U.S. patent application number 13/660747 was filed with the patent office on 2013-12-05 for controlling melt fracture in bimodal resin pipe.
This patent application is currently assigned to CHEVRON PHILLIPS CHEMICAL COMPANY LP. The applicant listed for this patent is CHEVRON PHILLIPS CHEMICAL COMPANY LP. Invention is credited to Paul J. Deslauriers, Yongwoo Inn, David C. Rohlfing, Ashish M. Sukhadia, Qing Yang.
Application Number | 20130319131 13/660747 |
Document ID | / |
Family ID | 49668641 |
Filed Date | 2013-12-05 |
United States Patent
Application |
20130319131 |
Kind Code |
A1 |
Inn; Yongwoo ; et
al. |
December 5, 2013 |
Controlling Melt Fracture in Bimodal Resin Pipe
Abstract
A method of improving processing of polyethylene resins
comprising obtaining a plurality of multimodal
metallocene-catalyzed polyethylene samples measuring the shear
stress as a function of shear rate for the plurality of multimodal
metallocene-catalyzed polyethylene samples using capillary
rheometry wherein the measuring yields values for a magnitude of
slip-stick, a stress for smooth to matte transition, and a shear
rate for smooth to matte transition; and identifying from the
plurality of multimodal metallocene-catalyzed polyethylene samples
individual multimodal metallocene-catalyzed polyethylene resins
having a reduced tendency to melt fracture characterized by a
magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
Inventors: |
Inn; Yongwoo; (Bartlesville,
OK) ; Deslauriers; Paul J.; (Owasso, OK) ;
Yang; Qing; (Bartlesville, OK) ; Sukhadia; Ashish
M.; (Bartlesville, OK) ; Rohlfing; David C.;
(Bloomington, IN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CHEVRON PHILLIPS CHEMICAL COMPANY LP |
The Woodlands |
TX |
US |
|
|
Assignee: |
CHEVRON PHILLIPS CHEMICAL COMPANY
LP
The Woodlands
TX
|
Family ID: |
49668641 |
Appl. No.: |
13/660747 |
Filed: |
October 25, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61654018 |
May 31, 2012 |
|
|
|
Current U.S.
Class: |
73/841 ;
702/43 |
Current CPC
Class: |
G06F 17/10 20130101;
G16C 20/20 20190201; F16L 9/00 20130101; G01N 3/24 20130101; C08L
23/04 20130101; G01N 11/04 20130101; C08F 110/02 20130101; Y10T
428/139 20150115; C08L 23/06 20130101; F16L 9/12 20130101 |
Class at
Publication: |
73/841 ;
702/43 |
International
Class: |
G01N 3/24 20060101
G01N003/24; G06F 17/10 20060101 G06F017/10 |
Claims
1. A method of improving processing of polyethylene resins
comprising: obtaining a plurality of multimodal
metallocene-catalyzed polyethylene samples; measuring the shear
stress as a function of shear rate for the plurality of multimodal
metallocene-catalyzed polyethylene samples using capillary
rheometry wherein the measuring yields values for a magnitude of
slip-stick, a stress for smooth to matte transition, and a shear
rate for smooth to matte transition; and identifying from the
plurality of multimodal metallocene-catalyzed polyethylene samples
individual multimodal metallocene-catalyzed polyethylene resins
having a reduced tendency to melt fracture characterized by a
magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
2. The method of claim 1 wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples comprises a
polymer blend.
3. The method of claim 1 wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples comprises a
higher molecular weight component and a lower molecular weight
component.
4. The method of claim 3 wherein the higher molecular weight
component has a peak molecular weight ranging from about 67 kg/mol
to about 600 kg/mol and the lower molecular weight component has a
peak molecular weight ranging from about 25 kg/mol to about 65
kg/mol.
5. The method of claim 1 wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples has a
molecular weight distribution of from about 5 to about 30.
6. The method of claim 1 wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples has a
magnitude of stick-slip of from greater than about 300 psi to about
1500 psi.
7. The method of claim 1 wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples has a shear
rate for smooth to matte transition of from greater than about 10
s.sup.-1 to about 100 s.sup.-1.
8. The method of claim 1 wherein the melt fracture is sharkskin
melt fracture, slip-stick fracture or gross melt fracture.
9. A method of improving processing of polyethylene resins
comprising: obtaining a known molecular weight distribution, a
known magnitude of slip-stick, a known stress for smooth to matte
transition, and a known shear rate for smooth to matte transition,
for each of a plurality of polyethylene resins; performing
chemometric analysis to determine an analytical relationship
between the known molecular weight distribution, the known
magnitude of slip-stick, the known stress for smooth to matte
transition, and the known shear rate for smooth to matte transition
for the plurality of polyethylene resins; obtaining a plurality of
multimodal metallocene-catalyzed polyethylene resins, each having a
known molecular weight distribution, an unknown magnitude of
slip-stick, an unknown stress for smooth to matte transition, and
an unknown shear rate for smooth to matte transition; utilizing the
analytical relationship to determine a value for the unknown
magnitude of slip-stick, a value for the unknown stress for smooth
to matte transition, and the unknown shear rate for smooth to matte
transition for each of the plurality of multimodal
metallocene-catalyzed polyethylene samples; and identifying from
the plurality of multimodal metallocene-catalyzed polyethylene
resins individual multimodal metallocene-catalyzed polyethylene
resins having a reduced tendency to melt fracture characterized by
a magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
10. The method of claim 9 wherein the analytical relationship is a
mathematical equation.
11. The method of claim 9 wherein the analytical relationship is
established using at least one chemometric technique selected from
the group consisting of Partial Least Squares Regression (PLS),
Multilinear Regression Analysis (MLR), Principal Components
Regression (PCR), Principal Component Analysis (PCA) and
Discriminant Analysis, Design of Experiment (DOE) and Response
Surface Methodologies.
12. The method of claim 9 wherein the plurality of polyethylene
resins comprises equal to or greater than about 10 samples.
13. The method of claim 9 wherein the known molecular weight
distribution is from about 5 to about 30.
14. The method of claim 9 wherein the known magnitude of slip-stick
is from about 300 psi to about 1500 psi.
15. The method of claim 9 wherein the known stress for smooth to
matte transition is less than about 200 kPa.
16. The method of claim 9 wherein the known shear rate for smooth
to matte transition is from greater than about 10 s.sup.-1 to about
100 s.sup.-1.
17. The method of claim 9 wherein the individual multimodal
metallocene-catalyzed polyethylene resins having a reduced tendency
to melt fracture comprise a higher molecular weight component and a
lower molecular weight component.
18. The method of claim 17 wherein the higher molecular weight
component has a peak molecular weight ranging from about 67 kg/mol
to about 600 kg/mol and the lower molecular weight component has a
peak molecular weight ranging from about 25 kg/mol to about 65
kg/mol.
19. The method of claim 9 wherein the individual multimodal
metallocene-catalyzed polyethylene resins having a reduced tendency
to melt fracture comprise a comonomer.
20. The method of claim 9 further comprising identifying individual
multimodal metallocene-catalyzed polyethylene resins having an
increased tendency to melt fracture.
21. The method of claim 1 further comprising forming one or more of
the individual multimodal metallocene-catalyzed polyethylene resins
having a reduced tendency to melt fracture into an article.
22. The method of claim 9 further comprising forming one or more of
the individual multimodal metallocene-catalyzed polyethylene resins
having a reduced tendency to melt fracture into an article.
23. The method of claim 1 further comprising providing one or more
of the individual multimodal metallocene-catalyzed polyethylene
resins having a reduced tendency to melt fracture to a user in need
thereof.
24. The method of claim 9 further comprising providing one or more
of the individual multimodal metallocene-catalyzed polyethylene
resins having a reduced tendency to melt fracture to a user in need
thereof.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application is a non-provisional of and claims
priority to U.S. Provisional Application No. 61/654,018, filed on
May 31, 2012 and entitled "Controlling Melt Fracture in Bimodal
Resin Pipe," which is incorporated by reference herein in its
entirety.
TECHNICAL FIELD
[0002] The present disclosure relates to polyethylene compositions
and pipe made from same, more specifically to multimodal
polyethylene compositions having improved processing
characteristics.
BACKGROUND
[0003] Polymeric pipes have replaced metal pipes in many
applications such as high-pressure fluid transportation. Polymeric
pipes have several advantages over metal pipes including being of
relatively lighter weight, more corrosion resistant, inexpensive,
more thermally and electrically insulative, tougher, more durable
and more easily shaped during manufacture. Such pipes are exposed
to numerous stresses during their lifetime that may result in
cracks or breaks that are expensive to repair, especially in
situations where the pipe is buried in a structure or underground.
As such polymeric pipes may be required to meet industry-defined
standards depending on their intended use.
[0004] Polymeric material used in the fabrication of pipe has often
been optimized to provide a more durable end-use article. One such
optimization may involve the use of a multimodal polymer
composition as the polymeric material. A challenge to the use of a
multimodal polymer composition as the polymeric material in the
fabrication of pipe is that these compositions, when melted to form
a polymer melt, may display poor processing characteristics such as
melt fractures, which are surface irregularities that occur during
the extrusion process when the production rate is increased. The
poor processing characteristics of these materials may result in a
reduced production rate and/or product having undesirable physical
properties and/or appearance. Thus there is a need for improved
polymeric compositions and methods of making and using same to
fabricate polymeric pipe.
SUMMARY
[0005] Disclosed herein is a method of improving processing of
polyethylene resins comprising obtaining a plurality of multimodal
metallocene-catalyzed polyethylene samples; measuring the shear
stress as a function of shear rate for the plurality of multimodal
metallocene-catalyzed polyethylene samples using capillary
rheometry wherein the measuring yields values for a magnitude of
slip-stick, a stress for smooth to matte transition, and a shear
rate for smooth to matte transition; and identifying from the
plurality of multimodal metallocene-catalyzed polyethylene samples
individual multimodal metallocene-catalyzed polyethylene resins
having a reduced tendency to melt fracture characterized by a
magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
[0006] Also disclosed herein is a method of improving processing of
polyethylene resins comprising obtaining a known molecular weight
distribution, a known magnitude of slip-stick, a known stress for
smooth to matte transition, and a known shear rate for smooth to
matte transition, for each of a plurality of polyethylene resins;
performing chemometric analysis to determine an analytical
relationship between the known molecular weight distribution, the
known magnitude of slip-stick, the known stress for smooth to matte
transition, and the known shear rate for smooth to matte transition
for the plurality of polyethylene resins; obtaining a plurality of
multimodal metallocene-catalyzed polyethylene resins, each having a
known molecular weight distribution, an unknown magnitude of
slip-stick, an unknown stress for smooth to matte transition, and
an unknown shear rate for smooth to matte transition; utilizing the
analytical relationship to determine a value for the unknown
magnitude of slip-stick, a value for the unknown stress for smooth
to matte transition, and the unknown shear rate for smooth to matte
transition for each of the plurality of multimodal
metallocene-catalyzed polyethylene samples; and identifying from
the plurality of multimodal metallocene-catalyzed polyethylene
resins individual multimodal metallocene-catalyzed polyethylene
resins having a reduced tendency to melt fracture characterized by
a magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIG. 1A is a schematic of the melt fracture behavior of a
conventional unimodal polyethylene composition.
[0008] FIG. 1B is a schematic of the melt fracture behavior of a
multimodal polyethylene base resin of the type disclosed
herein.
[0009] FIG. 2 is a plot of the predicted slip-stick values as a
function of the measured slip-stick values for the calibration
samples from Example 1.
[0010] FIG. 3 is a plot of the predicted slip-stick values as a
function of the measured slip-stick values for the calibration and
validation samples from Example 1.
[0011] FIG. 4 is a plot of the predicted onset for smooth to matte
transition as a function of the measured onset for smooth to matte
transition for the calibration samples from Example 1.
[0012] FIG. 5 is a plot of the predicted onset for smooth to matte
transition as a function of the measured onset for smooth to matte
transition for the calibration and validation samples from Example
1.
[0013] FIG. 6 is a plot of the predicted onset for the matte to
wavy transition as a function of the measured onset for the matte
to wavy transition for the calibration samples from Example 1.
[0014] FIG. 7 is a depiction of the molecular weight distribution
of a bimodal polymer sample.
[0015] FIG. 8 is a FIG. 8 is a plot of the magnitude of slip-stick
as a function of the weight fraction of the lower molecular weight
(LMW) component and the peak molecular weight.
[0016] FIG. 9 is a plot of the stress for the smooth to matte
transition as a function of the peak molecular weights of
components P1 and P2.
[0017] FIG. 10 is a schematic illustration of an embodiment of a
computer program product for implementing the disclosed
functionalities.
DETAILED DESCRIPTION
[0018] Disclosed herein are methods of identifying
metallocene-catalyzed polyethylene resins having desired processing
characteristics. In an embodiment, the method comprises obtaining a
plurality of multimodal metallocene-catalyzed polyethylene resins
and subjecting these resins to capillary rheometry in order to
measure the shear stress as a function of shear rate. The
rheometric measurements may be used to identify multimodal
metallocene-catalyzed polyethylene resins having one or more
desired processing characteristics.
[0019] Further disclosed herein are methods of making
metallocene-catalyzed polyethylene resins (also termed a PE base
resin), general features of said metallocene-catalyzed polyethylene
resins, methods for identifying metallocene-catalyzed polyethylene
resins having desired processing characteristics, methods of
modifying metallocene-catalyzed polyethylene resins to provide
desired processing characteristics, and methods of preparing
articles from metallocene-catalyzed polyethylene resins having
desired processing characteristics.
[0020] In an embodiment, a PE base resin of the present disclosure
is produced by any olefin polymerization method, using various
types of polymerization reactors and catalyst systems. As used
herein, a "base resin" refers to a resin that has not undergone a
modification to improve processability of the type described
herein. In other words, base resin refers to the PE starting
material that is accessed and modified according to the present
disclosure. Accordingly, the base resin may include virgin PE resin
or "fluff" as recovered from a polymerization process and prior to
the addition of any additives or modifiers and/or includes PE resin
recovered from a polymerization process that has undergone further
processing such as pelletization, which may include the addition of
a base additive package of the type commonly added to commercial PE
resins (e.g., antioxidants, stabilizer). In an embodiment, the PE
base resin has not undergone any modification (e.g., inclusion of
processing aids.) to improve the melt fracture characteristics of
the material. In an embodiment, the PE base resin does not include
any polymer processing aids (PPAs) of the type known to those
skilled in the art.
[0021] In an embodiment, the catalyst system for preparation of the
PE base resin comprises at least two metallocene complexes. Herein,
the term "metallocene" describes a compound comprising at least one
.eta..sup.3 to .eta..sup.5-cycloalkadienyl-type moiety, wherein
.eta..sup.3 to .eta..sup.5-cycloalkadienyl moieties include
cyclopentadienyl ligands, indenyl ligands, fluorenyl ligands, and
the like, including partially saturated or substituted derivatives
or analogs of any of these. Possible substituents on these ligands
include hydrogen, therefore the description "substituted
derivatives thereof" in this disclosure comprises partially
saturated ligands such as tetrahydroindenyl, tetrahydrofluorenyl,
octahydrofluorenyl, partially saturated indenyl, partially
saturated fluorenyl, substituted partially saturated indenyl,
substituted partially saturated fluorenyl, and the like. The
metallocenes may be combined with a solid activator, an aluminum
alkyl compound, an olefin monomer, and an olefin comonomer to
produce the desired bimodal polyolefin. The activity and the
productivity of the catalyst may be relatively high. As used
herein, the activity refers to the grams of polymer produced per
gram of solid catalyst charged per hour, and the productivity
refers to the grams of polymer produced per gram of solid catalyst
charged. Examples of such catalyst systems are disclosed in U.S.
patent application Ser. No. 11/209,006, filed Aug. 22, 2005 and
entitled "Polymerization Catalysts And Process For Producing
Bimodal Polymers In A Single Reactor," and U.S. patent application
Ser. No. 11/208,077, filed Aug. 19, 2005 and entitled
"Polymerization Catalysts and Process for Producing Bimodal
Polymers in a Single Reactor," each of which is incorporated herein
in its entirety.
[0022] As used herein, "polymerization reactor" includes any
reactor capable of polymerizing olefin monomers (e.g., ethylene) to
produce homopolymers and/or copolymers (e.g., PE homopolymers
and/or copolymers). Homopolymers and/or copolymers produced in the
reactor may be referred to as resin and/or polymers. The various
types of reactors include, but are not limited to those that may be
referred to as batch, slurry, gas-phase, solution, high pressure,
tubular, autoclave, or other reactor and/or reactors. Gas phase
reactors may comprise fluidized bed reactors or staged horizontal
reactors. Slurry reactors may comprise vertical and/or horizontal
loops. High pressure reactors may comprise autoclave and/or tubular
reactors. Reactor types may include batch and/or continuous
processes. Continuous processes may use intermittent and/or
continuous product discharge or transfer. Processes may also
include partial or full direct recycle of un-reacted monomer,
un-reacted comonomer, catalyst and/or co-catalysts, diluents,
and/or other materials of the polymerization process.
[0023] Polymerization reactor systems of the present disclosure may
comprise one type of reactor in a system or multiple reactors of
the same or different type, operated in any suitable configuration.
Production of polymers in multiple reactors may include several
stages in at least two separate polymerization reactors
interconnected by a transfer system making it possible to transfer
the polymers resulting from the first polymerization reactor into
the second reactor. Alternatively, polymerization in multiple
reactors may include the transfer, either manual or automatic, of
polymer from one reactor to subsequent reactor or reactors for
additional polymerization. Alternatively, multi-stage or multi-step
polymerization may take place in a single reactor, wherein the
conditions are changed such that a different polymerization
reaction takes place.
[0024] The desired polymerization conditions in one of the reactors
may be the same as or different from the operating conditions of
any other reactors involved in the overall process of producing the
polymer of the present disclosure. Multiple reactor systems may
include any combination including, but not limited to multiple loop
reactors, multiple gas phase reactors, a combination of loop and
gas phase reactors, multiple high pressure reactors or a
combination of high pressure with loop and/or gas reactors. The
multiple reactors may be operated in series or in parallel. In an
embodiment, any arrangement and/or any combination of reactors may
be employed to produce the polymer of the present disclosure.
[0025] According to one embodiment, the polymerization reactor
system may comprise at least one loop slurry reactor. Such reactors
are commonplace, and may comprise vertical or horizontal loops.
Monomer, diluent, catalyst system, and optionally any comonomer may
be continuously fed to a loop slurry reactor, where polymerization
occurs. Generally, continuous processes may comprise the continuous
introduction of a monomer, a catalyst, and/or a diluent into a
polymerization reactor and the continuous removal from this reactor
of a suspension comprising polymer particles and the diluent.
Reactor effluent may be flashed to remove the liquids that comprise
the diluent from the solid polymer, monomer and/or comonomer.
Various technologies may be used for this separation step including
but not limited to, flashing that may include any combination of
heat addition and pressure reduction; separation by cyclonic action
in either a cyclone or hydrocyclone; separation by centrifugation;
or other appropriate method of separation.
[0026] Typical slurry polymerization processes (also known as
particle-form processes) are disclosed in U.S. Pat. Nos. 3,248,179,
4,501,885, 5,565,175, 5,575,979, 6,239,235, 6,262,191 and
6,833,415, for example; each of which are herein incorporated by
reference in their entirety.
[0027] Suitable diluents used in slurry polymerization include, but
are not limited to, the monomer being polymerized and hydrocarbons
that are liquids under reaction conditions. Examples of suitable
diluents include, but are not limited to, hydrocarbons such as
propane, cyclohexane, isobutane, n-butane, n-pentane, isopentane,
neopentane, and n-hexane. Some loop polymerization reactions can
occur under bulk conditions where no diluent is used. An example is
polymerization of propylene monomer as disclosed in U.S. Pat. No.
5,455,314, which is incorporated by reference herein in its
entirety.
[0028] According to yet another embodiment, the polymerization
reactor may comprise at least one gas phase reactor. Such systems
may employ a continuous recycle stream containing one or more
monomers continuously cycled through a fluidized bed in the
presence of the catalyst under polymerization conditions. A recycle
stream may be withdrawn from the fluidized bed and recycled back
into the reactor. Simultaneously, polymer product may be withdrawn
from the reactor and new or fresh monomer may be added to replace
the polymerized monomer. Such gas phase reactors may comprise a
process for multi-step gas-phase polymerization of olefins, in
which olefins are polymerized in the gaseous phase in at least two
independent gas-phase polymerization zones while feeding a
catalyst-containing polymer formed in a first polymerization zone
to a second polymerization zone. One type of gas phase reactor is
disclosed in U.S. Pat. Nos. 4,588,790, 5,352,749, and 5,436,304,
each of which is incorporated by reference in its entirety
herein.
