U.S. patent application number 14/524024 was filed with the patent office on 2016-04-28 for high-performance, low-voltage electroosmotic pumps with molecularly thin nanomembranes.
The applicant listed for this patent is SiMPore Inc., University of Rochester. Invention is credited to Philippe Fauchet, Thomas Gaborski, James McGrath, Jessica Snyder, Christopher C. Striemer.
Application Number | 20160115951 14/524024 |
Document ID | / |
Family ID | 55791620 |
Filed Date | 2016-04-28 |
United States Patent
Application |
20160115951 |
Kind Code |
A1 |
Snyder; Jessica ; et
al. |
April 28, 2016 |
HIGH-PERFORMANCE, LOW-VOLTAGE ELECTROOSMOTIC PUMPS WITH MOLECULARLY
THIN NANOMEMBRANES
Abstract
Thin pnc-Si membranes operate as high-flow-rate EOPs at low
applied voltages. In at least some instances, this may be due to
the small electrical resistance presented by the membrane and high
electric fields across the molecularly thin membrane. The
normalized flow rates of some pnc-Si EOPs may be 20 times to
several orders of magnitude higher than other low-voltage EOPs.
Inventors: |
Snyder; Jessica; (Rochester,
NY) ; McGrath; James; (Fairpoint, NY) ;
Fauchet; Philippe; (Brentwood, TN) ; Gaborski;
Thomas; (Rochester, NY) ; Striemer; Christopher
C.; (Rochester, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
University of Rochester
SiMPore Inc. |
Rochester
West Henrietta |
NY
NY |
US
US |
|
|
Family ID: |
55791620 |
Appl. No.: |
14/524024 |
Filed: |
October 27, 2014 |
Current U.S.
Class: |
417/48 |
Current CPC
Class: |
F04B 43/046
20130101 |
International
Class: |
F04B 43/04 20060101
F04B043/04 |
Goverment Interests
FEDERALLY SPONSORED RESEARCH
[0001] This invention was made with government support under grant
number RZIEB007480 awarded by the National Institutes of Health.
The government has certain rights in the invention.
Claims
1. A micro-fluidics device comprising a micro-fluid input, a
micro-fluid output and an electroosmotic pump in fluid
communication with the micro-fluid input and output, the
electroosmotic pump including a nano-porous membrane having a
thickness of 2-100 nm, the electrosmotic pump configured to move a
fluid through the nano-porous membrane from the micro-fluid input
into the micro-fluid output.
2. The micro-fluidics device of claim 1, wherein the nano-porous
membrane includes pores having widths in the range of 2 nm-100
nm.
3. The micro-fluidics device of claim 1, wherein the thickness of
the nano-porous membrane is in the range of 5-40 nm.
4. The micro-fluidics device of claim 1, wherein the nano-porous
membrane is a nano-porous membrane comprising silicon.
5. The micro-fluidics device of claim 4, wherein the nano-porous
membrane is a nano-porous membrane comprising silicon nitride.
6. The micro-fluidics device of claim 1, wherein the nano-porous
membrane is a porous nanocrystaline silicon membrane.
7. The micro-fluidics device of claim 6, wherein the electroosmotic
pump comprises a substrate, a passage extending through the
substrate, and the porous nanocrystaline silicon membrane being
over the passage extending through the substrate.
8. The micro-fluidics device of claim 7, further comprising a
plurality of passages extending through the substrate and one or
more porous nanocrystaline silicon membranes over the plurality of
passages.
9. The microfluidics device of claim 7, wherein the substrate
comprises a silicon substrate.
10. The micro-fluidics device of claim 1, wherein the
electroosmotic pump is configured to move the fluid through the
nano-porous membrane at an applied voltage between 10 mV and 50
V.
11. The micro-fluidics device of claim 1, wherein the nano-porous
membrane comprises a zeta potential of approximately -5 mV to -40
mV.
12. The micro-fluidics device of claim 1, wherein the nano-porous
membrane comprises a zeta potential of approximately 100 mV to -100
mV.
13. The micro-fluidics device of claim 1, further comprising a
fluid channel extending from the micro-fluid output, wherein the
nano-porous membrane has an active area that is at least 25% of a
cross-sectional area of the fluid channel.
