
thermodynamics of equilibrium self-assembly. The Journal of
chemical physics, 2012. 136(24): p. 244904. [0677] 77. de Greef, T.
F., et al., Influence of selectivity on the supramolecular
polymerization of AB- type polymers capable of both AA and AB
interactions. J Am Chem Soc, 2008. 130(41): p. 13755-13764. [0678]
78. Petschek, R., P. Pfeuty, and J. C. Wheeler, Equilibrium
polymerization of chains and rings: A bicritical phenomenon.
Physical Review A, 1986. 34(3): p. 2391-2421. [0679] 79. Fang, Y.,
et al., Charge-assisted hydrogen bond-directed self-assembly of an
amphiphilic zwitterionic quinonemonoimine at the liquid-solid
interface. Chemical Communications, 2011. 47(40): p. 11255-11257.
[0680] 80. DeTar, D. F. and R. W. Novak, Carboxylic acid-amine
equilibria in nonaqueous solvents. J Am Chem Soc, 1970. 92(5): p.
1361-1365. [0681] 81. John Knight, F., Antimisting additives for
aviation fuels, 1983, U.S. Pat. No. 2,726,942 (December, 1955)
Arkis et al. 44/56; U.S. Pat. No. 2,936,223 (May, 1960) Lovett et
al. 44/56; U.S. Pat. No. 3,687,644 (August, 1972) Delafield et al.
44/56; U.S. Pat. No. 3,792,984 (February, 1974) Cole et al. 44/62;
U.S. Pat. No. 3,803,034 (April, 1974) Gaydasch 44/62; U.S. Pat. No.
3,812,034 (May, 1974) Gaydasch 44/62; U.S. Pat. No. 3,846,090
(November, 1974) Osmond et al. 44/62; U.S. Pat. No. 3,846,091
(November, 1974) Osmond et al. 44/62; U.S. Pat. No. 4,292,045
(September, 1981) Brooks et al. 44/62; U.S. Pat. No. 4,334,891
(June, 1982) Brooks et al. 44/62: US. [0682] 82. Wright, B. R.,
Hydrocarbon Fuels as A Terrorist Weapon: Safety, Flammability,
Testing, and Protecting Ourselves. The Forensic Examiner, 2004.
13(2): p. 14-19. [0683] 83. Brostow, W., Drag Reduction and
Mechanical Degradation in Polymer-Solutions in Flow. Polymer,
1983. 24(5): p. 631-638. [0684] 84. Hunston, D. L. and J. L. Zakin,
Flow-Assisted Degradation in Dilute Polystyrene Solutions. Polymer
Engineering and Science, 1980. 20(7): p. 517-523. [0685] 85. Yu, J.
F. S., J. L. Zakin, and G. K. Patterson, Mechanical Degradation of
High Molecular- Weight Polymers in Dilute-Solution. Journal of
Applied Polymer Science, 1979. 23(8): p. 2493-2512. [0686] 86.
(U.S.), N. R. C., Committee on Aviation Fuels with Improved Fire
Safety. Aviation fuels with improved fire safety: a proceedings,
1997, National Academy Press: Washington, D.C. [0687] 87. David, R.
L. A., M. H. Wei, and J. A. Kornfield, Effects of pairwise,
donor-accept or functional groups on polymer solubility, solution
viscosity and mist control. Polymer, 2009. 50(26): p. 6323-6330.
[0688] 88. David, R. L. A., Associative polymers as antimisting
agents and other functional materials via thiol-ene coupling, in
Chemistry and Chemical Engineering 2008, California Institute of
Technology: USA. [0689] 89. Henry F. Hamil, N. B. T. X., J. S. A.