[0029] According to still another embodiment, a high pressure
polymerization reactor may comprise a tubular reactor or an
autoclave reactor. Tubular reactors may have several zones where
fresh monomer, initiators, or catalysts are added. Monomer may be
entrained in an inert gaseous stream and introduced at one zone of
the reactor. Initiators, catalysts, and/or catalyst components may
be entrained in a gaseous stream and introduced at another zone of
the reactor. The gas streams may be intermixed for polymerization.
Heat and pressure may be employed appropriately to obtain optimal
polymerization reaction conditions.
[0030] According to yet another embodiment, the polymerization
reactor may comprise a solution polymerization reactor wherein the
monomer is contacted with the catalyst composition by suitable
stirring or other means. A carrier comprising an organic diluent or
excess monomer may be employed. If desired, the monomer may be
brought in the vapor phase into contact with the catalytic reaction
product, in the presence or absence of liquid material. The
polymerization zone is maintained at temperatures and pressures
that will result in the formation of a solution of the polymer in a
reaction medium. Agitation may be employed to obtain better
temperature control and to maintain uniform polymerization mixtures
throughout the polymerization zone. Adequate means are utilized for
dissipating the exothermic heat of polymerization.
[0031] Polymerization reactors suitable for the present disclosure
may further comprise any combination of at least one raw material
feed system, at least one feed system for catalyst or catalyst
components, and/or at least one polymer recovery system. Suitable
reactor systems for the present invention may further comprise
systems for feedstock purification, catalyst storage and
preparation, extrusion, reactor cooling, polymer recovery,
fractionation, recycle, storage, loadout, laboratory analysis, and
process control.
[0032] Conditions that are controlled for polymerization efficiency
and to provide polymer properties include, but are not limited to
temperature, pressure, type and quantity of catalyst or
co-catalyst, and the concentrations of various reactants.
Polymerization temperature can affect catalyst productivity,
polymer molecular weight and molecular weight distribution.
Suitable polymerization temperatures may be any temperature below
the de-polymerization temperature, according to the Gibbs Free
Energy Equation. Typically, this includes from about 60.degree. C.
to about 280.degree. C., for example, and/or from about 70.degree.
C. to about 110.degree. C., depending upon the type of
polymerization reactor and/or polymerization process.
[0033] Suitable pressures will also vary according to the reactor
and polymerization process. The pressure for liquid phase
polymerization in a loop reactor is typically less than 1000 psig.
Pressure for gas phase polymerization is usually at about 200-500
psig. High pressure polymerization in tubular or autoclave reactors
is generally run at about 20,000 to 75,000 psig. Polymerization
reactors can also be operated in a supercritical region occurring
at generally higher temperatures and pressures. Operation above the
critical point of a pressure/temperature diagram (supercritical
phase) may offer advantages.
[0034] The concentration of various reactants can be controlled to
produce polymers with certain physical and mechanical properties.
The proposed end-use product that will be formed by the polymer and
the method of forming that product may be varied to determine the
desired final product properties. Mechanical properties include,
but are not limited to tensile strength, flexural modulus, impact
resistance, creep, stress relaxation and hardness tests. Physical
properties include, but are not limited to density, molecular
weight, molecular weight distribution, melting temperature, glass
transition temperature, temperature melt of crystallization,
density, stereoregularity, crack growth, short chain branching,
long chain branching and rheological measurements.
[0035] The concentrations of monomer, co-monomer, hydrogen,
co-catalyst, modifiers, and electron donors are generally important
in producing specific polymer properties. Comonomer may be used to
control product density. Hydrogen may be used to control product
molecular weight. Co-catalysts may be used to alkylate, scavenge
poisons and/or control molecular weight. The concentration of
poisons may be minimized, as poisons may impact the reactions
and/or otherwise affect polymer product properties. Modifiers may
be used to control product properties and electron donors may
affect stereoregularity.
[0036] In an embodiment, a PE base resin of the type described
herein comprises a polymer blend, e.g., a blend of two or more
component polymers such as a higher molecular weight (HMW)
component and a lower molecular weight (LMW) component. The polymer
blend may be of any type compatible with and able to produce a PE
base resin of the type described herein. For example, the PE base
resin may be a physical or mechanical blend of polymers,
alternatively the PE base resin may be a reactor blend of polymers.
In an embodiment, a process for the preparation of a PE base resin
of the type disclosed herein comprises the preparation of each
component of the PE base resin independent of the other components.
The process may comprise polymerization of an alpha-olefin monomer
in the presence of a catalyst system under a first set of reaction
conditions to form a first component of the PE base resin. The
process may further comprise polymerization of an alpha-olefin in
the presence of a catalyst system under a second set of reaction
conditions to form a second component of the PE base resin. The
formation of the second component may be carried out in the
presence of the first component (e.g., a reactor blend) or in the
absence of the first component (and the two components subsequently
blended, for example via mechanical blending, co-extrusion, etc.).
It is to be understood adjustments of the reaction conditions to
which the catalyst system is subjected during polymerization may
substantively alter the resultant product. A process for
preparation of a PE base resin may further comprise contacting the
first and second components utilizing any appropriate methodology
(e.g., mechanical mixing). In such an embodiment, the resultant PE
base resin comprises a physical blend of the first and second
component.
[0037] Alternatively, a process for the preparation of a PE base
resin of the type disclosed herein comprises polymerization of an
alpha-olefin monomer in the presence of at least two different
catalytic materials or catalysts, for example a catalyst system
comprising at least two transition metal complexes. For example,
the catalyst system may comprise a first and a second transition
metal complex wherein the first and second transition metal
complexes are different. In an embodiment, the catalyst system
comprises at least two metallocene complexes and results in the
simultaneous formation of the two components of the PE base resin
when both catalysts are employed in a single reactor. In the
alternative, a first catalyst system comprising a first metallocene
complex that may be associated with a first reactor. Alpha-olefin
monomer may be contacted with the first catalyst system and reactor
and conditions adjusted such that polymerization of the
alpha-olefin monomer results and a first component of the PE base
resin is produced. The first component may then be contacted with a
second catalyst system and alpha-olefin monomer under conditions to
result in the polymerization of the alpha-olefin monomer and
formation of the second component of the PE base resin. In such an
embodiment, the components of the PE base resin are produced
sequentially. In the aforementioned embodiments employing at least
two metallocene complexes, the PE base resin formed may be
described as a reactor blend of the two components.
[0038] In an embodiment, the PE base resin comprises a multimodal
PE resin. Herein, the "modality" of a polymer resin refers to the
form of its molecular weight distribution curve, i.e., the
appearance of the graph of the polymer weight fraction as a
function of its molecular weight. The polymer weight fraction
refers to the weight fraction of molecules of a given size. A
polymer having a molecular weight distribution curve showing a
single peak may be referred to as a unimodal polymer, a polymer
having curve showing two distinct peaks may be referred to as
bimodal polymer, a polymer having a curve showing three distinct
peaks may be referred to as trimodal polymer, etc. Polymers having
molecular weight distribution curves showing more than one peak may
be collectively referred to as multimodal polymers or resins.
Unless otherwise indicated herein, references to a PE base resin is
understood to include a multimodal PE base resin, including but not
limited to a resin having a HMW component and a LMW component that
is produced from a catalyst system comprising at least two
metallocene complexes (e.g., a dual-metallocene catalyst). In an
embodiment, the PE base resin is a metallocene-catalyzed,
multimodal (e.g., bimodal) polyethylene copolymer with 1-hexene. In
an embodiment, the PE base resin is a dual-metallocene-catalyzed,
multimodal (e.g., bimodal) polyethylene copolymer. Examples of
suitable comonomers include without limitation unsaturated
hydrocarbons having from 3 to 20 carbon atoms such as propylene,
1-butene, 1-pentene, 1-hexene, 3-methyl-1-butene,
4-methyl-1-pentene, 1-heptene, 1-octene, 1-nonene, 1-decene, and
mixtures thereof. In an aspect, the comonomer is 1-hexene.
[0039] A polymer resin may have two or more components that may be
distinguishable from one another, for example based upon their
individual composition and/or molecular weight distribution. A
molecular weight distribution curve may be prepared for each
individual component of the polymer resin. For example, the
molecular weight distribution curve for the individual components
of the polymer resin may display a single peak and thus be
unimodal. The molecular weight distribution curves for the
individual components may be superimposed onto a common chart to
form the weight distribution curve for the polymer resin as a
whole. Upon such superimposition, the resultant curve for the
polymer resin as a whole may be multimodal or show n distinct peaks
corresponding to n polymer components of differing molecular weight
distributions. For example, a bimodal polymer resin may show two
distinct peaks corresponding to two individual components. For
example, a bimodal polymer resin may have a first component that
may be generally characterized as a higher molecular weight polymer
component and a second component that may be generally
characterized as a lower molecular weight polymer component. A
trimodal polymer composition may show three distinct peaks
corresponding to three individual polymer components.
Alternatively, superimposition of the molecular weight distribution
curves from the individual components may show a single peak that
is broadened in comparison with the curves for the individual
components corresponding to polymer fractions having different but
overlapping molecular weight distributions. Such compositions while
appearing unimodal may be deconvoluted into their individual
component peaks and can thus be shown to be a multimodal
composition.
[0040] The individual components of the PE base resin may comprise
a homopolymer, a copolymer, or blends thereof. In an aspect, the
components of the PE base resin may be a copolymer comprised of a
polymer of ethylene with one or more comonomers such as alpha
olefins. In an aspect, the PE base resin comprises a higher
molecular weight (HMW) component and a lower molecular weight (LMW)
component, for example a HMW copolymer component (e.g., a copolymer
of ethylene and 1-hexene) and a LMW copolymer component (e.g., a
copolymer of ethylene and 1-hexane). In an embodiment, the PE base
resin is a dual-metallocene polyethylene having a HMW component
comprised of polyethylene copolymer with 1-hexene and a LMW
component comprised of polyethylene copolymer with 1-hexene.
[0041] In an embodiment, the PE base resin comprises a LMW
component and a HMW component, wherein the LMW component is present
in the PE base resin in a weight fraction of from about 0.3 to
about 0.7, alternatively from about 0.4 to about 0.7 or
alternatively from about 0.5 to about 0.65 based on total weight of
the PE base resin, and the HMW component makes up the balance of
the PE base resin. In an embodiment, PE base resins of the type
disclosed herein may be characterized by a LMW component having a
peak molecular weight (M.sub.p) ranging from about 25 kg/mol to
about 65 kg/mol, alternatively from about 35 kg/mol to about 60
kg/mol, or alternatively from about 40 kg/mol to about 50 kg/mol
and a HMW component having a M.sub.p ranging from about 67 kg/mol
to about 600 kg/mol, alternatively from about 200 kg/mol to about
600 kg/mol, or alternatively from about 400 kg/mol to about 500
kg/mol. Herein, the M.sub.p refers to the peak molecular
weight.
[0042] It is to be understood that in the case of polymer blends
(e.g., physical or reactor blends) the individual components of the
blend may be described approximately herein. Thus, any metrics or
characteristics provided herein for the individual components of a
polymer blend are approximated for that portion of the material
corresponding to the designated component and are provided as
values for some portion of the material within the larger context
of the entire blend. Thus where it is not possible to measure the
characteristics of an individual component (e.g., reactor blend)
such characteristics when represented herein may contain some
contribution from other components of the blend.
[0043] The molecular weight distribution (MWD) of the PE base resin
may be characterized by the ratio of the weight average molecular
weight to the number average molecular weight, which is also
referred to as the polydispersity index (PDI) or more simply as
polydispersity. The number average molecular weight is the common
average of the molecular weights of the individual polymers
calculated by measuring the molecular weight of n polymer
molecules, summing the weights, and dividing by n. The weight
average molecular weight describes the molecular weight
distribution of a polymer composition and is calculated according
to equation 1:
M n = i N i M i 2 i N i M i ( 1 ) ##EQU00001##
where N.sub.i is the number of molecules of molecular weight
M.sub.i. All molecular weight averages are expressed in gram per
mole (g/mol).
[0044] In an embodiment, the individual components of the PE base
resin (e.g., the LMW component and the HMW component) have narrow
molecular weight distributions (MWD). More specifically, the HMW
component may have a PDI of from about 2 to about 5, alternatively
from about 2 to about 4, or alternatively from about 2 to about 3.
The LMW component may have a PDI of from about 2 to about 5,
alternatively from about 2 to about 4, or alternatively from about
2 to about 3. The resultant PE base resin (i.e., including both the
LMW and HMW components) may have a broad MWD of from about 5 to
about 30, alternatively from about 5 to about 20, or alternatively
from about 5 to about 10.
[0045] In an embodiment, a PE base resin prepared as described
herein may display one or more types of melt fracture during
polymer melt formation and processing such as extrusion molding.
The type, extent, and conditions under which the polymer melt
experiences melt fracture may vary depending on the polymer
microstructure. In an embodiment, a method of identifying a PE base
resin having desirable processing characteristics comprises
obtaining a plurality of PE base resins of the type disclosed
herein and measuring the shear stress as a function of shear rate
for the plurality of base resins using capillary rheometry.
[0046] Capillary rheometry is a technique whereby a sample
undergoes extrusion through a die of defined dimensions and the
shear pressure drop across the die is recorded at set volumetric
flow rates. In an embodiment, a PE base resin of the type disclosed
herein is the subject of a capillary extrusion experiment to
characterize the melt fracture behavior of the resin. The capillary
extrusion experiment may be carried out using any suitable
methodology. For example, the capillary extrusion experiments may
be carried out at 190.degree. C., using a dual-bore capillary
rheometer (Rosand RH-7, Malvern) operated in constant speed mode. A
capillary die with 1 mm diameter and of 16 mm length and an orifice
die with 1 mm diameter may be used. The entrance angle for the dies
can be 180.degree., and the contraction ratio from the reservoir
barrel to the die may be about 15. A step shear rate test can be
performed for a given sample to obtain the apparent wall shear rate
({dot over (.gamma.)}.sub.A) and apparent wall shear stress
(.sigma..sub.A) according to equation 2:
.gamma. . A = 4 Q .pi. R 3 and .sigma. A = R 2 .DELTA. P L ( 2 )
##EQU00002##
where R is the capillary radius, .DELTA.P is the measured pressure
drop across the capillary, L is the capillary length, and Q is the
imposed flow rate. Bagley and Rabinowitsch corrections are applied
to obtain more realistic shear stress value at the wall
(.sigma..sub.W) and shear rate ({dot over (.gamma.)}.sub.w)
respectively according to equation 3:
.sigma. W = R 2 ( .DELTA. P - P o L ) and .gamma. . W = ( 3 + b 4 )
.gamma. . A ( 3 ) ##EQU00003##
where P.sub.O is measured pressure for the orifice die and b=d(log
{dot over (.gamma.)}.sub.A)/d(log .sigma..sub.W). Extrudates can be
collected at different shear rates and imaged using an optical
microscope to identify onset critical stresses and shear rates of
the melt fractures.
[0047] In an embodiment, PE base resins of the type disclosed
herein display a surface melt fracture (SMF) that occurs at a
critical stress of less than about 200 kiloPascals (kPa),
alternatively from about 30 kPa to about 180 kPa. The critical
stress refers to the wall shear stresses that serves as the trigger
for the onset of a particular extrudate distortion or melt
fracture. SMF may also be referred to as the smooth to matte
transition or the sharkskin melt fracture (SSMF). The onset of SMF
is a polymer instability in the PE base resin that originates at
the exit of a die during extrusion of melted resin (i.e., melt)
through the die. The SMF may be attributable to the acceleration
(high stretching rate) of the melt as it exits the die. Without
wishing to be limited by theory, it is hypothesized that melt
leaving the die in the neighborhood of the wall experiences a
large, rapid, tensile deformation as the velocity field adjusts
from the no-slip boundary condition to the free-surface condition.
The large stresses on the free surface cause periodic cracks that
result into small amplitude periodic distortions termed sharkskin,
which is a visible surface defect present in the product being
produced from the die (e.g., pipe). The critical stress is related
to the onset of SMF.
[0048] In an embodiment, the PE base resins of this disclosure
display a reduced amount of slip-stick fracture (SSF) when compared
to a unimodal PE base resin or a PE that is not made using a
dual-metallocene catalyst. SSF is believed to occur when the shear
stress at the die wall exceeds the critical stress. When this
occurs, the melt jerks forward as a plug, relieving the pressure
behind it and allowing the oriented chain segments to recoil
somewhat. Once the pressure is relieved, the rate of movement of
the polymer slows and it re-establishes the non-slip boundary
condition. During SSF the pressure within the die fluctuates and
the polymer output is unsteady. The magnitude of SSF pressure
oscillation is recorded and correlated with the onset of melt
fractures. In an embodiment, a PE base resin of the type disclosed
herein displays a tendency to SSF pressure oscillation that is less
than a unimodal PE base resin or a PE that is not made using a
dual-metallocene catalyst. In an embodiment, a PE base resin of the
type disclosed herein is characterized by a magnitude of slip-stick
of from about 300 psi to about 1500 psi, alternatively from about
500 psi to about 1500 psi, alternatively from about 500 psi to
about 900 psi, or alternatively from about 600 psi to about 800
psi.
[0049] In an embodiment, a PE base resin of the type disclosed
herein may display surface melt fracture that occurs at a critical
shear rate of from about 10 s.sup.-1 to about 100 s.sup.-1,
alternatively from about 10 s.sup.-1 to about 50 s.sup.-1, or
alternatively from about 20 s.sup.-1 to about 40 s.sup.-1. Herein,
the shear rate refers to the extrusion speed that serves as the
trigger for the onset of a particular extrudate distortion or melt
fracture. This relates to the critical stress discussed previously
and the melt flow index/viscosity of a PE base resin.
[0050] The melt fracture behavior of a conventional unimodal PE
base resin and a PE base resin of the type disclosed herein is
schematized in FIGS. 1A and 1B, respectively. FIG. 1 show plots of
the log of shear rate in MegaPascals (MPa) units with the log of
shear stress in inverse seconds (1/s) units, each of which were
determined as described in more detail herein. In an embodiment, a
PE base resin displaying melt fracture behavior consistent with
FIG. 1B (e.g., the same as or substantially similar thereto) may be
referred to as having an about smooth curve of the log of shear
stress as a function of the log of shear rate. FIG. 1A shows four
regions associated with characteristics of the melt, namely smooth,
sharkskin, slip-stick, and gross melt fracture (GMF). FIG. 1B shows
four regions associated with characteristics of the melt, namely
smooth, matte, wavy, and gross melt fracture (GMF).
[0051] In an embodiment, a plurality of PE base resins of the type
disclosed herein are subjected to capillary rheometry. In an
embodiment, a method of identifying a PE base resin having a
reduced tendency to melt fracture comprises identifying a PE base
resin having a magnitude of slip-stick of greater than about 300
psi, a smooth to matte transition of greater than about 90 kPa of
stress and a shear rate of greater than about 10 s.sup.-1. Such
resins having a magnitude of slip-stick of greater than about 300
psi, a smooth to matte transition of greater than about 90 kPa of
stress and a shear rate of greater than about 10 s.sup.-1 and thus
a reduced tendency to melt fracture, are termed polymers with a
reduced melt fracture tendency (PRMT). The PRMTs may be selected
and further processed into articles (e.g., pipes) as described in
more detail herein.
[0052] In an embodiment, capillary extrusion experiments are
carried out and identify PE base resins characterized by at least
one of the following conditions a magnitude of slip-stick less than
about 300 psi; a smooth to matte transition of less than about 90
kPa of stress and a shear rate less than about 10 s.sup.-1. Such
resins may display an increased tendency to melt fracture and are
herein termed resins with increased melt fracture (RIM).
[0053] As disclosed herein a PRMT (e.g, metallocene-catalyzed
multimodal PE base resin) having a reduced tendency to melt
fracture may be characterized by a magnitude of slip-stick greater
than about 300 psi, a smooth to matte transition of greater than
about 90 kPa of stress and a shear rate greater than about 10
s.sup.-1. Further as disclosed herein, measurement of the magnitude
of slip-stick pressure oscillation and the stress and shear rate
for the smooth to matte transition may be made by capillary
extrusion experiments. As will be understood by one of ordinary
skill in the art, capillary extrusion experiments are both time and
labor intensive. In an embodiment, an alternative methodology for
identifying PE base resins having a reduced tendency to melt
fracture (e.g., PRMT) comprises relating one or more processing
characteristics of a PE base resin of the type disclosed herein
(e.g., melt fracture behavior) to measurements carried out using
techniques that inform on polymer microstructure such as Gel
Permeation Chromatography (GPC).
[0054] In an embodiment, an analytical relationship between the
polymer microstructure and processing characteristic is defined by
chemometric analysis. The analytical relationship may be in the
form of a mathematical equation. Chemometric analysis refers to the
application of statistical and pattern recognition techniques to
data provided by chemical analysis such as GPC data.