14. The micro-fluidics device of claim 13, wherein the active area
is at least 75% of the cross-sectional area.
15. A micro-fluidics device comprising a micro-fluid input, a
micro-fluid output and an electroosmotic pump in fluid
communication with the micro-fluid input and output, the
electroosmotic pump including a nano-porous membrane having a
thickness of 2-100 nm, the electrosmotic pump configured to move a
fluid through the nano-porous membrane from the micro-fluid input
into the micro-fluid output at a flow rate of 50-800
mLmin.sup.-1cm.sup.-2V.sup.-1, wherein cm corresponds to an active
area of the nano-porous membrane and V corresponds to a
transmembrane voltage of the nano-porous membrane.
16. The micro-fluidics device of claim 15, wherein the
electrosmotic pump is configured to move the fluid through the
nano-porous membrane from the micro-fluid input into the
micro-fluid output at a flow rate of 100-500 mLmin-1cm-2V-1.
17. A method of moving a fluid in a micro-fluidic device, the
micro-fluidic device comprising a micro-fluid input, a micro-fluid
output and an electroosmotic pump comprising a nano-porous membrane
having a thickness of less than 100 nm in fluid communication with
the micro-fluid input and output, the method comprising: applying a
voltage of less than 50 V across the nano-porous membrane; and in
response to the applied voltage, moving a fluid through the
nano-porous membrane at a normalized flow rate of 50-800
mLmin.sup.-1cm.sup.-2V.sup.-1, wherein cm corresponds to an active
area of the nano-porous membrane and V corresponds to a
transmembrane voltage of the nano-porous membrane.
18. The method of claim 17, wherein the nano-porous membrane
includes pores having widths in the range of 2 nm-100 nm and the
thickness of the nano-porous membrane is in the range of 5-40
nm.
19. The method of claim 17, wherein applying the voltage comprises
applying a voltage of less than 1 V across the nano-porous
membrane.
20. A micro-fluidics device comprising a fluid reservoir, a sample
input, and an electroosmotic pump in fluid communication with the
fluid reservoir and the sample input, the electroosmotic pump
including a nano-porous membrane having a thickness of 2-100 nm,
the electrosmotic pump configured to move a fluid from the fluid
reservoir through the nano-porous membrane to move a sample from
the sample input through a portion of the micro-fluidics
device.
21. A micro-fluidics device comprising an electroosmotic pump, a
cooling fluid, a heat source, and a heat sink, the electroosmotic
pump including a nano-porous membrane having a thickness of 2-100
nm, the electrosmotic pump configured to move the cooling fluid
past the heat source and to the heat sink.
Description
RELATED FIELDS
[0002] Electroosmotic pumps (EOPs), such as EOPs used in
microfluidics applications.
BACKGROUND
[0003] EOPs are a class of pumps in which fluid is driven through a
capillary or porous media within an electric field.
[0004] Electroosmotic flow results from the interaction between an
electric field and the diffuse layer of ions at a charged surface.
In capillaries or pores, the migration of the diffuse layer toward
the oppositely charged electrode causes the bulk fluid within the
channel to flow through viscous drag. In some instances, EOPs may
be designed to generate high flow rates in microchannels using
these principles. EOPs may, in at least some instances, present a
number of advantages over mechanical pumps, including the lack of
mechanical parts, pulse-free flows, and ease of control through
electrode actuation. In some instances, EOPs have been considered
for use as pumps for cooling circuits and microfluidic devices that
aid in drug delivery or diagnostics. Microfluidic devices may
facilitate the miniaturization of multistep laboratory processes
into small, low-cost, disposable units. The inclusion of multiple
steps into a single device increases the need for the precision
pumping of fluids on-chip.
[0005] High voltages (>1 kV) are often required for direct
current (dc) EOPs to achieve sufficient flow rates in
microchannels. However, devices with high-voltage EOPs require
bulky external power supplies and a skilled technician to operate,
which may defeat the ease of use and portability aims of a
microfluidic diagnostic tool in some instances. Recently,
low-voltage EOPs have been fabricated from porous silicon, alumina,
track-etched polymer, and carbon nanotube membranes. These
low-voltage EOPs are much thinner than their high-voltage
predecessors (60-350 .mu.m compared with >10 mm), but still have
drawbacks.