T. X. William D. Weatherford, and S. A. T. X. George E. Fodor,
Hydrocarbon compositions of high elongational viscosity and process
for making the same, 1988, U.S. Pat. No. 2,807,597 (September,
1957) Sonnenfeld et al. 60/29 . . . 7; U.S. Pat. No. 2,921,043
(January, 1960) Uraneck 60/45 . . . 5; U.S. Pat. No. 3,091,604
(May, 1963) Lukens 60/87 . . . 3; U.S. Pat. No. 3,395,134 (July,
1968) D'Aleilo 60/89 . . . 5; U.S. Pat. No. 3,467,604 (September,
1969) Michaels 60/2 . . . 5; U.S. Pat. No. 3,574,575 (April, 1971)
Gee et al. 44/62; U.S. Pat. No. 3,579,613 (May, 1971) Schaper et
al. 260/901; U.S. Pat. No. 3,658,492 (April, 1972) Messina 44/62;
U.S. Pat. No. 3,812,034 (May, 1974) Gaydasch 44/62; U.S. Pat. No.
3,920,605 (November, 1975) Sato et al. 0 4/2.1.7; U.S. Pat. No.
4,205,143 (May, 1980) Goodman 525/213; U.S. Pat. No. 4,288,511
(September, 1981) Myers et al. 430/17; U.S. Pat. No. 4,334,891
(June, 1982) Brooks et al. 44/62: US. [0690] 90. Ilan Duvdevani, L.
N. J., et al., Antimisting system for hydrocarbon fluids, 1985,
U.S. Pat. No. 3,475,358 (October, 1969) Bixler 524/521; U.S. Pat.
No. 3,546,142 (December, 1970) Michaels 524/521; U.S. Pat. No.
3,867,330 (February, 1975) Frisque 524/516; U.S. Pat. No. 4,118,439
(October, 1978) Marze 525/203: US. [0691] 91. Willauer, H. D., et
al., Flammability of aerosols generated by a rotary atomizer.
Combustion Science and Technology, 2007. 179(7): p. 1303-1326.
[0692] 92. Yaffee, M. L., Antimisting Research and Development for
Commercial Aircraft--Final Summary Report, in FAA report
DOT/FAA/CT-86/71986, Federal Aviation Administration Technical
Center: Atlantic City Airport, NJ. [0693] 93. Eagar, T. W. and C.
Musso, Why did the World Trade Center collapse? Science,
engineering, and speculation. Jom-Journal of the Minerals Metals
& Materials Society, 2001. 53(12): p. 8-11. [0694] 94. Aviation
Fuels with Improved Fire Safety: A Proceedings, in NRC Proceedings
1997: Washington D.C. [0695] 95. Wright, B., Assessment of Concepts
and Research for Commercial Aviation Fire-Safe Fuel, 2000, NASA
Lewis Research Center. [0696] 96. Joseph, D. D., G. S. Beavers, and
T. Funada, Rayleigh-Taylor instability of viscoelastic drops at
high Weber numbers. Journal of Fluid Mechanics, 2002. 453: p.
109-132. [0697] 97. Anna, S. L. and G. H. McKinley,
Elasto-capillary thinning and breakup of model elastic liquids.
Journal of Rheology, 2001. 45(1): p. 115-138. [0698] 98. Goldin,
M., et al., Breakup of a Laminar Capillary Jet of a Viscoelastic
Fluid. Journal of Fluid Mechanics, 1969. 38: p. 689-&. [0699]
99. Yu, J. H., S. V. Fridrikh, and G. C. Rutledge, The role of
elasticity in the formation of electrospun fibers. Polymer, 2006.
47(13): p. 4789-4797. [0700] 100. Christanti, Y. and L. M. Walker,
Effect of fluid relaxation time of dilute polymer solutions on jet
breakup due to a forced disturbance. Journal of Rheology, 2002.
46(3): p. 733-748. [0701] 101.Kowalik, R. M., et al., Enhanced Drag
Reduction Via Interpolymer Associations. Journal of Non-Newtonian
Fluid Mechanics, 1987. 24(1): p. 1-10. [0702] 102.Schulz, D. N., et
al., Hydrocarbon-Soluble Associating Polymers as Antimisting and
Drag-Reducing Agents. Acs Symposium Series, 1991. 462: p.
176-189.
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References