[0055] In an embodiment, the methodology of relating one or more
processing characteristics of a PE base resin of the type disclosed
herein (e.g., melt fracture behavior) to measurements carried out
using techniques that inform on polymer microstructure such as GPC
is used to identify a RIM, and such RIM may be modified as
disclosed herein to yield a PRMT. In an embodiment, a method
comprises relating the MWD profile of a polymer to the melt
fracture properties as determined by capillary rheometry.
[0056] In an embodiment, chemometric analysis is performed on data
obtained from a series of at least two training samples of PE base
resins of the type disclosed herein having different, known
compositions, which are studied to ascertain interrelationships
between the data and one or more known sample characteristics. In
an embodiment, the data comprises information on the polymer
microstructure (e.g., data as determined by GPC) and the one or
more sample characteristics comprise melt fracture behavior (e.g.,
melt fracture behavior of the type alternatively provided via
capillary analysis as described herein, that is the characteristics
used to identify a RIM or a PRMT). Alternatively, at least 5
training samples, or at least 10 training samples, or at least 20
training samples, or at least 30 training samples, or at least 40
training samples, or at least 50 training samples can be analyzed.
The limit to the number of training samples that can be analyzed
together usually is dictated by limitations of the software and
computer hardware employed, and no specific upper limit to the
number of samples to be used is contemplated.
[0057] Normally (as here), a range of training samples having
different compositions is tested so the differences in the data
obtained for the respective samples can be evaluated to find
changes in a pertinent dependent variable arising from changes in
an independent variable. One can, however, employ a set of training
samples that include some duplicate, triplicate, or more redundant
samples. The inclusion of redundant training samples in a set that
also includes many diverse training samples may reduce the
statistical error. Training samples optionally can be samples
characterized in prior work, the literature, by interpolation or
extrapolation from other training samples, or other sources, as
opposed to samples that are made physically available.
[0058] Another issue is the nature of the training samples
selected. Training samples normally will closely resemble the
desired test samples, so the properties of the test samples and the
training samples can readily be compared. The set of training
samples should include members having a range of properties that
goes beyond the expected properties of the test samples. Selecting
a broad range of training samples will allow a more robust model to
be developed, so the data obtained from the training samples can be
used for samples that may have properties somewhat different from
the expected ones.
[0059] Selecting a broad range of samples also allows the use of
interpolation instead of extrapolation to relate the properties of
the training samples to the test samples. The training samples can,
but need not be made by separating fractions of a test sample. In
an embodiment, materials other than those of the test samples can
be used as training samples or constituents of training samples.
Analytical data for the training samples can be measured, obtained
from literature values, derived from prior work, or obtained from a
combination of sources. The polymer microstructure data results
(e.g., as provided by GPC) or other polymer microstructure
information for the training samples are analyzed to find
correlations between polymer microstructure and the predicted melt
fracture behavior of the polymer. Analysis of the relationship
between the polymer microstructure (e.g., as provided by GPC data)
and the predicted melt fracture behavior may be carried out using
any suitable chemometric software. In an embodiment, the
chemometric software compares the polymer microstructure results
from the training samples and finds correlations between the
polymer microstructure results (e.g., GPC data) of the polymer and
the melt fracture behavior.
[0060] In an embodiment, chemometric analysis of the relevant data
(e.g., GPC data) is carried out using any suitable chemometric
technique. Examples of suitable chemometric techniques include but
are not limited to Partial Least Squares Regression (PLS),
Multilinear Regression Analysis (MLR), Principal Components
Regression (PCR), Principal Component Analysis (PCA) and
Discriminant Analysis, as well as Design of Experiment (DOE) and
Response Surface Methodologies. In an embodiment, the chemometric
analysis is carried out using PLS2. PLS refers to a wide class of
methods for modeling relations between sets of observed variables
by means of latent variables. The underlying assumption of all PLS
methods is that the observed data is generated by a system or
process which is driven by a small number of latent variables.
[0061] In an embodiment, a methodology for evaluating the melt
fracture characteristics of a polymer sample comprises identifying
at least two polymer training samples having different but known
melt fracture characteristics. The training samples may be
subjected to GPC to determine various characteristics of the
polymer sample such as the molecular weight distribution, amount of
each constituent present in the polymer sample, weight average
molecular weight and the like. Typically, the results of the GPC
analysis are determined using standard computer software to plot
and/or analyze the results of the chromatographic separation. In
the alternative, GPC data for the training samples may be obtained
from any suitable source (e.g., literature values). Analysis of the
GPC data may then be carried out to determine at least one
parameter that correlates with the known difference in melt
fracture characteristics among the training samples. Chemometric
analysis may be carried out to define the number of polymer
microstructure data, type of polymer microstructure data and
relationship between the polymer microstructure data that would
serve as a proxy for the observed melt fracture characteristics of
the PE base resins. It is to be understood that establishing that a
relationship exists between the proxy data (e.g., GPC) and the
actual characteristic being observed (e.g., melt fracture) and
analytically defining that relationship will be dependent on the
nature of the training samples chosen as discussed previously
herein.
[0062] In an embodiment, GPC data for polymer samples having
unknown melt fracture characteristics (test samples) are provided.
The values of the parameters determined to be correlated to melt
fracture characteristics in the training samples are identified for
the test samples. The analytical relationship found by analysis of
the training samples is applied to these parameter values
identified in the test samples and as a result the melt fracture
characteristics of the test samples are predicted. From such
predicted characteristics, the sample may be identified as a RIM or
a PRMT. For example, DOE of the GPC data for a set of training
samples may define a relationship between a melt fracture
characteristic (Y) and the polymer microstructure as an equation
having measurable variables (e.g., M.sub.p) and constants
determined by chemometric analysis of the training sample. Thus,
utilizing the data obtained from GPC analysis of the test samples
(e.g., Mp) and the mathematical relationship identified by
chemometric analysis of the training samples a melt fracture
characteristic for the test samples can be predicted.
[0063] In an embodiment, a method of identifying PE base resins
having one or more desired processing characteristics comprises
obtaining a plurality of PE base resins of the type disclosed
herein having a known molecular weight distribution, a known
magnitude of slip-stick, a known stress for a smooth to matte
transition, and a known shear rate (i.e., training samples). The
method may further comprise performing chemometric analysis to
determine an analytical relationship between the known molecular
weight distribution, the known magnitude of slip-stick, the known
stress for a smooth to matte transition, and the known shear rate
for the plurality of PE resins (i.e., training samples). The method
may further comprise obtaining a plurality of samples of multimodal
metallocene-catalyzed PE resins, each having a known molecular
weight distribution, an unknown magnitude of slip-stick, an unknown
stress for a smooth to matte transition, and an unknown shear rate
(i.e., test samples) and utilizing the analytical relationship to
determine a value for the unknown magnitude of slip-stick, a value
for the unknown stress for a smooth to matte transition, and a
value for the unknown shear rate for each of the plurality of
multimodal metallocene-catalyzed PE samples (i.e., test samples).
Based on the predicted melt fracture characteristics the method may
further comprise identifying multimodal metallocene-catalyzed PE
resins (e.g., PRMPs) having a reduced tendency to melt fracture
characterized by samples having a magnitude of slip-stick greater
than about 300 psi, a smooth to matte transition of greater than
about 90 kPa of stress and a shear rate greater than about 10
s.sup.-1. The method may further comprise forming the PRMPs into
articles such as pipe.
[0064] In an alternative embodiment, based on the predicted melt
fracture characteristics the method may further comprise
identifying multimodal metallocene-catalyzed PE resins (e.g., RIMs)
having an increased tendency to melt fracture characterized by
samples having a magnitude of slip-stick less than about 300 psi, a
smooth to matte transition of less than about 90 kPa of stress and
a shear rate less than about 10 s.sup.-1. The method may further
comprise modifying the identified RIM to decrease the tendency of
the material to melt fracture. The modified RIM may be analyzed
(e.g., via GPC) to determine molecular weight distribution, and
thereby predict melt fracture behavior (as described herein) of the
modified RIM, e.g., to determine whether the RIM has been modified
to yield a PRMP. The method may further comprise forming the PRMT
into articles such as pipe.
[0065] As described herein the flow properties determined by
capillary rheometry may be related to the entire MWD profile of the
polymer. Herein, the MWD is the metric used to inform on the
polymer microstructure. As will be understood by one of ordinary
skill in the art, the MWD of the polymer is dependent on several
factors. In an embodiment, a method comprises performing
chemometric analysis in order to establish the relationship between
one or more factors contributing to the MWD and the melt fracture
behavior of the polymer. For example, using statistical design of
experiment (DOE) and response surface methodology, the MWD profile
of a polymer in terms of its molecular weight components and their
subsequent effect on the capillary results may be determined.
[0066] In an embodiment, the MWD profile of a particular polymer is
described as the linear combination of n factors where n is equal
to or greater than 2, alternatively equal to or greater than about
3, or alternatively equal to or greater than about 4. In an
embodiment, n is 2 and the components are designated P1 and P2. In
such embodiments, P1 and P2 can each be assigned a M.sub.p, PDI,
and weight fraction composition. Using a combination of these two
components (i.e., P1 and P2), the effects of various MWD profiles
on the melt fracture characteristics of the polymer (i.e, capillary
response) can be explored in a systematic manner. The components of
the MWD (i.e., P1 and P2) can be represented using any suitable
peak shape such as Gaussian or Schluz-Flory. In an embodiment, the
components of the MWD (i.e., P1 and P2) are represented using log
normal (i.e., Gaussian) shaped peaks. In an embodiment, the polymer
is a physical blend or mixture of polymers where the exact number
of components is known as well as the nature of these components in
terms of M.sub.w and M.sub.n. In an embodiment, the MWD of a
polymer having been described initially as the linear combination
of two components (i.e., P1 and P2) can be further characterized by
the peak molecular weight of each component (M.sub.p P1 and M.sub.p
P2), the PDI of each component, and the weight fraction of each
component.
[0067] In an embodiment, the method further comprises digitally
generating MWD profiles by varying the individual parameters that
characterize the MWD (i.e., M.sub.p, PDI and weight fraction of
each component). Given that the MWD distribution is equal to unity
(i.e., 1) and is described by two component peaks (i.e., n=2), the
number of parameters that are used to describe the MWD can be
reduced from six to five, where the weight fraction composition of
P2 can be written in terms of the weight fraction of P1 (i.e., wt
frac. P2=1-wt frac. P1). Each of these parameters is illustrated in
FIG. 7. The MWD profile generated for each variation of parameters
may be utilized to predict a melt fracture characteristic (e.g.,
magnitude of slip-stick). Digitally varying the parameters and
identifying the relative contribution of each parameter and/or
combination of parameters to the particular melt fracture
characteristic may aid in elucidating the analytical relationship
between a particular parameter and/or combination of parameters and
the resultant melt fracture characteristic (e.g., magnitude of
slip-stick). In an embodiment, the relationship between one or more
of the varied parameters and the result (e.g., magnitude of
slip-stick) may be codified in the form of a mathematical algorithm
of the type previously disclosed herein and exemplified below. In
some embodiments, the algorithm includes all of the parameters of
the MWD identified to contribute to the resultant melt fracture
characteristic (e.g., magnitude of slip-stick).
[0068] In an embodiment, the method further comprises statistical
analysis of the results of the chemometric determinations to
identify parameters that significantly contribute to the resultant
melt fracture characteristic (e.g., magnitude of slip-stick).
Herein, "significant" refers to statistical significance which is
defined as the likelihood that the result obtained has occurred by
chance. The statistical significance of the analysis can determined
using any suitable methodology. For example, the method may further
comprise analysis of the variance in the results of the chemometric
determinations. Analysis of Variance (ANOVA) methods are used in
data analysis to determine differential expressions under different
experimental conditions. In a one-way ANOVA, there is one
experimental factor under investigation. For example, the factor
may be the effect of the peak molecular weight on the magnitude of
slip-stick. In a two-way ANOVA, there are two factors under
investigation, for example, the effect of the amount of the LMW
component and PDI of the LMW component on the magnitude of the
slip-stick. Each factor may have multiple levels. Interaction
between the two factors is also included in the ANOVA analysis.
ANOVA may also be carried out in order to determine whether there
are statistical differences among the means of measurements in
different measurement groups. As an example, the different
measurement groups may contain measurements of the magnitude of
slip-stick at different weight fractions of a particular component.
In each group, there may be several replicate measurements under
the same conditions. First, one finds the within-group variance and
the between-group variance. The within-group variance is the
measurement variance of measurements within a set of experiments
carried out under the same conditions. The between-group variance
is the measurement variance of the means of experiments carried out
under different conditions. The within-group variance reflects the
measurement error of the measurement technology, and the
between-group variance includes both the measurement error of the
measurement technology and changes caused by different conditions.
Then the between-group variance is compared to the within-group
variance. If the between-group variance is significantly larger
than the within-group variance, it may be concluded that the
different conditions have produced statistically significant
changes in the determinations of the melt fracture characteristics
(e.g., magnitude of slip-stick). In ANOVA analysis, the underlying
null-hypothesis is that all conditions have the same mean. With the
estimated mean squares and degrees of freedom, a p-value of
F-statistics can be calculated. The p-value is the probability that
the null-hypothesis may be accepted. When the p-value is lower than
a given threshold, for example p-value<0.01, the null-hypothesis
can be rejected and the alternative hypothesis, which means that
some of the experimental conditions have different means, can be
accepted. In other words, some experimental conditions have
produced changes in the melt fracture characteristics
[0069] In an embodiment, the algorithm describing the relationship
between one or more of the varied parameters and the result (e.g.,
magnitude of slip-stick) is modified to reflect only those
parameters found to contribute significantly to the result. As will
be understood by one of ordinary skill in the art, statistical
models may be constructed and extrapolated to produce values of
parameters that lie outside of the range observable or probable for
actual samples. For example, utilizing the methodologies disclosed
herein, models may be constructed which predict a negative value
for the magnitude of slip-stick. In such instances, the limitations
of the model are realized and the negative values obtained can be
assumed to have a value of zero.
[0070] The results of determining the relationship between the
individual parameters contributing to the MWD and a particular melt
fracture characteristic may be employed to identify the parameters
and/or combination of parameters that can be adjusted to modify the
melt fracture characteristic of a particular resin. In an
embodiment, a PMRT is prepared by blending n components having one
or more parameters (e.g., wt fraction of each component, PDI of
each component) determined to provide a polymer blend having one or
more desirable melt fracture characteristics. As will be understood
by one of ordinary skill in the art, the particular design of a
polymer having a reduced tendency to melt fracture (e.g., PRMT)
will be dependent on the results of the chemometric and statistical
analysis which will identify any relationships that exist between
the parameters contributing to the MWD and the particular melt
fracture characteristic. For example, the results of the
chemometric analysis may indicate that one of the significant
factors in the stress for the smooth to matte transition is peak
molecular weight of the LMW component. Consequently, adjusting the
peak molecular weight of the LMW component to within a range
indicated by the results of the chemometric analysis (e.g.,
adjustments responsive to the chemometric analysis results) would
be expected to produce a resin having a stress for the smooth to
matte transition within some user and/or process desired range.
Consequently there can be numerous polymer designs which display a
reduced tendency to melt fracture as such solutions to the problem
of melt fracture are dependent on a variety of parameters but may
be understood and employed in view of the disclosure herein (e.g.,
responsive to chemometric analysis).
[0071] For example, a method for reducing or eliminating melt
fracture (e.g., SMF) in a RIM of the type disclosed herein
comprises increasing the molecular weight of the LMW component. In
an embodiment, a method for reducing or eliminating melt fracture
(e.g., SMF) in a RIM of the type disclosed herein comprises
decreasing both the amount of the LMW component and the M.sub.w of
the HMW component. In an embodiment, a method for reducing or
eliminating melt fracture (e.g., SMF) in a RIM of the type
disclosed herein comprises introducing a polymer component having a
MWD peak mode that is disposed between the MWD peak modes of the
LMW component and HMW component. Such modifications may be carried
out by altering one or more process conditions during
polymerization of the LMW component and/or the HMW component (e.g.,
during formation of a reactor blend) and/or by replacing and/or
adding one or more components during formation of a mechanical
blend such as selecting an alternative LMW component and/or HMW
component than that present in the RIM and/or by adding an
additional component having a MWD peak mode between those of the
LMW and HMW components. In various embodiments, such modifications
of the RIM are effective to convert the RIM to a PRMT.
[0072] It is to be understood that the methodologies disclosed
herein are intended to provide modifications to components that are
constituents of a multimodal polymeric material. Further, it is to
be understood that in the case of a polymer blend it may be
difficult or impossible to independently act upon or characterize a
single component of the multicomponent blend without the influence
and/or presence of the other components of the blend. Thus, the
methods disclosed herein when referring to a component of a polymer
blend (e.g., HMW component) refer to the ability to act upon or
modify a portion of the polymer designated as the particular
component with the understanding that these components may not be
independent entities and/or that some impact may occur on another
component of the polymer.
[0073] Without wishing to be limited by theory, RIMs of the type
disclosed herein may exhibit the aforementioned melt fracture
characteristics such as shown in FIG. 1B as a result of the
composition having components that behave as discrete entities.
Under the processing conditions typically employed for manufacture
of an article from a RIM of the type disclosed herein, the LMW
component may result in migration toward the surface that is not
impeded by molecular entanglements to the HMW component. Thus, the
unique melt fracture and slip behaviors of RIMs of the type
disclosed herein are attributable to the fact that the MWD peaks of
the two components are considerably separated and the low mode has
a significant amount of LMW component such that entanglements are
limited within this mode. The molecular segregation of the LMW
components results in the concentration of these components near
the die wall during the extrusion flow which in turn results in
significant apparent wall slip and less elastic effects that
influence the melt fracture behavior. Accordingly, various
embodiments for modifying the melt fracture characteristics of the
RIM include holding constant the MWD peak associated with the HMW
component and modifying the MWD of the LMW component (e.g., moving
the location of and/or adjusting the size of the MWD peak
associated with the LWM component).
[0074] In an embodiment, the PRMT is a multimodal
metallocene-catalyzed resin. Further, such resins displaying a
magnitude of slip-stick greater than about 300 psi, a smooth to
matte transition of greater than about 90 kPa of stress, and a
shear rate greater than about 10 s.sup.-1 are characterized by a
reduced tendency to melt fracture.
[0075] PRMTs as described herein may be formed into various
articles, including but not limited to, household containers,
utensils, film products, drums, fuel tanks, pipes, geomembranes,
and liners. In an aspect, the PRMT of this disclosure is fabricated
into a pipe by a plastics shaping process such as extrusion. A
method of making a polymeric pipe comprises extruding the polymer
or copolymer in a molten state through a die to form the polymeric
pipe and cooling the pipe.
[0076] Pipe extrusion in the simplest terms is performed by
melting, conveying polyethylene pellets into a particular shape
(generally an annular shape), and solidifying that shape during a
cooling process. There are numerous steps to pipe extrusion as
provided below. The polymer feedstock can either be a pre-pigmented
polyethylene resin or it can be a mixture of natural polyethylene
and color concentrate (referred to as "Salt and Pepper blends"). In
North America, the most common feedstock for pipe extrusion is
"Salt and Pepper blends." In Europe and other areas of the world,
the most common feedstock for pipe extrusion is pre-pigmented
polyethylene resin. Feedstock is rigidly controlled to obtain the
proper finished product (pipe) and ultimate consumer
specifications.
[0077] The feedstock is then fed into an extruder. The most common
extruder system for pipe production is a single-screw extruder. The
purpose of the extruder is to melt, convey, and homogenize the
polyethylene pellets. Extrusion temperatures typically range from
178.degree. C. to 250.degree. C. depending upon the extruder screw
design and flow properties of the polyethylene.
[0078] The molten polymer is then passed through a die. The die
distributes the homogenous polyethylene polymer melt around a solid
mandrel, which forms it into an annular shape. Adjustments can be
made at the die exit to try to compensate for polymer sag through
the rest of the process. In order for the pipe to meet the proper
dimensional parameters, the pipe is then sized. There are two
methods for sizing: vacuum or pressure. Both employ different
techniques and different equipment.
[0079] Next, the pipe is cooled and solidified in the desired
dimensions. Cooling is accomplished by the use of several water
tanks where the outside pipe is either submerged or water is
sprayed on the pipe exterior. The pipe is cooled from the outside
surface to the inside surface. The interior wall and inside
surfaces of the pipe can stay very hot for a long period of time,
as polyethylene is a poor conductor of heat. Finally, the pipe is
printed and either coiled or cut to length.
[0080] In an embodiment, the PRMT is used to prepare the pipe has a
density of greater than about 0.925 g/ml to about 0.942 g/ml,
alternatively from about 0.928 to about 0.940 g/ml or alternatively
from about 0.930 g/ml to about 0.940 g/ml as determined in
accordance with ASTM D1505.