SUMMARY
[0006] Thin pnc-Si membranes operate as high-flow-rate EOPs at low
applied voltages. In at least some instances, this may be due to
the small electrical resistance presented by the membrane and high
electric fields across the molecularly thin membrane. The
normalized flow rates of some pnc-Si EOPs may be 20 times to
several orders of magnitude higher than other low-voltage EOPs.
[0007] In one non-limiting example, a micro-fluidics device may
include a micro-fluid input, a micro-fluid output and an
electroosmotic pump in fluid communication with the micro-fluid
input and output, the electroosmotic pump including a nano-porous
membrane having a thickness of 2-100 nm, the electrosmotic pump
configured to move a fluid through the nano-porous membrane from
the micro-fluid input into the micro-fluid output.
[0008] In this non-limiting example, the nano-porous membrane may
include pores having widths in the range of 2 nm-100 nm.
[0009] In this non-limiting example, the thickness of the
nano-porous membrane may be in the range of 5-40 nm.
[0010] In this non-limiting example, the nano-porous membrane may
be a nano-porous membrane comprising silicon.
[0011] In this non-limiting example, the nano-porous membrane may
be a nano-porous membrane comprising silicon nitride.
[0012] In this non-limiting example, the nano-porous membrane may
be a porous nanocrystaline silicon membrane.
[0013] In this non-limiting example, the electroosmotic pump may
include a substrate, a passage extending through the substrate, and
the porous nanocrystaline silicon membrane being over the passage
extending through the substrate.
[0014] In this non-limiting example, the micro-fluidics device may
also include a plurality of passages extending through the
substrate and one or more porous nanocrystaline silicon membranes
over the plurality of passages.
[0015] In this non-limiting example, the substrate may be a silicon
substrate.
[0016] In this non-limiting example, the electroosmotic pump may be
configured to move the fluid through the nano-porous membrane at an
applied voltage between 10 mV and 50 V.
[0017] In this non-limiting example, the nano-porous membrane may
have a zeta potential of approximately -5 mV to -40 mV.
[0018] In this non-limiting example, the nano-porous membrane may
have a zeta potential of approximately 100 mV to -100 mV.
[0019] In this non-limiting example, the micro-fluidics device may
also include a fluid channel extending from the micro-fluid output,
wherein the nano-porous membrane has an active area that is at
least 25% of a cross-sectional area of the fluid channel.
[0020] In this non-limiting example, the active area may be at
least 75% of the cross-sectional area.
[0021] In another non-limiting example, a micro-fluidics device may
include a micro-fluid input, a micro-fluid output and an
electroosmotic pump in fluid communication with the micro-fluid
input and output, the electroosmotic pump including a nano-porous
membrane having a thickness of 2-100 nm, the electrosmotic pump
configured to move a fluid through the nano-porous membrane from
the micro-fluid input into the micro-fluid output at a flow rate of
50-800 mLmin.sup.-1cm.sup.-2V.sup.-1, wherein cm corresponds to an
active area of the nano-porous membrane and V corresponds to a
transmembrane voltage of the nano-porous membrane.
[0022] In this non-limiting example, the electrosmotic pump may be
configured to move the fluid through the nano-porous membrane from
the micro-fluid input into the micro-fluid output at a flow rate of
100-500 mLmin.sup.-1cm.sup.-2V.sup.-1.
[0023] In another non-limiting example, a method of moving a fluid
in a micro-fluidic device, the micro-fluidic device including a
micro-fluid input, a micro-fluid output and an electroosmotic pump
comprising a nano-porous membrane having a thickness of less than
100 nm in fluid communication with the micro-fluid input and
output, the method may include: applying a voltage of less than 50
V across the nano-porous membrane; and in response to the applied
voltage, moving a fluid through the nano-porous membrane at a
normalized flow rate of 50-800 mLmin.sup.-1cm.sup.-2V.sup.-1,
wherein cm corresponds to an active area of the nano-porous
membrane and V corresponds to a transmembrane voltage of the
nano-porous membrane.
[0024] In this non-limiting example, the nano-porous membrane may
include pores having widths in the range of 2 nm-100 nm and the
thickness of the nano-porous membrane is in the range of 5-40
nm.