[0081] A majority of the field failures in pressure pipe (gas
transport) applications are attributable to a brittle fracture mode
referred to as slow crack growth (SCG). This has led to the
development of many lab-scale tests, such as the Pennsylvania Notch
Tensile Test (PENT; ASTM F1473) and the Full Notch Creep Test
(FNCT; ISO 16770.3), to predict the resistance to SCG of various
polyethylenes. In the PENT test, rectangular bars notched (to
ensure brittle fracture) are subjected to a constant load at
80.degree. C. until they finally break. The time to failure is
recorded and is generally thought to be reflective of the SCG
resistance of the polymer. A pipe prepared from the PRMTs disclosed
herein may display PENT values of from about 500 hours to about
20,000 hours, alternatively from about 550 hours to about 20,000
hours, or alternatively from about 600 hours to about 20,000
hours.
[0082] A modified Charpy impact test, referred to as the
Razor-Notched Charpy Impact Test, has emerged as a useful indicator
of the resistance to RCP fractures. This modified Charpy test is
described in detail in ASTM F2231. This test involves measuring the
impact energy when a thin molded rectangular plaque (with a razor
notch) is impacted by a swinging pendulum. This test can be
performed at multiple temperatures; enabling one to determine the
temperature at which the failure mode changes from ductile to
brittle. The results from this test are as follows: (i) impact
energy (in Joules) at room temperature and (ii) the lowest
temperature at which the failure was clearly ductile (hinge break
with an impact energy>0.15 J); for convenience, this temperature
will be referred to as the Charpy ductile to brittle critical
temperature, Charpy T.sub.db. Generally speaking, a higher
room-temperature impact energy and a lower Charpy T.sub.db means
the ensuing pipe will have better RCP resistance.
[0083] A pipe prepared from the PRMTs disclosed herein may have a
Charpy T.sub.db less than about -25.degree. C.; alternatively, the
Charpy T.sub.db is less than about -15.degree. C., or
alternatively, the Charpy T.sub.db may be less than about
-10.degree. C. Charpy impact energy is a measure of an article's
impact toughness. Test articles of polymer produced in accordance
with the present disclosure may have a Charpy impact energy of from
about 1.0 J to about 3.0 J, or alternatively from about 1.0 J to
about 2.58 J as determined in accordance with ASTM F2231
razor-notched Charpy impact test at room temperature.
[0084] In an embodiment, a pipe prepared from a PRMT of the type
disclosed herein is characterized by the flexural modulus. The
flexural modulus may be defined as the ratio, within the elastic
limit, of the applied stress on a test specimen in flexure, to the
corresponding strain in the outermost fibers of the specimen. In an
embodiment, a pipe prepared from a PRMT of the type disclosed
herein has a flexural modulus, 2% secant of from about 80 kpsi to
about 110 kpsi, alternatively from about 85 kpsi to about 105 kpsi,
or alternatively from about 90 kpsi to about 100 kpsi as determined
in accordance with ASTM D790 using an injection molded test
specimen having a 16.1 inch span depth at a rate of 0.5 in/min.
[0085] In an embodiment, a pipe prepared from a PRMT of the type
described herein exhibits an elongation at break of greater than
about 400%, alternatively greater than about 450% or alternatively
greater than about 500% as determined in accordance with ASTM D638.
The elongation at break refers to the elongation which corresponds
to the tensile breaking strength.
[0086] In an embodiment, a pipe prepared from a PRMT of the type
described herein displays an increased Young's modulus. Young's
modulus is a measure of the stiffness of a material and is defined
as the ratio of the rate of change of stress with strain. Young's
modulus can be determined experimentally from the slope of a
stress-strain curve created during tensile tests conducted on a
sample of a material, as determined in accordance with ASTM D638.
In an embodiment, the PRMT is used to make a Type IV bar and
exhibits a Young's modulus ranging from about 120 kpsi to about 190
kpsi, alternatively from about 120 kpsi to about 185 kpsi, or
alternatively from about 120 kpsi to about 180 kpsi when determined
in accordance with ASTM D638 at a speed of 2 in/min.
[0087] In an embodiment, a pipe prepared from a PRMT of the type
described herein exhibits a tensile strength at yield of from about
2600 psi to less than about 3,000 psi, alternatively from 2600 psi
to about 2950 psi, or alternatively 2600 psi to about 2,900 psi as
determined in accordance with ASTM D638. The tensile strength at
yield refers to the tensile stress where an increase in expansion
is admitted without an increase in gaining the weight on
stress-strain curve. In an embodiment, a pipe prepared from a PRMT
of the type described herein exhibits a tensile strength at break
of greater than about 4000 psi, alternatively greater than about
4500 psi, or alternatively greater than about 5000 psi as
determined in accordance with ASTM D638. The tensile strength at
break refers to the tensile stress at the moment the material is
destroyed. For both the tensile strength at yield and the tensile
strength at break, the pipe prepared from the PRMT was a Type IV
bar which was tested at 2 in/min.
[0088] In an embodiment, a pipe prepared from a PRMT of the type
described herein displays a thermal stability of greater than about
220.degree. C. as determined in accordance with ASTM D3350.
[0089] In an embodiment, a pipe prepared from a PRMT of the type
disclosed herein is characterized by the extent to which it can
resist rapid crack propagation (RCP). The Small-Scale Steady-State
(S4) test is the current standard for measuring the RCP resistance
of polyethylene pipes. In the S4 test, the pipe specimens are seven
diameters long and are sealed at both ends and pressurized with
air. Typically, pipe specimens are conditioned externally at the
test temperature, and then moved to the S4 rig for testing. A sharp
chisel-edged striker impacts the pipe at one end and drives a
fast-running crack through the main section of the pipe. While the
crack propagates, internal disc baffles spaced along the pipe
length suppress axial decompression ahead of it, so that the
pressure at the crack-tip is approximately equal to the test
pressure during the entire course of crack growth. This promotes
steady-state crack growth. Further, in the S4 test, a containment
cage around the specimen prevents flaring of the pipe. This also
limits the failure mode to steady-state crack propagation while
minimizing ductile transient bursting. The S4 test details and
procedures are described in the ISO 13477 standard. The test can be
performed at a fixed temperature to determine the critical pressure
(P.sub.c) required to sustain RCP. Alternatively, a series of tests
at a given/fixed operating pressure (usually 5 bars) and at various
temperatures can be used to measure the critical temperature
(T.sub.c) for RCP to be sustained. Generally speaking, the
temperature of a pipe must be below a critical limit even for RCP
to be initiated. Once RCP is initiated, the pressure within the
pipe must exceed a critical value to sustain steady state crack
propagation. Therefore, for a pipe, low S4 T.sub.c and high S4
P.sub.c will help minimize RCP failures.
[0090] The lower the S4 critical temperature the better, since it
results in a broader end-use temperature range for the pipe. A pipe
fabricated from the PRMTs disclosed herein, having an 8-inch
nominal outer diameter with a standard diameter ratio (SDR=OD/t,
where t=wall thickness) of about 11, may have a critical
temperature value (T.sub.c) determined according to ISO DIS 13477
(S4 test) of equal to or less than about 0.degree. C.
[0091] Another method of evaluating the SCG resistance is by
determining the tensile natural draw ratio (tensile NDR) of the
resin. There is some evidence that the tensile NDR is directly
related to the SCG resistance of HDPE such that the lower the
tensile NDR the higher the resistance to SCG. A description of the
correlation of SCG to tensile NDR may be found in: E. Laurent,
Comprehensive Evaluation of the Long-Term Mechanical Properties of
PE100 Resin Meeting the Requirements of Modern Installation
Techniques, Plastic Pipes XI Proceedings of the International
Conference, Woodhead Publishing Limited (2001); and in an article
by L. Hubert, et al published in 2002 in the Journal of Applied
Polymer Science Volume 84 page 2308 each of which is incorporated
herein by reference in its entirety. In an embodiment, a pipe
prepared from a PRMT of the type disclosed herein has a NDR of less
than about 500% as determined in accordance with ASTM D 638 for a
Type IV bar at a rate of 2 in/min.
[0092] In an embodiment, a PRMT of the type disclosed herein
displays a melt flow rate (MFR) of less than about 0.4 g/10 min.
The MFR is a measurement of the viscosity of a polymer through a
defined orifice at a constant temperature and may be determined in
accordance with ASTM D1238 using a 2.16 kg loading.
[0093] In an embodiment, a pipe prepared from a PRMT of the type
disclosed herein is characterized by a hydrostatic design basis
(HDB) at 23.degree. C. of from about 1200 psi to less than about
1530 psi and a HDB at 60.degree. C. of from about 960 psi to less
than about 1200 psi. The HDB test is used for the purpose of
determining the long-term strength characteristic of a plastic pipe
and may be determined in accordance with ASTM D2837.
[0094] The design stress of a plastic pipe is often referred to as
its long-term hydrostatic strength (LTHS) or the minimum required
strength (MRS). LTHS, estimated using ASTM D 2837 (USA standard),
is the estimated tensile stress in the wall of a pipe in the
circumferential orientation which, when applied continuously, will
cause failure of the pipe at 100,000 hours. The MRS of a pipe,
estimated using the ISO 9080 standard, is the functional equivalent
of the LTHS (with a desired lifetime of 50 years) used
internationally. The LTHS and/or MRS of a pipe are used to certify
gas pipes according to either ASTM D2513 and/or ISO 4437. In other
words, these values determine the maximum load that such pipes can
bear during their utilization for the transportation of natural
gas. In an aspect, the PRMTs disclosed herein may be fabricated
into pipe having a MRS of ranging from about
8.ltoreq..sigma.LPL<10 MPa.
[0095] In an embodiment, a method of assessing melt fracture
potential comprises obtaining at least one metallocene-catalyzed
polymer sample and performing a capillary extrusion test on the at
least one metallocene-catalyzed polymer sample. The method may
further comprise identifying a metallocene-catalyzed polymer sample
having a magnitude of slip-stick greater than about 300 psi; a
smooth to matte transition greater than about 90 kPa and a shear
rate of greater than about 10 s.sup.-1 wherein said identified
polymer sample has an increased melt fracture potential when
compared to a conventional resin.
[0096] In an embodiment, a method of assessing melt fracture
potential comprises obtaining at least one metallocene-catalyzed
polymer sample. The method may further comprise performing a
capillary extrusion test on the at least one metallocene-catalyzed
polymer sample. The method may further comprise identifying a
metallocene-catalyzed polymer sample having a magnitude of
slip-stick less than about 300 psi; a smooth to matte transition
less than about 90 kPa and a shear rate of less than about 10
s.sup.-1 wherein said identified polymer sample has an increased
melt fracture potential when compared to a conventional resin not
having a magnitude of slip-stick greater than about 300 psi; a
smooth to matte transition greater than about 90 kPa and a shear
rate of greater than about 10 s.sup.-1.
[0097] In a method of assessing melt fracture potential comprises
performing capillary rheometry on a polymer sample to obtain
measurements of the shear stress as a function of the shear rate.
The method may further comprise plotting the shear stress as a
function of shear rate to obtain a plot of the melt fracture
behavior. The method may further comprise comparing the plot of
melt fracture behavior of the polymer sample to a plot of the melt
fracture behavior of a conventional resin. In an embodiment, the
method further comprises identifying polymer samples having melt
fracture behavior characterized by a magnitude of slip-stick
greater than about 300 psi; a smooth to matte transition of greater
than about 90 kPa and a shear rate greater than about 10
s.sup.-1.
[0098] In an embodiment, a method of identifying polymer samples
having poor processing characteristics comprises obtaining a
plurality of metallocene-catalyzed multimodal polyethylene polymer
samples. The method may further comprise measuring the shear stress
as a function of shear rate for the plurality of dual
metallocene-catalyzed polyethylene polymer samples. The method may
further comprises identifying dual metallocene-catalyzed
polyethylene polymer samples having melt fracture behavior
characterized by a magnitude of slip-stick greater than about 300
psi; a smooth to matte transition greater than about 90 kPa and a
shear rate greater than about 10 s.sup.-1.
[0099] In an embodiment, a method of assessing melt fracture
characteristics of one or more multimodal metallocene-catalyzed
polyethylene resins comprises for a training set comprising a
plurality of multimodal metallocene-catalyst polyethylene resins,
determining melt fracture characteristics comprising a magnitude of
slip-stick, a stress for a smooth to matte transition and a shear
rate. The method may further comprise measuring a molecular weight
distribution for each resin in the training set. The method may
further comprise determining a relationship between the melt
fracture characteristics and the molecular weight distribution of
the training set. The method may further comprise providing one or
more validation samples of multimodal metallocene-catalyzed resin
having a known molecular weight distribution and an unknown melt
fracture characteristic. The method may further comprise predicting
the melt fracture characteristics of the validation samples via the
relationship.
[0100] In an embodiment, a method of predicting melt fracture
behavior of a multimodal metallocene-catalyzed polyethylene resin
comprises determining the melt fracture behavior of at least two
polyethylene resins by capillary rheometry. The method may further
comprise determining the molecular weight distribution of the at
least two polyethylene resins. The method may further comprise
performing chemometric analysis to establish a mathematical
relationship between the melt fracture behavior and the molecular
weight distribution for the at least two polyethylene resins. The
method may further comprise obtaining the molecular weight
distribution of the multimodal metallocene-catalyzed polyethylene
resin. The method may further comprise utilizing the mathematical
relationship to predict the melt fracture behavior of the
multimodal metallocene-catalyzed polyethylene resin.
[0101] In an embodiment, a method of identifying polyethylene (PE)
resins having one or more desired processing characteristics
comprises obtaining a plurality of PE resins each having a known
molecular weight distribution, a known magnitude of slip-stick, a
known stress for a smooth to matte transition, and a known shear
rate. The method may further comprise performing chemometric
analysis to determine a mathematical relationship between the known
molecular weight distribution, the known magnitude of slip-stick,
the known stress for a smooth to matte transition, and the known
shear rate for the plurality of PE resins. The method may further
comprise obtaining a plurality of samples of the multimodal
metallocene-catalyzed PE resins, each having a known molecular
weight distribution, an unknown magnitude of slip-stick, an unknown
stress for a smooth to matte transition, and an unknown shear rate.
The method may further comprise utilizing the mathematical
relationship to determine a value for the unknown magnitude of
slip-stick, a value for the unknown stress for a smooth to matte
transition, and a value for the unknown shear rate for each of the
plurality of multimodal metallocene-catalyzed PE samples. The
method may further comprise identifying the multimodal
metallocene-catalyzed PE resins having a reduced tendency to melt
fracture characterized by samples having a magnitude of slip-stick
greater than about 300 psi; a smooth to matte transition of greater
than about 90 kPa of stress and a shear rate greater than about 10
s.sup.-1.
[0102] In an embodiment, a method of preparing pipe comprises
identifying a multimodal metallocene-catalyzed PE resin having a
reduced tendency to melt fracture characterized a magnitude of
slip-stick greater than about 300 psi; a smooth to matte transition
of greater than about 90 kPa of stress, and a shear rate greater
than about 10 s.sup.-1. The method may further comprise forming the
multimodal metallocene-catalyzed PE resin into the pipe.
[0103] In an embodiment, a pipe formed from a multimodal
metallocene-catalyzed PE resin having a reduced tendency to melt
fracture is characterized by a magnitude of slip-stick greater than
about 300 psi; a smooth to matte transition of greater than about
90 kPa of stress and a shear rate greater than about 10
s.sup.-1.
[0104] In an embodiment, a method of preparing a medium-density
polyethylene pipe comprise identifying a multimodal
metallocene-catalyzed PE resin having a density of greater than
about 0.925 g/ml to about 0.940 g/ml, a magnitude of slip-stick
greater than about 300 psi; a smooth to matte transition of greater
than about 90 kPa of stress, and a shear rate greater than about 10
s.sup.-1. The method may further comprise forming the multimodal
multimodal metallocene-catalyzed PE resin into pipe.
[0105] In an embodiment, a method comprises identifying a
multimodal metallocene-catalyzed PE resin a higher molecular weight
(HMW) component and a lower molecular weight (LMW) component; and
characterized by at least one of the following conditions a
magnitude of slip-stick less than about 300 psi; a smooth to matte
transition of greater than about 90 kPa of stress and a shear rate
less than about 10 s.sup.-1. The method may further comprise
treating the multimodal metallocene-catalyzed PE resin to provide a
modified polymer wherein the treatment comprises at least one of
the following (i) increasing the weight average molecular weight of
the LMW component; (ii) introducing a bridging polymer; (iii)
decreasing the amount of LMW component and decreasing a weight
average molecular weight of the HMW component; and (iv) introducing
a polymer processing aid to the multimodal metallocene-catalyzed PE
resin wherein the modified polymer is characterized by a magnitude
of slip-stick greater than about 300 psi; a smooth to matte
transition of greater than about 90 kPa of stress, and a shear rate
greater than about 10 s.sup.-1.
[0106] FIG. 10 illustrates a computer system 780 suitable for
implementing one or more embodiments disclosed herein. The computer
system 780 includes a processor 782 (which may be referred to as a
central processor unit or CPU) that is in communication with memory
devices including secondary storage 784, read only memory (ROM)
786, random access memory (RAM) 788, input/output (I/O) devices
790, and network connectivity devices 792. The processor 782 may be
implemented as one or more CPU chips.
[0107] It is understood that by programming and/or loading
executable instructions onto the computer system 780, at least one
of the CPU 782, the RAM 788, and the ROM 786 are changed,
transforming the computer system 780 in part into a particular
machine or apparatus having the novel functionality taught by the
present disclosure. It is fundamental to the electrical engineering
and software engineering arts that functionality that can be
implemented by loading executable software into a computer can be
converted to a hardware implementation by well known design rules.
Decisions between implementing a concept in software versus
hardware typically hinge on considerations of stability of the
design and numbers of units to be produced rather than any issues
involved in translating from the software domain to the hardware
domain. Generally, a design that is still subject to frequent
change may be preferred to be implemented in software, because
re-spinning a hardware implementation is more expensive than
re-spinning a software design. Generally, a design that is stable
that will be produced in large volume may be preferred to be
implemented in hardware, for example in an application specific
integrated circuit (ASIC), because for large production runs the
hardware implementation may be less expensive than the software
implementation. Often a design may be developed and tested in a
software form and later transformed, by well known design rules, to
an equivalent hardware implementation in an application specific
integrated circuit that hardwires the instructions of the software.
In the same manner as a machine controlled by a new ASIC is a
particular machine or apparatus, likewise a computer that has been
programmed and/or loaded with executable instructions may be viewed
as a particular machine or apparatus.
[0108] The secondary storage 784 is typically comprised of one or
more disk drives or tape drives and is used for non-volatile
storage of data and as an over-flow data storage device if RAM 788
is not large enough to hold all working data. Secondary storage 784
may be used to store programs which are loaded into RAM 788 when
such programs are selected for execution. The ROM 786 is used to
store instructions and perhaps data which are read during program
execution. ROM 786 is a non-volatile memory device which typically
has a small memory capacity relative to the larger memory capacity
of secondary storage 784. The RAM 788 is used to store volatile
data and perhaps to store instructions. Access to both ROM 786 and
RAM 788 is typically faster than to secondary storage 784. The
secondary storage 784, the RAM 788, and/or the ROM 786 may be
referred to in some contexts as computer readable storage media
and/or non-transitory computer readable media.
[0109] I/O devices 790 may include printers, video monitors, liquid
crystal displays (LCDs), touch screen displays, keyboards, keypads,
switches, dials, mice, track balls, voice recognizers, card
readers, paper tape readers, or other well-known input devices.
[0110] The network connectivity devices 792 may take the form of
modems, modem banks, Ethernet cards, universal serial bus (USB)
interface cards, serial interfaces, token ring cards, fiber
distributed data interface (FDDI) cards, wireless local area
network (WLAN) cards, radio transceiver cards such as code division
multiple access (CDMA), global system for mobile communications
(GSM), long-term evolution (LTE), worldwide interoperability for
microwave access (WiMAX), and/or other air interface protocol radio
transceiver cards, and other well-known network devices. These
network connectivity devices 792 may enable the processor 782 to
communicate with an Internet or one or more intranets. With such a
network connection, it is contemplated that the processor 782 might
receive information from the network, or might output information
to the network in the course of performing the above-described
method steps. Such information, which is often represented as a
sequence of instructions to be executed using processor 782, may be
received from and outputted to the network, for example, in the
form of a computer data signal embodied in a carrier wave.
[0111] Such information, which may include data or instructions to
be executed using processor 782 for example, may be received from
and outputted to the network, for example, in the form of a
computer data baseband signal or signal embodied in a carrier wave.
The baseband signal or signal embodied in the carrier wave
generated by the network connectivity devices 792 may propagate in
or on the surface of electrical conductors, in coaxial cables, in
waveguides, in an optical conduit, for example an optical fiber, or
in the air or free space. The information contained in the baseband
signal or signal embedded in the carrier wave may be ordered
according to different sequences, as may be desirable for either
processing or generating the information or transmitting or
receiving the information. The baseband signal or signal embedded
in the carrier wave, or other types of signals currently used or
hereafter developed, may be generated according to several methods
well known to one skilled in the art. The baseband signal and/or
signal embedded in the carrier wave may be referred to in some
contexts as a transitory signal.
[0112] The processor 782 executes instructions, codes, computer
programs, scripts which it accesses from hard disk, floppy disk,
optical disk (these various disk based systems may all be
considered secondary storage 784), ROM 786, RAM 788, or the network
connectivity devices 792. While only one processor 782 is shown,
multiple processors may be present. Thus, while instructions may be
discussed as executed by a processor, the instructions may be
executed simultaneously, serially, or otherwise executed by one or
multiple processors. Instructions, codes, computer programs,
scripts, and/or data that may be accessed from the secondary
storage 784, for example, hard drives, floppy disks, optical disks,
and/or other device, the ROM 786, and/or the RAM 788 may be
referred to in some contexts as non-transitory instructions and/or
non-transitory information.
[0113] In an embodiment, the computer system 780 may comprise two
or more computers in communication with each other that collaborate
to perform a task. For example, but not by way of limitation, an
application may be partitioned in such a way as to permit
concurrent and/or parallel processing of the instructions of the
application. Alternatively, the data processed by the application
may be partitioned in such a way as to permit concurrent and/or
parallel processing of different portions of a data set by the two
or more computers. In an embodiment, virtualization software may be
employed by the computer system 780 to provide the functionality of
a number of servers that is not directly bound to the number of
computers in the computer system 780. For example, virtualization
software may provide twenty virtual servers on four physical
computers. In an embodiment, the functionality disclosed above may
be provided by executing the application and/or applications in a
cloud computing environment. Cloud computing may comprise providing
computing services via a network connection using dynamically
scalable computing resources. Cloud computing may be supported, at
least in part, by virtualization software. A cloud computing
environment may be established by an enterprise and/or may be hired
on an as-needed basis from a third party provider. Some cloud
computing environments may comprise cloud computing resources owned
and operated by the enterprise as well as cloud computing resources
hired and/or leased from a third party provider.
[0114] In an embodiment, some or all of the functionality disclosed
above may be provided as a computer program product. The computer
program product may comprise one or more computer readable storage
medium having computer usable program code embodied therein to
implement the functionality disclosed above. The computer program
product may comprise data structures, executable instructions, and
other computer usable program code. The computer program product
may be embodied in removable computer storage media and/or
non-removable computer storage media. The removable computer
readable storage medium may comprise, without limitation, a paper
tape, a magnetic tape, magnetic disk, an optical disk, a solid
state memory chip, for example analog magnetic tape, compact disk
read only memory (CD-ROM) disks, floppy disks, jump drives, digital
cards, multimedia cards, and others. The computer program product
may be suitable for loading, by the computer system 780, at least
portions of the contents of the computer program product to the
secondary storage 784, to the ROM 786, to the RAM 788, and/or to
other non-volatile memory and volatile memory of the computer
system 780. The processor 782 may process the executable
instructions and/or data structures in part by directly accessing
the computer program product, for example by reading from a CD-ROM
disk inserted into a disk drive peripheral of the computer system
780. Alternatively, the processor 782 may process the executable
instructions and/or data structures by remotely accessing the
computer program product, for example by downloading the executable
instructions and/or data structures from a remote server through
the network connectivity devices 792. The computer program product
may comprise instructions that promote the loading and/or copying
of data, data structures, files, and/or executable instructions to
the secondary storage 784, to the ROM 786, to the RAM 788, and/or
to other non-volatile memory and volatile memory of the computer
system 780.
[0115] In some contexts, a baseband signal and/or a signal embodied
in a carrier wave may be referred to as a transitory signal. In
some contexts, the secondary storage 784, the ROM 786, and the RAM
788 may be referred to as a non-transitory computer readable medium
or a computer readable storage media. A dynamic RAM embodiment of
the RAM 788, likewise, may be referred to as a non-transitory
computer readable medium in that while the dynamic RAM receives
electrical power and is operated in accordance with its design, for
example during a period of time during which the computer 780 is
turned on and operational, the dynamic RAM stores information that
is written to it. Similarly, the processor 782 may comprise an
internal RAM, an internal ROM, a cache memory, and/or other
internal non-transitory storage blocks, sections, or components
that may be referred to in some contexts as non-transitory computer
readable media or computer readable storage media. In an
embodiment, the computer system 780 is utilized to improve the
processing of polymers of the type disclosed herein (e.g., PE base
resin). In such an embodiment, information obtained as described
herein may serve as input to an analysis component of the computer
stored in memory that when executed on the processor, configures
the processor to receive a shear stress as a function of shear rate
for a plurality of multimodal metallocene-catalyzed polyethylene
samples, wherein the determination of the shear stress as a
function of the shear rate comprises using capillary rheometry
determine values for a slip-stick, a smooth to matte transition,
and a shear rate for each of the plurality of multimodal
metallocene-catalyzed polyethylene samples based on the shear
stress and the shear rate identify individual multimodal
metallocene-catalyzed polyethylene resins from the plurality of
multimodal metallocene-catalyzed polyethylene samples having a
reduced tendency to melt fracture characterized by a magnitude of
slip-stick greater than about 300 psi, a smooth to matte transition
of greater than about 90 kPa of stress, and a shear rate greater
than about 10 s.sup.-1; an output an identification of the
individual multimodal metallocene-catalyzed polyethylene resins to
the output device.
[0116] The following are additional enumerated embodiments of the
concepts disclosed herein.
[0117] A first embodiment which is a method of improving processing
of polyethylene resins comprising obtaining a plurality of
multimodal metallocene-catalyzed polyethylene samples; measuring
the shear stress as a function of shear rate for the plurality of
multimodal metallocene-catalyzed polyethylene samples using
capillary rheometry wherein the measuring yields values for a
magnitude of slip-stick, a stress for smooth to matte transition,
and a shear rate for smooth to matte transition; and identifying
from the plurality of multimodal metallocene-catalyzed polyethylene
samples individual multimodal metallocene-catalyzed polyethylene
resins having a reduced tendency to melt fracture characterized by
a magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
[0118] A second embodiment which is the method of the first
embodiment wherein each of the plurality of multimodal
metallocene-catalyzed polyethylene samples comprises a polymer
blend.
[0119] A third embodiment which is the method of any of the first
through second embodiments wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples comprises a
higher molecular weight component and a lower molecular weight
component.
[0120] A fourth embodiment which is the method of the third
embodiment wherein the higher molecular weight component has a peak
molecular weight ranging from about 67 kg/mol to about 600 kg/mol
and the lower molecular weight component has a peak molecular
weight ranging from about 25 kg/mol to about 65 kg/mol.
[0121] A fifth embodiment which is the method of any of the first
through fourth embodiments wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples has a
molecular weight distribution of from about 5 to about 30.
[0122] A sixth embodiment which is the method of any of the first
through fifth embodiments wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples has a
magnitude of stick-slip of from greater than about 300 psi to about
1500 psi.
[0123] A seventh embodiment which is the method of any of the first
through sixth embodiments wherein each of the plurality of
multimodal metallocene-catalyzed polyethylene samples has a shear
rate for smooth to matte transition of from greater than about 10
s.sup.-1 to about 100 s.sup.-1.
[0124] An eight embodiment which is the method of any of the first
through seventh embodiments wherein the melt fracture is sharkskin
melt fracture, slip-stick fracture or gross melt fracture.
[0125] A ninth embodiment which is a method of improving processing
of polyethylene resins comprising obtaining a known molecular
weight distribution, a known magnitude of slip-stick, a known
stress for smooth to matte transition, and a known shear rate for
smooth to matte transition, for each of a plurality of polyethylene
resins; performing chemometric analysis to determine an analytical
relationship between the known molecular weight distribution, the
known magnitude of slip-stick, the known stress for smooth to matte
transition, and the known shear rate for smooth to matte transition
for the plurality of polyethylene resins; obtaining a plurality of
multimodal metallocene-catalyzed polyethylene resins, each having a
known molecular weight distribution, an unknown magnitude of
slip-stick, an unknown stress for smooth to matte transition, and
an unknown shear rate for smooth to matte transition; utilizing the
analytical relationship to determine a value for the unknown
magnitude of slip-stick, a value for the unknown stress for smooth
to matte transition, and the unknown shear rate for smooth to matte
transition for each of the plurality of multimodal
metallocene-catalyzed polyethylene samples; and identifying from
the plurality of multimodal metallocene-catalyzed polyethylene
resins individual multimodal metallocene-catalyzed polyethylene
resins having a reduced tendency to melt fracture characterized by
a magnitude of slip-stick greater than about 300 psi, a stress for
smooth to matte transition greater than about 90 kPa, and a shear
rate for smooth to matte transition greater than about 10
s.sup.-1.
[0126] A tenth embodiment which the method of the ninth embodiment
wherein the analytical relationship is a mathematical equation.
[0127] An eleventh embodiment which is the method of the tenth
embodiment wherein the analytical relationship is established using
at least one chemometric technique selected from the group
consisting of Partial Least Squares Regression, Multilinear
Regression Analysis, Principal Components Regression, Principal
Component Analysis, Discriminant Analysis, Design of Experiment,
and Response Surface Methodologies.
[0128] A twelfth embodiment which is the method of any of the ninth
through eleventh embodiments wherein the plurality of polyethylene
resins comprises equal to or greater than about 10 samples.
[0129] A thirteenth embodiment which is the method of any of the
ninth through twelfth embodiments wherein the known molecular
weight distribution is from about 5 to about 30.
[0130] A fourteenth embodiment which is the method of any of the
ninth through thirteenth embodiments wherein the known magnitude of
slip-stick is from about 300 psi to about 1500 psi.
[0131] A fifteenth embodiment which is the method of any of the
ninth through fourteenth embodiments wherein the known stress for a
smooth to matte transition is less than about 200 kPa.
[0132] A sixteenth embodiment which is the method of any of the
ninth through fifteenth embodiments wherein the known shear rate
for smooth to matte transition is from greater than about 10
s.sup.-1 to about 100 s.sup.-1.
[0133] A seventeenth embodiment which is the method of any of the
ninth through sixteenth embodiments wherein the individual
multimodal metallocene-catalyzed polyethylene resins having a
reduced tendency to melt fracture comprise a higher molecular
weight component and a lower molecular weight component.
[0134] An eighteenth embodiment which is the method of the
seventeenth embodiment wherein the higher molecular weight
component has a peak molecular weight ranging from about 67 kg/mol
to about 600 kg/mol and the lower molecular weight component has a
peak molecular weight ranging from about 25 kg/mol to about 65
kg/mol.
[0135] A nineteenth embodiment which is the method of any of the
ninth through eighteenth embodiments wherein the individual
multimodal metallocene-catalyzed polyethylene resins having a
reduced tendency to melt fracture comprise a comonomer.
[0136] A twentieth embodiment which the method of any of the ninth
through nineteenth embodiments further comprising identifying
individual multimodal metallocene-catalyzed polyethylene resins
having an increased tendency to melt fracture.
[0137] A twenty-first embodiment which is the method of any of the
first through eight embodiments further comprising forming one or
more of the individual multimodal metallocene-catalyzed
polyethylene resins having a reduced tendency to melt fracture into
an article.
[0138] A twenty-second embodiment which is the method of any of the
ninth through twentieth embodiments further comprising forming one
or more of the individual multimodal metallocene-catalyzed
polyethylene resins having a reduced tendency to melt fracture into
an article.
[0139] A twenty-third embodiment which is the method of any of the
first through eight or twenty-first embodiments further comprising
providing one or more of the individual multimodal
metallocene-catalyzed polyethylene resins having a reduced tendency
to melt fracture to a user in need thereof.
[0140] A twenty-fourth embodiment which is the method of any of the
ninth through twentieth or twenty-second embodiments further
comprising providing one or more of the individual multimodal
metallocene-catalyzed polyethylene resins having a reduced tendency
to melt fracture to a user in need thereof.
EXAMPLES
[0141] For each of the following examples molecular weights and
molecular weight distributions were obtained using a PL 220 GPC/SEC
high temperature chromatography unit (Polymer Laboratories, now an
Agilent Company) with 1,2,4-trichlorobenzene (TCB) as the solvent,
with a flow rate of 1 mL/minute at a temperature of 145.degree. C.
BHT (2,6-di-tert-butyl-4-methylphenol) at a concentration of 0.5
g/L was used as a stabilizer in the TCB. An injection volume of 400
.mu.L was used with a nominal polymer concentration of 1.0 mg/mL.
Dissolution of the sample in stabilized TCB was carried out by
heating at 150.degree. C. for about 5 hours with occasional, gentle
agitation. The columns used were three PLgel 20 m Mixed A LS
columns (7.5.times.300 mm) and were calibrated with the integral
method using a broad linear polyethylene standard (Chevron Phillips
Chemical Company Marlex.RTM. BHB 5003 polyethylene) for which the
molecular weight distribution had been determined. An IR4 detector
(Polymer Char, Spain) was used for the concentration detection.
[0142] A PLS2 calibration curve was generated using Pirouette
chemometric software (Infometrix) to correlate the polymer
microstructure obtained by GPC] to the melt fracture behavior as
determined by capillary rheometry. A four component calibration
model was calculated and optimized using the process of cross
validation. The calibration model was verified using a
cross-validation approach.
Example 1
[0143] PLS analysis of the MWD data of various metallocene
polyethylenes (M-PE) and Ziegler-Natta polyethylenes (ZN-PE)
provided a predicted melt fracture characteristic (Y) which was
compared to the measured characteristic. Table 1 provides data on
the predicted and measured slip-stick values (psi) (Y=slip-stick
value) for 55 polyethylene samples while FIG. 2 is a graphical
representation of a calibration curve prepared from the data in
Table 1. The slip-stick values of nine polyethylene samples were
predicted using the calibration curve of FIG. 2 and the results are
presented in Table 2. FIG. 3 is plot of the predicted magnitude
values (psi) for slip-stick as a function of the measured magnitude
values (psi) for slip-stick for both the calibration samples and
validation samples. In addition to the predicted and measured
values of Y, each table provides conventional measures of the
statistical significance of the data in the form of the Mahalanobis
distance, F ratio, probability and leverage. These samples were
used to validate the calibration training set.
[0144] Table 3 provides data on the predicted and measured values
in kilPascal (kPa) for the smooth to matte transition (Y=smooth to
matte transition) for 55 polyethylene samples while FIG. 4 is a
graphical representation of a calibration curve prepared from the
data in Table 3. The values for the smooth to matte transition for
several polyethylene samples were predicted using the calibration
curve of FIG. 4 and the results are presented in Tables 4-6. These
samples were used to validate the calibration training set. FIG. 4
is plot of the predicted magnitude values (kPa) for the smooth to
matte transition as a function of the measured magnitude values
(kPa) for the smooth to matte transition for the calibration
samples. FIG. 5 is a plot of the predicted magnitude values (kPa)
for smooth to matte transition as a function of the measured
magnitude values (kPa) for the smooth to matte transition for both
the calibration samples and validation samples. FIG. 6 is a plot of
the predicted magnitude values (kPa) for the onset of wavy
transition as a function of the measured magnitude values (kPa) for
the onset of wavy transition for the calibration samples.
TABLE-US-00001 TABLE 1 Sample Cat Structure Residual Upper Lower
Mahalanobis No. type. type Measured Y Predicted Y Y Limit Limit
Distance F Ratio Probability Leverage 1 M-PE BM 0 88 -88 253 -77
4.689452 0.633723 0.570243 0.086842 2 M-PE BM 0 -28 28 139 -194
5.800618 0.835267 0.63486 0.107419 3 M-PE BM 0 -26 26 136 -188
2.633439 0.741116 0.606587 0.048767 4 M-PE BM 0 -17 17 157 -191
11.267695 2.460193 0.876928 0.208661 5 M-PE BM 0 -16 16 150 -183
5.725693 1.174878 0.7164 0.106031 6 M-PE BM 23 9 14 170 -152
1.923788 0.193044 0.337712 0.035626 7 M-PE BM 26 125 -99 290 -40
4.577909 1.075055 0.695205 0.084776 8 M-PE BM 29 -29 58 138 -197
6.864896 2.990719 0.910087 0.127128 9 M-PE BM 39 33 6 201 -134
6.656994 0.469325 0.503538 0.123278 10 M-PE BM 82 129 -47 297 -38
6.340309 0.229147 0.365756 0.117413 11 M-PE BM 85 43 42 204 -118
1.801648 0.440555 0.490096 0.033364 12 M-PE BM 96 120 -24 283 -43
3.287461 0.429704 0.484861 0.060879 13 M-PE BM 98 124 -26 287 -39
3.52283 0.64812 0.575402 0.065238 14 M-PE TM 115 129 -14 290 -32
2.059048 1.0367 0.686508 0.038131 15 M-PE BM 177 318 -141 481 155
3.497214 0.827687 0.632693 0.064763 16 M-PE TM 181 221 -40 382 59
2.273243 0.258925 0.386902 0.042097 17 M-PE TM 205 222 -17 388 56
5.390471 0.663727 0.580889 0.099824 18 M-PE TM 235 296 -61 457 136
1.278223 1.215226 0.724422 0.023671 19 M-PE TM 280 278 2 439 118
1.522296 0.984203 0.67406 0.028191 20 M-PE TM 300 362 -62 522 201
1.297488 1.053023 0.690249 0.024028 21 M-PE BM 302 385 -83 561 208
13.109332 0.853596 0.640025 0.242765 22 M-PE BM 305 470 -165 629
311 0.628161 0.242451 0.375403 0.011633 23 M-PE TM 329 319 10 483
155 4.188392 0.271828 0.39559 0.077563 24 M-PE BM 346 308 38 475
141 6.075836 1.784714 0.812379 0.112515 25 M-PE BM 415 333 82 497
168 4.458403 0.747879 0.608721 0.082563 26 M-PE TM 415 353 62 514
192 1.635425 0.142301 0.292399 0.030286 27 M-PE BM 424 513 -89 673
353 1.172451 2.288236 0.863346 0.021712 28 M-PE TM 425 299 126 460
138 1.718942 0.57019 0.546274 0.031832 29 ZN-PE BM 440 480 -40 640
320 1.064778 0.324859 0.428746 0.019718 30 M-PE TM 469 486 -17 647
325 2.041597 1.036271 0.686409 0.037807 31 M-PE BM 469 500 -31 660
341 0.766478 0.316317 0.423658 0.014194 32 M-PE TM 485 343 142 503
183 1.222706 0.56069 0.542509 0.022643 33 M-PE BM 499 488 10 654
323 5.17874 0.355525 0.446308 0.095903 34 ZN-PE BM 503 627 -124 791
463 4.157712 0.830472 0.633491 0.076995 35 M-PE TM 517 415 102 576
254 1.824844 1.438857 0.764022 0.033793 36 M-PE TM 518 471 47 631
310 1.750413 0.309239 0.419372 0.032415 37 M-PE BM 537 474 62 640
309 5.147545 0.443338 0.491424 0.095325 38 ZN-PE BM 547 665 -118
827 503 2.504622 0.990738 0.675645 0.046382 39 ZN-PE BM 580 538 42
697 379 0.317906 0.306911 0.417948 0.005887 40 ZN-PE BM 590 663 -73
825 502 2.199406 0.889679 0.6499 0.04073 41 M-PE TM 625 462 163 622
302 1.120593 0.449243 0.494221 0.020752 42 ZN-PE BM 634 695 -61 856
535 1.57108 1.183749 0.718189 0.029094 43 M-PE BM 663 539 124 704
375 4.274136 1.670804 0.797908 0.079151 44 M-PE BM 705 713 -9 879
548 5.195957 0.228689 0.365418 0.096221 45 M-PE BM 707 804 -97 972
636 6.814694 1.341158 0.747668 0.126198 46 M-PE BM 731 778 -47 944
611 5.682072 0.809082 0.627296 0.105224 47 ZN-PE/M-PE TM 740 814
-74 977 651 3.360436 0.085846 0.229261 0.06223 48 M-PE BM 759 745
14 910 579 5.213402 0.524056 0.52751 0.096545 49 M-PE BM 790 757 34
921 592 4.548491 0.367159 0.452702 0.084231 50 ZN-PE BM 875 755 120
916 595 1.876904 1.482164 0.770849 0.034757 51 ZN-PE/M-PE TM 879
810 69 973 648 3.194673 0.171523 0.319467 0.059161 52 ZN-PE/M-PE TM
920 813 108 976 650 3.257771 0.130208 0.280263 0.060329 53
ZN-PE/M-PE TM 1011 1026 -14 1193 858 6.690147 0.331866 0.432853
0.123892 54 ZN-PE/M-PE TM 1062 956 105 1126 787 7.956915 0.705278
0.594986 0.14735 55 M-PE BM 1218 1227 -10 1402 1053 11.668286
1.841389 0.819117 0.216079
TABLE-US-00002 TABLE 2 Structure Upper Lower Mahalanobis Sample No.