[0025] In this non-limiting example, applying the voltage may be
applying a voltage of less than 1 V across the nano-porous
membrane.
[0026] In another non-limiting example, a micro-fluidics device may
include a fluid reservoir, a sample input, and an electroosmotic
pump in fluid communication with the fluid reservoir and the sample
input, the electroosmotic pump including a nano-porous membrane
having a thickness of 2-100 nm, the electrosmotic pump configured
to move a fluid from the fluid reservoir through the nano-porous
membrane to move a sample from the sample input through a portion
of the micro-fluidics device.
[0027] In another non-limiting example, a micro-fluidics device may
include an electroosmotic pump, a cooling fluid, a heat source, and
a heat sink, the electroosmotic pump including a nano-porous
membrane having a thickness of 2-100 nm, the electrosmotic pump
configured to move the cooling fluid past the heat source and to
the heat sink.
BRIEF DESCRIPTION OF DRAWINGS
[0028] FIG. 1 schematically shows an example of a micro-fluidics
device including an EOP.
[0029] FIG. 2 schematically shows an example of another
micro-fluidics device including an EOP.
[0030] FIG. 3 shows four examples of porous nanocrystalline silicon
(pnc-Si) chips with one, three, six, or nine 200.times.200-.mu.m
windows of freestanding membrane. A 15-nm-thick pnc-Si membrane
extends over each window on the silicon chips.
[0031] FIG. 4 shows in cross-section a pnc-Si membrane over a
window extending through a silicon substrate.
[0032] FIG. 5 shows a transmission electron micrograph image of a
pnc-Si membrane.
[0033] FIG. 6 graphically illustrates pore diameters distribution
of the membrane of FIG. 5.
[0034] FIG. 7 shows an electroosmosis testing device. pnc-Si chips
are sealed between two PET chambers, and a dc power supply
maintains a constant voltage across two Pt electrodes. KCl solution
that flows into the receiving chamber was continuously removed and
weighed at intervals to determine electroosmosis rate.
[0035] FIG. 8 graphically illustrates electroosmotic transport of
KCl measured over time for untreated pnc-Si chips with active areas
shown in FIG. 3. All measurements were performed at an applied
voltage of 20 V. Dotted line indicates a nine-window chip without
pnc-Si material.
[0036] FIG. 9 graphically illustrates electroosmotic flow rates of
untreated pnc-Si membranes as a function of active area at an
applied voltage of 20 V. Theoretical points are calculated using
the pore characteristics, current, and zeta potential of the
particular experimental point.
[0037] FIG. 10 shows a streaming potential testing device. pnc-Si
chips are sealed between two threaded polycarbonate chambers.
Ag/AgCl electrodes measure voltage difference between cells as KCl
is pressurized through chamber.
[0038] FIG. 11 is an image of the polycarbonate device of FIG. 10.
Ag/AgCl electrodes are threaded into a small piece of silicon
cording and are compressed into the end of each chamber with
polycarbonate screws. Each chamber is filled with KCl and the
membrane chip is recessed into one of the chambers between two
O-rings. The chambers are threaded together, and excess KCl leaves
through the pressure inlet/outlet. A KCl reservoir is attached to
the pressure inlet and pressurized by compressed N.sub.2. The
potential difference between the two chambers is measured with a
voltmeter.
[0039] FIG. 12 is a plot of streaming potential vs. pressure data
for native and modified membranes. The offset in the y intercept is
caused by slight differences in Ag/AgCl wires and chamber assembly.
The slope of these curves can be used to determine the zeta
potential using Eq. 6 (discussed below). Note that in solving for
the zeta potential in this example we use an average pore radius
for a. This is because the streaming potential relationship is not
additive in this particular example and cannot be easily determined
for a pore distribution.
[0040] FIG. 13 is a plot of electroosmotic transport of modified
pnc-Si membranes. In this particular example, higher flow rates are
observed for oxidized membrane. In this particular example, amino
silanization reduces the flow rate, but does not change the
direction of the flow.
[0041] FIG. 14 charts zeta potential measured through
electroosmotic (EO) and streaming potential (SP) experiments. In
this instance, oxidation increases the zeta potential whereas amino
silanization reduces the zeta potential.