Cat type. type Measured Y Predicted Y Residual Y Limit Limit
Distance F Ratio Probability Leverage 56 M-PE BM 0 -13 13 156 -182
7.6880 2.0368 0.8403 0.1424 57 M-PE BM 0 -16 16 150 -183 5.7257
1.1749 0.7164 0.1060 58 M-PE BM 76 94 -19 261 -73 6.2220 0.5418
0.5349 0.1152 59 M-PE TM 224 245 -21 406 84 1.9931 0.1997 0.3431
0.0369 60 M-PE BM 389 363 26 528 197 4.9512 0.8698 0.6445 0.0917 61
ZN-PE BM 445 489 -44 648 329 0.9934 0.4117 0.4760 0.0184 62 M-PE BM
610 585 25 747 424 2.3449 1.0511 0.6898 0.0434 63 M-PE BM 771 805
-34 973 636 7.0441 1.7967 0.8138 0.1304 64 ZN-PE BM 785 692 93 853
531 1.9709 0.6158 0.5637 0.0365
TABLE-US-00003 TABLE 3 95% CL 95% CL Residual Upper Lower Sample
Structure Measured Y Predicted Y Y Limit Limit Mahalanobis No. Cat
type. type (kPa) (kPa) (kPa) (kPa) (kPa) Distance F Ratio
Probability Leverage 65 M-PE BM 26 43 -17 70 15 5.28302 0.60381
0.559417 0.09434 66 M-PE BM 30 46 -16 73 19 2.703169 3.544509
0.934763 0.048271 67 M-PE BM 41 30 11 58 2 6.791506 0.674373
0.58479 0.121277 68 M-PE BM 47 42 5 69 15 2.04752 0.21828 0.357731
0.036563 69 M-PE BM 52 54 -2 82 26 4.292444 1.905774 0.826772
0.076651 70 M-PE BM 52 38 14 65 10 3.331579 0.99675 0.677365
0.059492 71 M-PE BM 54 40 14 67 13 2.209805 0.063193 0.197509
0.039461 72 M-PE TM 54 53 1 80 26 1.938798 0.871222 0.64515
0.034621 73 M-PE BM 55 32 23 60 5 2.820709 0.170083 0.318298
0.05037 74 M-PE BM 56 59 -3 87 31 5.889243 0.878045 0.647012
0.105165 75 M-PE BM 56 68 -12 95 41 2.342684 1.210574 0.723809
0.041834 76 M-PE TM 57 64 -7 91 37 2.000884 0.347987 0.442239
0.03573 77 M-PE TM 61 81 -20 108 54 1.083685 0.492962 0.514319
0.019352 78 M-PE TM 61 77 -16 104 50 1.602323 0.437354 0.488733
0.028613 79 M-PE BM 63 70 -7 98 43 2.992918 3.138032 0.917765
0.053445 80 M-PE TM 64 66 -2 93 39 1.210406 0.848122 0.638743
0.021614 81 M-PE BM 67 89 -22 116 61 4.573915 1.435869 0.76386
0.081677 82 M-PE BM 67 89 -22 117 61 4.189096 0.565609 0.544664
0.074805 83 M-PE TM 67 73 -6 100 46 1.356554 0.496362 0.515812
0.024224 84 ZN-PE BM 67 97 -30 124 71 0.109069 0.124188 0.274066
0.001948 85 M-PE BM 69 74 -5 102 47 2.373091 3.201317 0.920706
0.042377 86 M-PE TM 71 63 8 90 36 1.078215 0.910404 0.655661
0.019254 87 M-PE TM 73 57 16 84 30 1.915975 0.474808 0.506211
0.034214 88 M-PE TM 74 72 2 99 46 1.092725 0.523947 0.527654
0.019513 89 M-PE TM 76 81 -5 107 54 0.881971 0.871174 0.645137
0.015749 90 M-PE BM 76 96 -20 122 69 0.295858 1.400256 0.758039
0.005283 91 M-PE TM 77 55 22 82 28 2.559104 2.04462 0.841386
0.045698 92 M-PE TM 77 80 -3 107 53 1.272153 1.285069 0.73794
0.022717 93 M-PE BM 82 81 1 108 53 2.981837 0.206155 0.348348
0.053247 94 ZN-PE BM 83 105 -22 132 78 1.942585 1.262393 0.733738
0.034689 95 M-PE BM 88 87 1 113 60 0.35911 1.416235 0.760672
0.006413 96 M-PE TM 89 80 9 107 53 0.894821 0.874843 0.64614
0.015979 97 M-PE BM 98 81 17 109 54 3.877832 0.222874 0.361203
0.069247 98 ZN-PE BM 99 106 -7 133 79 1.446633 0.767448 0.615039
0.025833 99 M-PE BM 100 114 -14 141 86 4.174528 2.378543 0.871038
0.074545 100 ZN-PE BM 104 113 -9 140 86 0.799369 1.105997 0.702275
0.014274 101 M-PE BM 106 102 4 132 73 12.342955 0.444051 0.491936
0.22041 102 M-PE BM 108 114 -6 141 86 4.454492 0.779766 0.618799
0.079545 103 ZN-PE BM 110 110 0 136 83 0.949288 0.526221 0.528609
0.016952 104 ZN-PE BM 110 108 2 135 81 1.241156 0.488042 0.512144
0.022163 105 ZN-PE BM 110 107 3 134 81 1.12129 0.436844 0.488487
0.020023 106 M-PE BM 110 98 12 126 71 3.647568 0.588353 0.55354
0.065135 107 M-PE BM 113 115 -2 143 88 4.201627 1.382741 0.75511
0.075029 108 M-PE BM 120 105 15 132 77 3.490929 0.811559 0.628265
0.062338 109 ZN-PE/M-PE TM 121 128 -7 154 101 1.465725 0.091316
0.236306 0.026174 110 M-PE BM 121 98 24 125 70 3.35217 0.587111
0.553062 0.05986 111 ZN-PE/M-PE TM 123 126 -3 153 99 1.524436
0.077956 0.218827 0.027222 112 ZN-PE/M-PE TM 125 127 -2 154 100
1.587229 0.067539 0.204038 0.028343 113 M-PE BM 128 117 11 144 89
4.179567 0.307286 0.418318 0.074635 114 M-PE BM 128 112 16 140 85
3.750068 2.928592 0.907129 0.066966 115 ZN-PE/M-PE TM 145 151 -6
179 124 3.673731 0.130649 0.280803 0.065602 116 ZN-PE/M-PE TM 158
149 9 176 121 3.22575 0.17626 0.323696 0.057603 117 ZN-PE/M-PE TM
162 154 8 182 126 5.568025 0.263315 0.390016 0.099429 118
ZN-PE/M-PE TM 164 149 15 177 122 3.470207 0.203697 0.346405
0.061968 119 ZN-PE/M-PE TM 166 153 13 181 125 5.457026 0.214731
0.355018 0.097447 120 ZN-PE/M-PE TM 174 152 22 180 125 5.088583
0.358921 0.448342 0.090868 121 M-PE BM 177 183 -6 211 155 7.493027
0.616065 0.563992 0.133804
TABLE-US-00004 TABLE 4 95% CL 95% CL Upper Lower Structure Measured
Y Predicted Y Residual Y Limit Limit Mahalanobis Cat type. type
(kPa) (kPa) (kPa) (kPa) (kPa) Distance F Ratio Probability Leverage
112 M-PE BM 24 23 1 51 -5 5.982789 1.99459 0.836293 0.106836 113
M-PE BM 21 30 -9 59 1 9.041662 3.48069 0.932372 0.161458 114 M-PE
BM 25 28 -3 56 -1 8.167974 2.390947 0.872009 0.145857 115 M-PE BM
30 24 6 53 -4 7.772788 1.569992 0.784292 0.1388
TABLE-US-00005 TABLE 5 95% CL Upper 95% CL Lower Observed Pipe
Resins Measured Y (kPa) Predicted Y (kPa) Limit Limit SS-MF PPA C1
48 55 82 27 yes yes C2 44 45 72 18 yes yes C3 44 45 72 18 yes yes
C4 82 64 18 114 NA no C5 NA 69 96 41 yes yes C6 NA 89 116 62 NA no
C7 NA 89 116 62 yes yes I1 108 116 143 88 NA no I2 NA 116 144 88 no
no I3 NA 116 144 88 no yes
TABLE-US-00006 TABLE 6 Measured Measured shear rate Pipe Resins Y
(kPa) (1/s) Observed SS-MF PPA C1 48 16 yes yes C2 44 17 yes yes C3
47 2.5 NA no C4 44 11 yes yes C5 NA NA yes yes C6 NA NA yes yes C7
NA NA yes yes I1 108 26 NA no I2 NA NA no yes I3 NA NA no yes
Example 2
[0145] Using two Gaussian peak shapes, various MWD profiles were
digitally generated by varying six parameters, the Mp, PDI and
weight fraction of peak 1(P1) and Mp, PDI and weight fraction of
peak 2 (P2). P1 is also referred to as the lower molecular weight
(LMW) component while P2 is also referred to as the higher
molecular weight (HMW) component. Recognizing that if the area
under the MWD distribution is equal to unity (i.e., 1) and is
described by two component peaks, the number of variables can be
reduced to five, where the weight fraction composition of peak 2
can be written in terms of the weight fraction of peak 1 (i.e., wt
frac. p2=1-wt frac. p1). These parameters are illustrated in FIG.
8. To explore the influence of these five parameters on the
magnitude of slip-stick as predicted as from the above PLS2 method,
a DOE of the five parameters was generated as below in Table 7.
Also appearing in Table 7 are the M.sub.w, M.sub.n and PDI of the
results MWD profile obtained by the combination of the two
components as well as the values for the predicted magnitude of the
slip-stick generated from the analysis of the resulting MWD profile
using the PLS2 model.
TABLE-US-00007 TABLE 7 Other values Blend Blend Std PDI Magnitude
Mw Mn Mn Mw Mn Order Run Mp P1 Mp P2 PDI P1 P2 Wt Frac P1
Slip-stick Matte P1 Mw P2 P1 P2 kg/mol kg/mol Blend PDI 21 1
63.24555 94.86833 2.5 2.5 0.3 1388 189 100 150 40 60 135 52 2.5875
25 2 11.18034 505.9644 5 2.5 0.3 167 36 25 800 5 320 568 16
35.29141 27 3 32.27486 245.2889 3.75 3.75 0.5 645 116 63 475 17 127
269 29 9.123355 19 4 11.18034 212.4265 5 5 0.3 629 107 25 475 5 95
340 15 22.90526 10 5 32.27486 245.2889 3.75 3.75 0.5 562 130 63 475
17 127 269 29 9.123355 31 6 12.90994 67.08204 3.75 5 0.3 583 115 25
150 7 30 113 15 7.6875 28 7 15.81139 413.1182 2.5 3.75 0.7 -323 24
25 800 10 213 258 14 18.38711 14 8 44.72136 505.9644 5 2.5 0.3 428
65 100 800 20 320 590 58 10.14063 20 9 27.95085 357.7709 5 5 0.3
560 93 63 800 13 160 579 35 16.42203 7 10 63.24555 505.9644 2.5 2.5
0.7 580 101 100 800 40 320 310 54 5.715625 9 11 63.24555 67.08204
2.5 5 0.7 1179 170 100 150 40 30 115 36 3.1625 29 12 11.18034
212.4265 5 5 0.3 712 93 25 475 5 95 340 15 22.90526 11 13 11.18034
94.86833 5 2.5 0.3 1097 162 25 150 5 60 113 14 8.0625 26 14
63.24555 67.08204 2.5 5 0.3 1041 158 100 150 40 30 135 32 4.1625 17
15 15.81139 94.86833 2.5 2.5 0.7 74 70 25 150 10 60 63 13 4.6875 23
16 63.24555 505.9644 2.5 2.5 0.3 428 65 100 800 40 320 590 103
5.715625 8 17 63.24555 357.7709 2.5 5 0.3 899 125 100 800 40 160
590 84 7.00625 12 18 12.90994 67.08204 3.75 5 0.3 666 102 25 150 7
30 113 15 7.6875 22 19 15.81139 94.86833 2.5 2.5 0.3 927 149 25 150
10 60 113 24 4.6875 13 20 11.18034 505.9644 5 2.5 0.7 -65 32 25 800
5 320 258 7 36.29141 15 21 44.72136 67.08204 5 5 0.3 851 142 100
150 20 30 135 26 5.175 32 22 31.62278 260.8746 2.5 5 0.7 459 104 50
583 20 117 210 27 7.89 3 23 44.72136 94.86833 5 2.5 0.7 935 149 100
150 20 60 115 25 4.6 6 24 44.72136 357.7709 5 5 0.7 687 119 100 800
20 160 310 27 11.43125 2 25 15.81139 413.1182 2.5 3.75 0.7 -240 10
25 800 10 213 258 14 18.38711 24 26 44.72136 94.86833 5 2.5 0.3
1241 177 100 150 20 60 135 38 3.6 4 27 11.18034 67.08204 5 5 0.7
203 75 25 150 5 30 63 7 9.375 30 28 27.95085 357.7709 5 5 0.3 477
107 63 800 13 160 579 35 16.42203 16 29 15.81139 67.08204 2.5 5 0.5
171 79 25 150 10 30 88 15 5.833333 18 30 31.62278 260.8746 2.5 5
0.7 376 118 50 583 20 117 210 27 7.89 5 31 15.81139 505.9644 2.5
2.5 0.3 4 25 25 800 10 320 568 31 18.26641 1 32 12.24745 357.7709
4.166667 5 0.566666667 99 54 25 800 6 160 361 10 35.05596
[0146] An analysis of variance (ANOVA) was carried out on the
values calculated from the PLS2 data for the slip-stick melt
fracture and the results are given in Tables 8, 9, and 110.
TABLE-US-00008 TABLE 8 Sum of Mean F p-value Source Squares df
Square Value Prob > F Model 5527071 15 368471.4164 36.91696
<0.0001 A-Mp P1 1600828 1 1600827.965 160.3861 <0.0001 B-Mp
P2 783015.4 1 783015.3965 78.4499 <0.0001 C-PDI LMW 97880.79 1
97880.79312 9.806625 0.0064 D-PDI HMW 428.771 1 428.7710289
0.042958 0.8384 E-Wt frac LMW 175349.7 1 175349.7336 17.5682 0.0007
AB 85.06823 1 85.06823224 0.008523 0.9276 AC 132153 1 132152.9765
13.24034 0.0022 AD 6772.471 1 6772.470625 0.67853 0.4222 AE
357916.6 1 357916.5942 35.85947 <0.0001 BC 403.4945 1
403.4944702 0.040426 0.8432 BD 293699.2 1 293699.1753 29.42556
<0.0001 BE 78878.29 1 78878.29386 7.902774 0.0125 CD 7930.625 1
7930.625265 0.794565 0.3859 CE 14450.72 1 14450.72244 1.44781
0.2464 DE 72350.18 1 72350.18158 7.248726 0.0160 Residual 159697.4
16 9981.089078 Lack of Fit 129697.4 10 12969.74253 2.593949 0.1278
Pure Error 30000 6 5000 Cor Total 5686769 31
[0147] The Model F-value of 36.92 implies the model is significant.
There is only a 0.01% chance that a "Model F-Value" this large
could occur due to noise. Further, the values of "Prob>F" less
than 0.0500 indicate model terms are significant The results
demonstrate that in this case A, B, C, E, AC, AE, BD, BE, DE are
significant model terms as values greater than 0.1000 indicate the
model terms are not significant. A better model can be obtained by
removing insignificant model terms (not counting those required to
support hierarchy), in order to demonstrate the influence of all
the terms. The "Lack of Fit F-value" of 2.59 implies the Lack of
Fit is not significant relative to the pure error. There is a
12.78% chance that a "Lack of Fit F-value" this large could occur
due to noise. Further statistical evaluation provided the
following:
TABLE-US-00009 TABLE 9 Std. Dev. 99.9054 R-Squared 0.971918 Mean
545.1094 Adj R-Squared 0.945591 C.V. % 18.32759 Pred R-Squared
0.87355 PRESS 719089.8 Adeq Precision 22.77148
[0148] The "Pred R-Squared" of 0.8736 is in reasonable agreement
with the "Adj R-Squared" of 0.9456. This value improves to 0.9277
with insignificant terms removed. "Adeq Precision" is a measure of
the signal to noise ratio. A ratio greater than 4 is desirable. The
observed ratio of 22.771 indicates an adequate signal suggesting
this model can be used to navigate the design space.
TABLE-US-00010 TABLE 10 Coefficient Standard 95% CI 95% CI Factor
Estimate df Error Low High VIF Intercept 593.1529 1 22.40955147
545.6468 640.659 A-Mp P1 364.2112 1 28.75874163 303.2453 425.177
1.461032 B-Mp P2 -249.026 1 28.11571834 -308.629 -189.424 1.456545
C-PDI LMW 73.14195 1 23.35644523 23.6285 122.6554 1.481018 D-PDI
HMW -4.69935 1 22.67325858 -52.7645 43.36581 1.416389 E-Wt frac LMW
-89.574 1 21.37068513 -134.878 -44.2702 1.240368 AB -3.07806 1
33.34130335 -73.7585 67.60234 1.536049 AC -108.375 1 29.78381408
-171.514 -45.2363 1.395963 AD 24.59074 1 29.85292932 -38.6946
87.87612 1.599554 AE 166.8858 1 27.86874874 107.8067 225.9649
1.398294 BC 5.444599 1 27.07921396 -51.9608 62.84997 1.24382 BD
152.3825 1 28.09134774 92.83146 211.9335 1.328869 BE 74.52588 1
26.51046512 18.32621 130.7256 1.245329 CD -20.955 1 23.50841841
-70.7906 28.8806 1.387308 CE 27.04579 1 22.47728138 -20.6039
74.69549 1.261851 DE 59.39209 1 22.05960613 12.62781 106.1564
1.272873
[0149] The sign of the coefficient estimate indicated the magnitude
of influence and direction of effect for the particular parameter
or combination of parameters. For example increasing the M.sub.p
P1, increased the slip-stick magnitude while increasing the M.sub.p
of P2 decreased the slip-stick magnitude (greater MW difference
between components, therefore less overlap).
[0150] The analysis of the variance was recalculated omitting runs
7, 15, 25, and 29 in the analysis. These runs were omitted because
the chemometric model identified these runs as outliers with a
probability greater than the cutoff of 0.999. The results of this
second ANOVA analysis are presented in Tables 11-13.
TABLE-US-00011 TABLE 11 ANOVA for Response Surface 2FI Model
Analysis of variance table [Partial sum of squares - Type III] Sum
of Mean F p-value Source Squares df Square Value Prob > F Model
3646082 15 243072.1025 41.75056 <0.0001 A-Mp P1 895118.2 1
895118.2205 153.7473 <0.0001 B-Mp P2 600640.3 1 600640.3064
103.1672 <0.0001 C-PDI P1 21689.74 1 21689.73544 3.725473 0.0776
D-PDI P2 5012.122 1 5012.121606 0.860892 0.3718 E-Wt frac P1 115814
1 115814.024 19.89245 0.0008 AB 1790.978 1 1790.978376 0.307622
0.5893 AC 57380.55 1 57380.54663 9.855799 0.0085 AD 4863.659 1
4863.658861 0.835392 0.3787 AE 110499.6 1 110499.6017 18.97963
0.0009 BC 4646.01 1 4646.009525 0.798008 0.3893 BD 240247.8 1
240247.8178 41.26545 <0.0001 BE 36791.94 1 36791.93615 6.319457
0.0272 CD 2766.34 1 2766.340376 0.475152 0.5037 CE 3.189822 1
3.189821631 0.000548 0.9817 DE 12859.12 1 12859.11567 2.208708
0.1630 Residual 69864.11 12 5822.008807 Lack of Fit 52641.61 7
7520.229384 2.183257 0.2035 Pure Error 17222.5 5 3444.5 Cor Total
3715946 27
[0151] The Model F-value of 41.75 implies the model is significant.
There is only a 0.01% chance that a "Model F-Value" this large
could occur due to noise. Values of "Prob>F" less than 0.0500
indicate model terms are significant. In this case A, B, E, AC, AE,
BD, BE are significant model terms. Values greater than 0.1000
indicate the model terms are not significant. The "Lack of Fit
F-value" of 2.18 implies the Lack of Fit is not significant
relative to the pure error. There is a 20.35% chance that a "Lack
of Fit F-value" this large could occur due to noise.