[0042] FIG. 15 charts pnc-Si electrical resistance. Resistance of
pnc-Si membranes is compared with identical form factor chips with
windows lacking freestanding pnc-Si material. In this particular
example, pnc-Si membranes impart negligible resistance to the
system. The "no chip" bar indicates the resistance of the system
lacking a silicon chip. The inset of FIG. 15 shows a typical I-V
curve from a six-window (0.24-mm2 active area) pnc-Si chip. Error
bars are SDs.
[0043] FIG. 16 is a table of normalized electroosmotic flow rates
for some examples of low-voltage EOPs.
[0044] FIG. 17 shows an example of an EOP prototype pump using a
polycarbonate housing that seals a circular pnc-Si membrane chip
between two viton O-rings. Silver wire electrodes were wound to
produce more surface area and painted with AgCl. Tubing with a
1-.mu.m diameter was attached to the inlet and outlet ports of the
device.
[0045] FIG. 18 shows the EOP prototype pump of FIG. 17 driven with
a constant-current circuit that switched polarity using a relay (on
breadboard). The flow rate was visualized by filming the movement
of the solution front in the tubing under a dissection
microscope.
[0046] FIGS. 19-21 show screen captures from the film of the EOP
prototype pumping in FIG. 18, showing the prototype pumping fluid.
The inlet and outlet tubes are shown side by side, and the fluid is
moving left toward the negative electrode in the bottom tube
(current 0.6 mA, voltage 2.05 V changing polarity every 30 s;
scale, mm). FIG. 19 shows a screen capture at 15s and FIG. 20 shows
a screen capture at 30s. The fluid has moved 1.5 mm in the 15s
between images FIGS. 19 and 20. FIG. 21 shows a screen capture at
55 s. The polarity has changed at this point and the fluid is
flowing left toward the negative electrode in the top tube.
[0047] FIG. 22 charts voltage during the time span of the FIG.
19-21 screen captures and volumetric flow rate as calculated from
individual screen captures during that time span.
[0048] FIG. 23 shows a comparison of flow rate under applied
pressure. In this example, electroosmotic volumetric flow rate was
measured under regulated air pressure in the micro-EOP prototype of
FIG. 18 for three applied voltages and a single direction through
the EOP. The applied pressure reduces the flow rate and stalls
electroosmotic flow in the range of 0.5-1.5 kPa for voltages
1,000-1,500 mV.
[0049] FIG. 24 plots normalized volumetric flow rate (Q/Qmax)
against normalized pressure (P/Pmax). The plotted solid line
represents Eq. 8 (discussed below).
[0050] FIG. 25 is a table of electroosmotic flow through examples
of 15- and 30-nm pnc-Si membranes under back pressure.
[0051] FIG. 26 is a table of hydraulic permeability of examples of
15- and 30-nm pnc-Si membranes.
DETAILED DESCRIPTION OF DRAWINGS
[0052] We have developed an electroosmotic pump that includes a
nanoporous membrane that, in some instances, may be more than two
orders of magnitude thinner than membrane materials previously used
in an EOP. Such pumps could be used for portable microfluidic
devices, cooling circuits, precision fluid (drug) delivery systems,
or for other uses. Such pumps may facilitate high electroosmotic
flow rates for low voltages.
[0053] In one embodiment, the membrane is an ultrathin (e.g. in a
range of 2-100 nm, 10-60 nm, or 15-30 nm in various non-limiting
examples) nano-porous membrane material called porous
nanocrystalline silicon (pnc-Si). pnc-Si membranes may be
fabricated on silicon- or silica-based platforms, or other
platforms. pnc-Si membranes may be fabricated on silicon nitride
platforms in one non-limiting example. pnc-Si membranes may be
fabricated using techniques standard to the microelectronics
industry. In some examples, the silicon platform enables control of
freestanding membrane area and industrial-scale manufacturing. U.S.
Pat. No. 8,152,290, issued May 22, 2012 to Striemer et al., the
entire contents of which are hereby incorporated by reference,
describes non-limiting examples of methods of manufacturing pnc-Si
membranes. FIG. 4 schematically shows in cross section a pnc-Si
membrane over a single window extending through a silicon
substrate.