TABLE-US-00012 TABLE 12 Std. Dev. 76.30209 R-Squared 0.981199 Mean
634.3231 Adj R-Squared 0.957697 C.V. % 12.0289 Pred R-Squared
0.830489 PRESS 629894.2 Adeq Precision 25.6499
[0152] The "Pred R-Squared" of 0.8305 is in reasonable agreement
with the "Adj R-Squared" of 0.9577. "Adeq Precision" measures the
signal to noise ratio. A ratio greater than 4 is desirable. The
ratio of 25.650 indicates an adequate signal. This model can be
used to navigate the design space.
TABLE-US-00013 TABLE 13 Coefficient Standard 95% CI 95% CI Factor
Estimate df Error Low High VIF Intercept 610.5575 1 19.66770497
567.7052 653.4097 A-Mp P1 326.8809 1 26.36244948 269.442 384.3197
1.922928 B-Mp P2 -269.068 1 26.49052347 -326.785 -211.35 1.939074
C-PDI P1 41.86738 1 21.69127339 -5.39385 89.1286 1.835677 D-PDI P2
-20.6497 1 22.25555151 -69.1403 27.84103 2.163345 E-Wt frac
-81.5786 1 18.29077861 -121.431 -41.7264 1.288823 P1 AB 16.49979 1
29.74882271 -48.3173 81.31691 1.853276 AC -78.4567 1 24.99101268
-132.907 -24.0059 1.178035 AD 24.90805 1 27.25176476 -34.4684
84.28455 2.108865 AE 132.2034 1 30.34580877 66.08557 198.3212
2.466812 BC 22.86528 1 25.59604243 -32.9037 78.63426 1.630753 BD
142.7778 1 22.22631509 94.35085 191.2048 1.263168 BE 64.64975 1
25.71739256 8.616362 120.6831 1.848938 CD -16.1917 1 23.48968122
-67.3714 34.98788 2.184276 CE -0.59048 1 25.22645567 -55.5542
54.37325 2.482783 DE 32.96268 1 22.17958266 -15.3625 81.28784
2.116413
[0153] The ANOVA analysis identified parameters and combinations of
parameters that significantly contribute to the final result (i.e.,
melt fracture characteristic.) Thus, the following equation for the
magnitude of slip-stick was as follows:
Example 3
[0154] The influence of the M.sub.p, weight fraction, and PDI of
each component on the stress for the smooth-matte transition as
predicted as from the PLS2 method was investigated as described in
Example 2. ANOVA analyses of the results are as given in Tables
14-16.
TABLE-US-00014 TABLE 14 ANOVA for Response Surface 2FI Model
Analysis of variance table [Partial sum of squares - Type III]
p-value Sum of Mean F Prob > Source Squares df Square Value F
Model 51102.59 15 3406.839578 39.88098 <0.0001 A-Mp 7643.991 1
7643.991138 89.48172 <0.0001 P1 B-Mp 11607.42 1 11607.42056
135.8782 <0.0001 P2 C-PDI 0.031347 1 0.031346975 0.000367 0.9850
P1 D-PDI 68.18712 1 68.18712105 0.798209 0.3892 P2 E-Wt 3.847193 1
3.847192622 0.045036 0.8355 frac P1 AB 102.232 1 102.2320311
1.196744 0.2954 AC 41.02346 1 41.02346341 0.480227 0.5015 AD
374.6486 1 374.648561 4.385693 0.0581 AE 169.4842 1 169.4841845
1.984007 0.1843 BC 126.7865 1 126.7865247 1.484182 0.2465 BD
4510.72 1 4510.720235 52.80317 <0.0001 BE 469.385 1 469.3850287
5.494692 0.0371 CD 32.88382 1 32.88382283 0.384943 0.5466 CE
466.9518 1 466.9518388 5.466209 0.0375 DE 2.65918 1 2.659179683
0.031129 0.8629 Re- 1025.102 12 85.42517353 sidual Lack 542.3064 7
77.47234358 0.802331 0.6191 of Fit Pure 482.7957 5 96.55913545
Error Cor 52127.7 27 Total
[0155] The Model F-value of 39.88 implies the model is significant.
There is only a 0.01% chance that a "Model F-Value" this large
could occur due to noise. Values of "Prob>F" less than 0.0500
indicate model terms are significant. In this case A, B, BD, BE, CE
are significant model terms. Values greater than 0.1000 indicate
the model terms are not significant. The "Lack of Fit F-value" of
0.80 implies the Lack of Fit is not significant relative to the
pure error. There is a 61.91% chance that a "Lack of Fit F-value"
this large could occur due to noise.
TABLE-US-00015 TABLE 15 Std. Dev. 9.242574 R-Squared 0.980335 Mean
109.8957 Adj R-Squared 0.955753 C.V. % 8.410316 Pred R-Squared
0.791041 PRESS 10892.57 Adeq Precision 23.48872
[0156] The "Pred R-Squared" of 0.7910 is in reasonable agreement
with the "Adj R-Squared" of 0.9558. "Adeq Precision" measures the
signal to noise ratio. A ratio greater than 4 is desirable. The
ratio of 23.489 indicates an adequate signal. This model can be
used to navigate the design space.
TABLE-US-00016 TABLE 16 Coefficient Standard 95% CI 95% CI Factor
Estimate df Error Low High VIF Intercept 112.537 1 2.382375371
107.3463 117.7278 A-Mp P1 30.20713 1 3.193318715 23.24948 37.16477
1.922928 B-Mp P2 -37.4043 1 3.208832488 -44.3958 -30.4129 1.939074
C-PDI P1 -0.05033 1 2.627492916 -5.77515 5.674483 1.835677 D-PDI P2
-2.40854 1 2.695844679 -8.28228 3.465205 2.163345 E-Wt frac P1
0.470184 1 2.215586442 -4.35716 5.297532 1.288823 AB 3.942093 1
3.603514627 -3.90929 11.79348 1.853276 AC -2.0978 1 3.027194744
-8.69349 4.497893 1.178035 AD 6.913059 1 3.301042663 -0.2793
14.10541 2.108865 AE 5.177581 1 3.675828346 -2.83136 13.18652
2.466812 BC 3.777226 1 3.100482806 -2.97815 10.5326 1.630753 BD
19.56383 1 2.692303232 13.69781 25.42986 1.263168 BE 7.302224 1
3.115182109 0.514825 14.08962 1.848938 CD 1.765354 1 2.845336458
-4.4341 7.96481 2.184276 CE -7.14424 1 3.055714267 -13.8021
-0.48641 2.482783 DE 0.474014 1 2.686642471 -5.37968 6.327705
2.116413
[0157] The ANOVA analysis identified parameters and combinations of
parameters that significantly contribute to the final result (i.e.,
melt fracture characteristic.) Thus, the following equation for the
magnitude of slip-stick was determined to be:
TABLE-US-00017 SS mag = 1812.278 9.036292 *Mp P1 -4.03563 *Mp P2
189.7406 *PDI P1 -185.012 *PDI P2 -3555.25 *Wt frac P1 -3.22874 *Mp
P1 * PDI P1 33.63554 *Mp P1 * Wt frac P1 0.533459 *Mp P2 * PDI P2
1.775348 *Mp P2 * Wt frac P1 -21.6275 *PDI P1 * PDI P2 130.5963
*PDI P1 * Wt frac P1 219.8794 *PDI P2 * Wt frac P1
[0158] The methodologies disclosed herein may be used to optimize
the design of a polymer blend having designated melt fracture
characteristics. Tables 17a-24a provide the optimization
constraints for chemometric analysis while tables 17b-27b provide
the solutions determined based on the constraints. FIG. 8 is a plot
of the magnitude of slip-stick as a function of the weight fraction
of the lower molecular weight (LMW) component and the peak
molecular weight for the based on the results of chemometric
analysis while FIG. 9 is a plot of the stress for the smooth to
matte transition as a function of the peak molecular weights of
components P1 and P2.
TABLE-US-00018 TABLE 17a Constraints Lower Upper Lower Upper Name
Goal Limit Limit Weight Weight Importance Mp P1 is in range 11.18
63.25 1 1 3 Mp P2 is in range 67.08 505.964425 1 1 3 PDI LMW is in
range 2 5 1 1 3 PDI HMW is in range 2 5 1 1 3 Wt frac LMW maximize
0.3 0.7 1 1 3 SS mag is in range 300 1388.445312 1 1 3 Matte is in
range 90 189.119156 1 1 3
TABLE-US-00019 TABLE 17b Solutions Blend Blend Wt P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number Mp P1 Mp P2 PDI P1 PDI P2 frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 54 18.51 67.08
4.07 4.87 0.7 300 92 37 9 148 30 71 12 6.1 55 11.18 79.18 2 2.42
0.68 300 141 16 8 123 51 50 11 4.6 16 14.91 70.91 2.25 3.16 0.7 309
130 22 10 126 40 53 13 4.2 45 20.97 82.23 2.01 4.13 0.7 312 120 30
15 167 40 71 18 3.9 46 20.63 217.37 3.94 3.77 0.7 317 98 41 10 422
112 155 14 10.9 22 22.11 232.99 3.84 2.92 0.7 346 105 43 11 398 136
150 16 9.6 5 15.81 94.87 2.5 2.5 0.7 373 138 25 10 150 60 62 13 4.7
15 28.25 276.03 3.66 4.51 0.7 375 100 54 15 586 130 214 20 10.6 53
33.69 387.2 2.92 4.47 0.7 380 103 58 20 819 183 286 27 10.6 37
21.65 102.47 4.86 4.74 0.7 388 92 48 10 223 47 100 13 7.8 6 28.3
296.51 4.38 4.83 0.7 399 94 59 14 652 135 237 19 12.8 48 17.84
111.27 4.91 4.09 0.7 399 97 40 8 225 55 95 11 8.8 32 22.1 240.8
4.68 2.85 0.7 399 99 48 10 407 143 155 14 11.0 2 31.62 260.87 2.5 5
0.7 406 110 50 20 583 117 210 27 7.9 29 11.34 68.44 2.82 2.02 0.7
417 147 19 7 97 48 43 9 4.7 35 34.84 347.06 3.12 4.3 0.7 428 107 62
20 720 167 259 27 9.7 11 27.43 174.94 2.59 2.98 0.7 442 129 44 17
302 101 121 23 5.3 26 28 187.31 2.56 2.15 0.7 464 135 45 18 275 128
114 24 4.8 24 27.07 75.37 4.94 4.87 0.7 465 100 60 12 166 34 92 15
6.1 12 42.25 452.43 2.59 4.2 0.7 476 110 68 26 927 221 326 36 9.1 8
13.45 102.46 4.35 2.2 0.7 510 129 28 6 152 69 65 9 7.4 38 40.57
322.68 4.68 3.14 0.7 568 107 88 19 572 182 233 26 9.1 20 55.85
424.07 4.43 2.17 0.7 596 99 118 27 625 288 270 36 7.4 42 39.29
230.1 4.35 4.73 0.7 608 115 82 19 500 106 207 25 8.3 43 61.89
477.51 4.81 2.34 0.7 623 93 136 28 730 312 314 39 8.1 10 55.4
418.54 3.62 2.72 0.7 637 110 105 29 690 254 281 40 7.1 44 30.04
134.32 3.76 2.47 0.7 644 140 58 15 211 85 104 21 5.1 56 11.18 68.56
5 2.03 0.67 671 138 25 5 98 48 49 7 6.9 3 44.72 357.77 5 5 0.7 672
113 100 20 800 160 310 27 11.4 34 61.94 462.08 2.58 2.58 0.7 673
113 99 39 742 288 292 52 5.6 9 54.17 424.34 4.63 3.38 0.7 678 109
117 25 780 231 316 34 9.2 40 50.52 389.58 4.78 3.75 0.7 681 112 110
23 754 201 304 31 9.7 7 41.26 84.62 4.5 4.69 0.7 697 126 88 19 183
39 116 23 5.1 36 59.44 407.26 4.25 3.01 0.7 749 117 123 29 707 235
298 39 7.6 50 59.77 501.49 4.64 3.96 0.7 765 115 129 28 998 252 390
38 10.3 41 57.16 354.59 2.24 2.97 0.7 776 135 86 38 611 206 243 51
4.8 31 52.33 324.83 2.94 4.23 0.7 786 135 90 31 668 158 263 40 6.5
52 38.76 96.39 2.49 2.26 0.7 827 168 61 25 145 64 86 30 2.9 25
59.34 451.14 3.48 4.19 0.7 829 130 111 32 923 220 355 43 8.3 13
56.66 316.85 2.89 3.54 0.7 845 140 96 33 596 168 246 44 5.6 18
56.36 363.99 4.2 4.63 0.7 849 133 116 28 783 169 316 37 8.6 14
50.34 157.45 3.15 4.52 0.7 850 145 89 28 335 74 163 35 4.7 27 62.09
396.93 2.3 3.42 0.7 865 137 94 41 734 215 286 54 5.3 33 55.83
267.12 2.93 3.3 0.7 875 145 96 33 485 147 212 43 5.0 49 51.82
112.73 3.33 4.85 0.7 876 145 95 28 248 51 141 33 4.3 21 60.21
344.68 3.36 3.74 0.7 890 139 110 33 667 178 277 43 6.4 51 48.75
123.5 2.49 3.52 0.7 902 159 77 31 232 66 123 37 3.4 28 61 435.35
4.39 4.69 0.7 906 135 128 29 943 201 372 39 9.5 47 58.76 272.81
2.35 3.22 0.7 931 151 90 38 490 152 210 49 4.2 17 62.43 474.6 2.03
4.51 0.7 943 145 89 44 1008 223 365 58 6.3 19 54.95 197.64 2.2 3.86
0.7 946 157 82 37 388 101 174 46 3.8 4 44.72 94.87 5 2.5 0.7 956
158 100 20 150 60 115 25 4.6 39 45.3 93.11 3.88 2.27 0.7 974 169 89
23 140 62 105 28 3.7 23 58.83 213.65 4 2.46 0.7 986 155 118 29 335
136 183 38 4.8 30 49.54 80 3.28 2.28 0.7 1061 180 90 27 121 53 99
32 3.1 1 63.25 67.08 2.5 5 0.7 1147 168 100 40 150 30 115 36
3.2
TABLE-US-00020 TABLE 18a Constraints Lower Upper Lower Upper Impor-
Name Goal Limit Limit Weight Weight tance Mp P1 is in range 11.18
63.25 1 1 3 Mp P2 is in range 67.08 505.964425 1 1 3 PDI is in
range 2 5 1 1 3 LMW PDI is in range 2 5 1 1 3 HMW Wt frac maximize
0.3 0.7 1 1 3 LMW SS mag is in range 300 1388.445312 1 1 3 Matte is
in range 90 189.119156 1 1 3
TABLE-US-00021 TABLE 18b Solutions Blend Blend Mp P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number P1 Mp P2 PDI P1 PDI P2 Wt frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 54 18.51 67.08
4.07 4.87 0.7 300 92 37 9 148 30 71 12 6.1 55 11.18 79.18 2 2.42
0.68 300 141 16 8 123 51 50 11 4.6 16 14.91 70.91 2.25 3.16 0.7 309
130 22 10 126 40 53 13 4.2 45 20.97 82.23 2.01 4.13 0.7 312 120 30
15 167 40 71 18 3.9 46 20.63 217.37 3.94 3.77 0.7 317 98 41 10 422
112 155 14 10.9 22 22.11 232.99 3.84 2.92 0.7 346 105 43 11 398 136
150 16 9.6 5 15.81 94.87 2.5 2.5 0.7 373 138 25 10 150 60 62 13 4.7
15 28.25 276.03 3.66 4.51 0.7 375 100 54 15 586 130 214 20 10.6 53
33.69 387.2 2.92 4.47 0.7 380 103 58 20 819 183 286 27 10.6 37
21.65 102.47 4.86 4.74 0.7 388 92 48 10 223 47 100 13 7.8 6 28.3
296.51 4.38 4.83 0.7 399 94 59 14 652 135 237 19 12.8 48 17.84
111.27 4.91 4.09 0.7 399 97 40 8 225 55 95 11 8.8 32 22.1 240.8
4.68 2.85 0.7 399 99 48 10 407 143 155 14 11.0 2 31.62 260.87 2.5 5
0.7 406 110 50 20 583 117 210 27 7.9 29 11.34 68.44 2.82 2.02 0.7
417 147 19 7 97 48 43 9 4.7 35 34.84 347.06 3.12 4.3 0.7 428 107 62
20 720 167 259 27 9.7 11 27.43 174.94 2.59 2.98 0.7 442 129 44 17
302 101 121 23 5.3 26 28 187.31 2.56 2.15 0.7 464 135 45 18 275 128
114 24 4.8 24 27.07 75.37 4.94 4.87 0.7 465 100 60 12 166 34 92 15
6.1 12 42.25 452.43 2.59 4.2 0.7 476 110 68 26 927 221 326 36 9.1 8
13.45 102.46 4.35 2.2 0.7 510 129 28 6 152 69 65 9 7.4 38 40.57
322.68 4.68 3.14 0.7 568 107 88 19 572 182 233 26 9.1 20 55.85
424.07 4.43 2.17 0.7 596 99 118 27 625 288 270 36 7.4 42 39.29
230.1 4.35 4.73 0.7 608 115 82 19 500 106 207 25 8.3 43 61.89
477.51 4.81 2.34 0.7 623 93 136 28 730 312 314 39 8.1 10 55.4
418.54 3.62 2.72 0.7 637 110 105 29 690 254 281 40 7.1 44 30.04
134.32 3.76 2.47 0.7 644 140 58 15 211 85 104 21 5.1 56 11.18 68.56
5 2.03 0.67 671 138 25 5 98 48 49 7 6.9 3 44.72 357.77 5 5 0.7 672
113 100 20 800 160 310 27 11.4 34 61.94 462.08 2.58 2.58 0.7 673
113 99 39 742 288 292 52 5.6 9 54.17 424.34 4.63 3.38 0.7 678 109
117 25 780 231 316 34 9.2 40 50.52 389.58 4.78 3.75 0.7 681 112 110
23 754 201 304 31 9.7 7 41.26 84.62 4.5 4.69 0.7 697 126 88 19 183
39 116 23 5.1 36 59.44 407.26 4.25 3.01 0.7 749 117 123 29 707 235
298 39 7.6 50 59.77 501.49 4.64 3.96 0.7 765 115 129 28 998 252 390
38 10.3 41 57.16 354.59 2.24 2.97 0.7 776 135 86 38 611 206 243 51
4.8 31 52.33 324.83 2.94 4.23 0.7 786 135 90 31 668 158 263 40 6.5
52 38.76 96.39 2.49 2.26 0.7 827 168 61 25 145 64 86 30 2.9 25
59.34 451.14 3.48 4.19 0.7 829 130 111 32 923 220 355 43 8.3 13
56.66 316.85 2.89 3.54 0.7 845 140 96 33 596 168 246 44 5.6 18
56.36 363.99 4.2 4.63 0.7 849 133 116 28 783 169 316 37 8.6 14
50.34 157.45 3.15 4.52 0.7 850 145 89 28 335 74 163 35 4.7 27 62.09
396.93 2.3 3.42 0.7 865 137 94 41 734 215 286 54 5.3 33 55.83
267.12 2.93 3.3 0.7 875 145 96 33 485 147 212 43 5.0 49 51.82
112.73 3.33 4.85 0.7 876 145 95 28 248 51 141 33 4.3 21 60.21
344.68 3.36 3.74 0.7 890 139 110 33 667 178 277 43 6.4 51 48.75
123.5 2.49 3.52 0.7 902 159 77 31 232 66 123 37 3.4 28 61 435.35
4.39 4.69 0.7 906 135 128 29 943 201 372 39 9.5 47 58.76 272.81
2.35 3.22 0.7 931 151 90 38 490 152 210 49 4.2 17 62.43 474.6 2.03
4.51 0.7 943 145 89 44 1008 223 365 58 6.3 19 54.95 197.64 2.2 3.86
0.7 946 157 82 37 388 101 174 46 3.8 4 44.72 94.87 5 2.5 0.7 956
158 100 20 150 60 115 25 4.6 39 45.3 93.11 3.88 2.27 0.7 974 169 89
23 140 62 105 28 3.7 23 58.83 213.65 4 2.46 0.7 986 155 118 29 335
136 183 38 4.8 30 49.54 80 3.28 2.28 0.7 1061 180 90 27 121 53 99
32 3.1 1 63.25 67.08 2.5 5 0.7 1147 168 100 40 150 30 115 36
3.2
TABLE-US-00022 TABLE 19a Constraints Lower Upper Lower Upper Impor-
Name Goal Limit Limit Weight Weight tance Mp P1 is in range 11.18
63.25 1 1 3 Mp P2 is in range 67.08 505.9644 1 1 3 PDI P1 is in
range 2 3 1 1 3 PDI P2 is in range 2 3 1 1 3 Wt frac P1 maximize
0.3 0.7 1 1 3 SS mag is in range 300 1388.445 1 1 3 Matte is in
range 90 189.1192 1 1 3
TABLE-US-00023 TABLE 19b Solutions Blend Blend Mp P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number P1 Mp P2 PDI P1 PDI P2 Wt frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 28 22.42 221.01
2.96 2.99 0.7 303 112 39 13 382 128 142 18 7.9 8 13.37 78.57 2.31
2.82 0.7 306 133 20 9 132 47 54 12 4.6 2 21.54 169.78 2.04 2.22 0.7
331 134 31 15 253 114 97 20 4.8 29 20.48 138.4 2.35 2.91 0.7 348
129 31 13 236 81 93 18 5.2 4 28.5 260.16 2.77 2.29 0.7 350 117 47
17 394 172 151 23 6.4 23 16.93 145.57 2.75 2.1 0.7 354 133 28 10
211 100 83 14 5.9 34 16.74 94.61 2.69 2.9 0.7 368 131 27 10 161 56
68 14 5.0 14 17.25 111.78 2.61 2.58 0.7 373 134 28 11 180 70 73 14
5.1 1 15.81 94.87 2.5 2.5 0.7 373 138 25 10 150 60 62 13 4.7 7
15.25 101.85 2.54 2.18 0.7 382 142 24 10 150 69 62 13 4.8 16 18.37
101.78 2.06 2.09 0.7 410 149 26 13 147 70 63 17 3.7 12 15.45 85.03
2.94 2.09 0.7 461 145 26 9 123 59 55 12 4.6 18 20.75 71.69 2.85
2.96 0.7 483 138 35 12 123 42 62 16 3.9 9 45.5 378.94 2.63 2.83 0.7
498 112 74 28 637 225 243 38 6.4 32 51.31 382.15 2.35 2.37 0.7 565
117 79 33 588 248 232 45 5.1 27 44.77 279.49 2.89 2.41 0.7 629 130
76 26 434 180 183 35 5.2 5 31.21 96.43 2.98 2.78 0.7 662 149 54 18
161 58 86 23 3.8 21 61.94 462.08 2.53 2.53 0.7 666 112 99 39 735
291 289 53 5.5 15 45.65 263.59 2.62 2.88 0.7 673 135 74 28 447 155
186 37 5.0 13 56.53 320.97 2.15 2.39 0.7 776 138 83 39 496 208 207
51 4.1 17 41.87 152.71 2.19 2.2 0.7 780 161 62 28 227 103 111 36
3.1 20 51.14 250.93 2.87 2.53 0.7 796 144 87 30 399 158 180 40 4.5
22 43.78 124.44 2.61 2.75 0.7 846 161 71 27 206 75 111 34 3.3 35
46.56 171.48 2.78 2.13 0.7 850 159 78 28 250 117 129 36 3.6 33
48.01 175.71 2.33 2.46 0.7 854 160 73 31 276 112 134 40 3.3 30
50.48 160.59 2.06 2.49 0.7 927 167 72 35 253 102 127 44 2.9 19
53.41 168.55 2.39 2.57 0.7 970 166 83 35 270 105 139 43 3.2 3 46.12
79.16 2.06 2.14 0.7 1002 185 66 32 116 54 81 37 2.2 24 54.19 148.01
2.52 2.67 0.7 1014 170 86 34 242 91 133 42 3.2 10 51.39 102.27 2.11
2.75 0.7 1028 177 75 35 170 62 103 41 2.5 6 60.72 174.06 2.73 2.48
0.7 1100 173 100 37 274 111 152 46 3.3 25 55.53 102.14 2.99 2.04
0.7 1144 186 96 32 146 72 111 38 2.9 26 59.01 71.75 2.87 2.84 0.7
1202 188 100 35 121 43 106 37 2.9 31 60.49 87.99 2.79 2.77 0.7 1213
187 101 36 146 53 115 40 2.9 11 62.96 130.5 2.93 2.06 0.7 1224 187
108 37 187 91 132 45 2.9 36 11.68 244.73 3 2.97 0.51 300 97 20 7
422 142 217 13 17.2
TABLE-US-00024 TABLE 20a Constraints Lower Upper Lower Upper Name
Goal Limit Limit Weight Weight Importance Name minimize 11.18034
63.24555 1 1 3 Mp P1 maximize 67.08204 505.9644 1 1 3 Mp P2 is in
range 2.5 5 1 1 3 PDI P1 is equal to 2.50 2.5 5 1 1 3 PDI P2
maximize 0.3 0.7 1 1 3 Wt frac P1 is in range 300 1388.445 1 1 3
Matte is in range 90 189.1192 1 1 3
TABLE-US-00025 TABLE 20b Solutions Blend Blend PDI PDI Wt P1 Mw P1
Mn P2 Mw P2 Mn Mw Mn Blend Number Mp P1 Mp P2 P1 P2 frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 29 14.96 249.08
5 2.5 0.7 300 90 33 7 394 158 142 9 15 24 22.27 287.88 4.97 2.5 0.7
341 90 50 10 455 182 171 14 12 25 24.21 298.49 4.97 2.5 0.7 353 90
54 11 472 189 179 15 12 26 19.48 273.47 4.95 2.5 0.7 320 90 43 9
432 173 160 12 13 18 22.78 296.63 4.74 2.5 0.7 314 90 50 10 469 188
175 15 12 14 21.97 293.87 4.67 2.5 0.7 300 90 47 10 465 186 173 14
12 7 24.75 312.94 4.51 2.5 0.7 300 90 53 12 495 198 185 16 11 5
24.88 313.9 4.5 2.5 0.7 300 90 53 12 496 199 186 16 11 11 26.16
320.87 4.5 2.5 0.7 310 90 55 12 507 203 191 17 11 9 25.28 317.39
4.46 2.5 0.7 300 90 53 12 502 201 188 17 11 3 25.61 319.05 4.45 2.5
0.7 300 90 54 12 504 202 189 17 11 6 26.27 323.11 4.43 2.5 0.7 303
90 55 12 511 204 192 17 11 1 26.73 326.94 4.38 2.5 0.7 300 90 56 13
517 207 194 18 11 10 26.46 324.74 4.37 2.5 0.7 300 90 55 13 513 205
193 18 11 16 25.54 313.87 4.37 2.5 0.7 300 91 53 12 496 199 186 17
11 2 26.93 328.36 4.36 2.5 0.7 300 90 56 13 519 208 195 18 11 39
36.62 380.5 4.36 2.5 0.7 379 90 76 18 602 241 234 24 10 4 27.63
333.47 4.31 2.5 0.7 300 90 57 13 527 211 198 19 11 8 28.14 336.6
4.27 2.5 0.7 300 90 58 14 532 213 200 19 11 28 34.97 374.83 4.24
2.5 0.7 353 90 72 17 593 237 228 24 10 23 31.92 358.8 4.22 2.5 0.7
325 90 66 16 567 227 216 22 10 21 28.1 331.13 4.15 2.5 0.7 300 92
57 14 524 209 197 19 10 13 30 348.83 4.1 2.5 0.7 300 91 61 15 552
221 208 21 10 12 30.7 355.75 4.08 2.5 0.7 300 90 62 15 562 225 212
21 10 15 31.65 362.87 4 2.5 0.7 300 90 63 16 574 229 216 22 10 17
31.15 356.61 3.99 2.5 0.7 300 91 62 16 564 226 213 22 10 19 32.59
369.98 3.92 2.5 0.7 300 90 65 16 585 234 221 23 10 27 34.39 379.94
3.91 2.5 0.7 315 90 68 17 601 240 228 24 9 22 33.24 374.92 3.86 2.5
0.7 300 90 65 17 593 237 224 23 10 38 33.19 345.89 3.29 2.5 0.7 307
99 60 18 547 219 206 25 8 32 37.11 394.15 3.17 2.5 0.7 300 94 66 21
623 249 233 29 8 33 37.25 395.52 3.15 2.5 0.7 300 94 66 21 625 250
234 29 8 35 39.66 425.65 3.14 2.5 0.7 300 90 70 22 673 269 251 31 8
34 35.78 375.69 3.12 2.5 0.7 300 97 63 20 594 238 222 28 8 40 38.3
400.26 2.91 2.5 0.7 300 96 65 22 633 253 236 31 8 41 39.48 413.82
2.85 2.5 0.7 300 94 67 23 654 262 243 32 8 51 37.22 286.55 2.79 2.5
0.7 445 120 62 22 453 181 179 30 6 48 43.8 463.98 2.59 2.5 0.7 300
90 70 27 734 293 269 37 7 44 38.68 394.22 2.58 2.5 0.7 300 99 62 24
623 249 230 33 7 45 37.66 380.05 2.57 2.5 0.7 300 101 60 23 601 240
223 32 7 46 38.71 392.75 2.52 2.5 0.7 300 100 61 24 621 248 229 33
7 50 37.17 286.18 2.5 2.5 0.7 429 122 59 24 452 181 177 32 6
average 30.6997619 20 23.69 309.32 4.5 2.5 0.69 300 90 50 11 489
196 186 16 12 31 29.59 328.19 5 2.5 0.69 398 90 66 13 519 208 207
19 11 42 39.78 421.67 2.93 2.5 0.69 300 92 68 23 667 267 254 32 8
30 21.12 292.68 4.71 2.5 0.67 328 91 46 10 463 185 183 14 13 36
27.8 321.45 5 2.5 0.67 396 90 62 12 508 203 209 18 12 37 13.62
255.86 4.85 2.5 0.66 300 90 30 6 405 162 157 9 17 43 11.18 246.86
4.87 2.5 0.65 300 90 25 5 390 156 153 8 20 47 20.11 295.39 5 2.5
0.61 391 90 45 9 467 187 210 14 15 49 18.34 298.64 4.09 2.5 0.58
308 91 37 9 472 189 220 15 15 52 11.19 288 3.7 2.5 0.49 300 90 22 6
455 182 243 11 21 53 11.18 253.04 5 2.5 0.48 536 100 25 5 400 160
220 10 22
TABLE-US-00026 TABLE 21a Constraints Lower Upper Lower Upper Name
Goal Limit Limit Weight Weight Importance Mp P1 minimize 11.18034
63.24555 1 1 3 Mp P2 maximize 200 505.9644 1 1 3 PDI P1 is in range
2 5 1 1 3 PDI P2 is equal to 2.00 2.5 5 1 1 3 Wt frac P1 is equal
to 0.70 0.3 0.7 1 1 3 SS mag is in range 300 1388.445 1 1 3 Matte
is in range 90 189.1192 1 1 3
TABLE-US-00027 TABLE 21b Solutions Blend Blend Mp P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number P1 Mp P2 PDI P1 PDI P2 Wt frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 16 46.41 233.29
2.45 2 0.7 692 146 73 30 330 165 150 39 3.8 5 31.62 260.87 2.5 2
0.7 337 123 50 20 369 184 146 27 5.3 11 42.58 256.36 2.52 2 0.7 574
136 68 27 363 181 156 36 4.3 8 56.49 445.72 2.81 2 0.7 531 101 95
34 630 315 255 46 5.5 15 59.9 372.59 2.99 2 0.7 732 122 104 35 527
263 231 47 4.9 4 50.44 413.87 3.14 2 0.7 477 101 89 28 585 293 238
39 6.1 9 49.28 307.33 3.26 2 0.7 648 126 89 27 435 217 193 37 5.2
17 61.89 444.83 3.58 2 0.7 644 103 117 33 629 315 271 45 6.1 19
62.66 479.96 3.61 2 0.7 596 95 119 33 679 339 287 45 6.3 18 61.18
282.4 3.63 2 0.7 921 143 117 32 399 200 201 43 4.7 10 32.27 245.29
3.75 2 0.7 474 120 62 17 347 173 148 23 6.5 12 55.7 288.79 3.88 2
0.7 815 134 110 28 408 204 199 38 5.2 20 36.02 204.1 4.41 2 0.7 658
131 76 17 289 144 140 23 6.0 14 45.14 232 4.44 2 0.7 757 134 95 21
328 164 165 29 5.7 3 47.08 378.96 4.48 2 0.7 529 99 100 22 536 268
231 31 7.5 1 28.13 318.9 4.5 2 0.7 334 93 60 13 451 225 177 18 9.6
7 53.82 376.14 4.52 2 0.7 642 106 114 25 532 266 240 35 6.9 22
62.21 285.46 4.69 2 0.7 938 138 135 29 404 202 215 39 5.6 6 32.69
254.74 4.82 2 0.7 545 113 72 15 360 180 158 21 7.7 21 46.18 205.97
4.9 2 0.7 840 139 102 21 291 146 159 28 5.7 2 44.72 357.77 5 2 0.7
553 99 100 20 506 253 222 28 8.0 13 11.18 212.43 5 2 0.7 317 99 25
5 300 150 108 7 15.3
TABLE-US-00028 TABLE 22a Constraints Lower Upper Lower Upper Impor-
Name Goal Limit Limit Weight Weight tance Mp P1 minimize 11.18
63.25 1 1 3 Mp P2 maximize 275 505.9644 1 1 3 PDI P1 is in range
2.5 3 1 1 3 PDI P2 is in range 2 2.3 1 1 3 Wt frac P1 is in range
0.6 0.65 1 1 3 SS mag maximize 300 1388.445 1 1 3 Matte maximize 90
189.1192 1 1 3
TABLE-US-00029 TABLE 22b Solutions Blend Blend Mp P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number P1 Mp P2 PDI P1 PDI P2 Wt frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 1 52.32 353.07
2.5 2.3 0.65 635 120 83 33 535 233 241 47 5.1 2 52.86 352.81 2.5
2.3 0.65 646 121 84 33 535 233 242 48 5.1 3 52.42 352.01 2.58 2.3
0.65 640 121 84 33 534 232 242 47 5.2 4 52.17 350.9 2.61 2.3 0.65
638 120 84 32 532 231 241 46 5.2 5 52.18 355.86 2.62 2.3 0.65 630
119 84 32 540 235 244 46 5.3 6 52.71 351.21 2.6 2.3 0.65 648 121 85
33 533 232 242 47 5.2 7 52.12 349.06 2.5 2.3 0.64 639 121 82 33 529
230 243 48 5.1 8 52.38 351.72 2.75 2.3 0.65 644 120 87 32 533 232
243 45 5.4 9 52.36 350.45 2.91 2.3 0.65 649 119 89 31 531 231 244
44 5.5 10 53.94 369.36 2.5 2.29 0.65 638 118 85 34 559 244 251 49
5.1 11 52.16 350.37 2.99 2.3 0.65 647 119 90 30 531 231 245 43 5.6
12 51.7 347.37 2.5 2.23 0.65 628 121 82 33 519 233 235 47 5.0 13
52.93 344.28 2.95 2.3 0.65 671 121 91 31 522 227 242 44 5.5 14
52.13 352.35 2.95 2.3 0.63 646 118 90 30 534 232 254 45 5.7 15
52.16 350.27 2.52 2.3 0.61 643 118 83 33 531 231 258 49 5.2 16
52.28 347.24 2.5 2.11 0.65 631 121 83 33 504 239 230 47 4.9 17
52.29 348.17 2.62 2.12 0.65 633 120 85 32 507 239 232 46 5.0 18
51.8 346.26 2.7 2.3 0.6 650 118 85 32 525 228 261 48 5.4 19 51.72
341.49 2.98 2.3 0.61 661 119 89 30 518 225 256 45 5.7 20 52.48
342.98 3 2.3 0.6 674 119 91 30 520 226 263 46 5.7
TABLE-US-00030 TABLE 23a Constraints Lower Upper Lower Upper Impor-
Name Goal Limit Limit Weight Weight tance Mp P1 minimize 11.18
63.25 1 1 3 Mp P2 is equal to 275 505.9644 1 1 3 340.00 PDI P1 is
in range 2.5 3 1 1 3 PDI P2 is equal 2 2.3 1 1 3 to 2.10 Wt frac P1
maximize 0.6 0.65 1 1 3 SS mag maximize 300 1388.445 1 1 3 Matte
maximize 90 189.1192 1 1 3
TABLE-US-00031 TABLE 23b Solutions Blend Blend Mp P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number P1 Mp P2 PDI P1 PDI P2 Wt frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 7 51.8 340 2.93
2.1 0.65 646 120 89 30 493 235 230 44 5.3 6 51.89 340 2.86 2.1 0.65
646 121 88 31 493 235 229 44 5.2 5 51.95 340 2.76 2.1 0.65 644 121
86 31 493 235 229 45 5.1 3 52.07 340 2.59 2.1 0.65 642 122 84 32
493 235 227 46 4.9 1 52.11 340 2.5 2.1 0.65 640 122 82 33 493 235
226 47 4.8 2 52.29 340 2.55 2.1 0.65 645 122 84 33 493 235 227 47
4.8 4 52.4 340 2.5 2.1 0.65 646 123 83 33 493 235 226 47 4.8 8
63.25 340 2.5 2.1 0.7 862 138 100 40 493 235 218 53 4.1
TABLE-US-00032 TABLE 24a Constraints Lower Upper Lower Upper Impor-
Name Goal Limit Limit Weight Weight tance Mp P1 minimize 11.18
63.25 1 1 3 Mp P2 is equal to 275 505.9644 1 1 3 340.00 PDI P1 is
in range 2.5 3 1 1 3 PDI P2 is equal 2 2.3 1 1 3 to 2.10 Wt frac P1
maximize 0.6 0.7 1 1 3 SS mag maximize 300 1388.445 1 1 3 Matte
maximize 90 189.1192 1 1 3
TABLE-US-00033 TABLE 24b Solutions Blend Blend Mp P1 Mw P1 Mn P2 Mw
P2 Mn Mw Mn Blend Number P1 Mp P2 PDI P1 PDI P2 Wt frac P1 SS mag
Matte kg/mol kg/mol kg/mol kg/mol kg/mol kg/mol PDI 5 51.73 340
2.66 2.1 0.7 626 124 84 32 493 235 207 43 4.8 8 52.06 340 2.79 2.1
0.7 636 124 87 31 493 235 209 42 5.0 4 52.26 340 2.66 2.1 0.7 637
125 85 32 493 235 207 43 4.8 6 52.28 340 2.5 2.1 0.7 634 125 83 33
493 235 206 45 4.6 9 52.32 340 2.92 2.1 0.7 645 123 89 31 493 235
210 41 5.1 7 52.33 340 2.76 2.1 0.7 641 124 87 31 493 235 209 43
4.9 1 52.47 340 2.5 2.1 0.7 637 126 83 33 493 235 206 45 4.6 3
52.65 340 2.55 2.1 0.7 642 126 84 33 493 235 207 44 4.7 10 52.78
340 2.92 2.1 0.7 654 124 90 31 493 235 211 42 5.1 2 53.07 340 2.5
2.1 0.7 650 126 84 34 493 235 207 45 4.6 11 52.08 340 2.98 2.1 0.7
642 123 90 30 493 235 211 41 5.2
Example 4
[0159] Chemometric analysis and validation of the analysis was
carried out on a variety of polymer samples. Additionally the
results of the chemometric analysis allowed for the digital
generation of samples having a variety of molecular weight
distributions in order to assess parameters significant to the melt
fracture characteristics investigated. Data relating to these
analyses carried out using the methodologies disclosed herein for
polyethylene resins are presented in Data sets A-X.
[0160] Without further elaboration, it is believed that one skilled
in the art can, using the description herein, utilize the present
invention to its fullest extent. While aspects of the invention
have been shown and described, modifications thereof can be made by
one skilled in the art without departing from the spirit and
teachings of the invention. The aspects and examples described
herein are exemplary only, and are not intended to be limiting.
Many variations and modifications of the invention disclosed herein
are possible and are within the scope of the invention. Where
numerical ranges or limitations are expressly stated, such express
ranges or limitations should be understood to include iterative
ranges or limitations of like magnitude falling within the
expressly stated ranges or limitations (e.g., from about 1 to about
10 includes, 2, 3, 4, etc.; greater than 0.10 includes 0.11, 0.12,
0.13, etc.). Use of the term "optionally" with respect to any
element of a claim is intended to mean that the subject element is
required, or alternatively, is not required. Both alternatives are
intended to be within the scope of the claim. Use of broader terms
such as comprises, includes, having, etc. should be understood to
provide support for narrower terms such as consisting of,
consisting essentially of, comprised substantially of, etc.
[0161] Accordingly, the scope of protection is not limited by the
description set out above but is only limited by the claims which
follow, that scope including all equivalents of the subject matter
of the claims. Each and every claim is incorporated into the
specification as an aspect of the present invention. Thus, the
claims are a further description and are an addition to the
detailed description of the present invention. The disclosures of
all patents, patent applications, and publications cited herein are
hereby incorporated by reference, to the extent that they provide
exemplary, procedural or other details supplementary to those set
forth herein.
* * * * *