[0054] Pore distributions in pnc-Si membranes may be controlled in
some instances by fabrication temperatures and ramp rates during a
rapid thermal crystallization step. Pores can be directly viewed in
the ultrathin membrane and characterized with transmission electron
microscopy (TEM). Such pnc-Si membranes may exhibit little
resistance to the diffusion of small molecules and may have high
permeability to water and air.
[0055] We have developed EOPs incorporating pnc-Si membranes that
exhibit high electroosmotic flow rates at low applied voltages,
which may be due to the high electric fields achieved over the
ultrathin membranes. In one non-limiting example, such an EOP has
been shown to pressurize fluid through 0.5 mm diameter capillary
tubing at voltages as low as 250 mV. In another non-limiting
example, an EOP with a low active area (0.36 mm.sup.2) generates
electroosmotic flow rates of 10 .mu.L/min at voltages of 20 V or
lower. In some instances, an EOP may generate electroosmotic flow
rates at voltages of 250 mV to 20 V. In some instances, an EOP may
generate electroosmotic flow rates at voltages as low as 10 mV. In
some instances, an EOP may generate electroosmotic flow at voltages
in the range of 10 mV to 20 V.
[0056] As discussed further below, these flow rates may be compared
with electroosmotic theory by calculating electroosmotic flow using
pore distributions from TEM micrographs. As also discussed below,
surface modifications in some instances may change the zeta
potential of the material and influence the electroosmotic flow
rates. Surface modifications, such as plasma oxidation or
silanization, can influence the electroosmotic flow rates through
pnc-Si membranes by alteration of the zeta potential of the
material. Non-limiting embodiments of the present invention may
provide ultralow voltage and on-chip pumping in microfluidic
systems with low back pressures (for example, without limitation,
at backpressures of 0.3-4 PSI).
[0057] In some examples, the thermodynamic efficiency of a pnc-Si
EOPs may be low, such as less than 0.01% due to low stalling
pressures. In other examples, the thermodynamic efficiency may be
improved orders of magnitude by bringing the electrodes closer to
the membrane and reducing the applied voltage.
[0058] FIG. 1 shows one non-limiting and schematic example of a
microfluidic device (in this instance, a "Lab-on-a-Chip") including
a pnc-Si EOP. Microfluidic devices like the one shown in FIG. 1 may
be made of glass, silicon, polymer (e.g. PDMS), or another
material. In the particular example shown in FIG. 1, a fluid
reservoir 10 connects through a micro-fluid channel to a
micro-fluid input of the EOP 12. The EOP 12 may be used to push a
fluid from the fluid reservoir 10 through a micro-fluid output of
the EOP 12 and down-stream micro-fluid channels in order to, for
instance, drive a sample introduced into the micro-fluidics device
at sample injection port 14. Using the EOP 12, the sample may be
driven to, through, past, or otherwise relative to other units of
the micro-fluidics device, such as the filter 16 and sensor 18
shown in FIG. 1 or other units such as mixers, binding sites, or
other microfluidic components. In some instances, sample injection
port 14 could be located upstream of the EOP 12 instead of
downstream. FIG. 1 is just one example of how an EOP could be
incorporated into a microfluidic Lab-on-a-Chip, and many other
configurations are possible.
[0059] FIG. 2 shows one non-limiting and schematic example of a
microfluidic cooling circuit including a pnc-Si EOP. In this
example, the EOP 20 is connected by microfluidic inputs and outputs
to a microfluidic circuit, and pumps fluid from a reservoir 22 to a
CPU 24 (or other object to be cooled) and then to a heat exchanger
26 or radiator to cool the fluid.
[0060] Experimental and theoretical analyses demonstrate the
feasibility and advantages of using non-limiting embodiments of
EOPs incorporating pnc-Si membranes.
Methods
[0061] pnc-Si Fabrication: The non-limiting examples of pnc-Si
membranes in the below described studies were made on
200-.mu.m-<100> silicon-thick wafers using the methods
described in Striemer et al. (2007) Charge-and sized-based
separation of macromolecules using ultrathin silicon membranes,
Nature 445(7129):749-753 (the entire contents of which are hereby
incorporated by reference). The photoresist was spin-coated on the
surface of the wafers, and chrome masks were used to define the
geometry of the 6.5-mm-diameter experimental chips and
3-mm-diameter imaging chips. The masks also defined the intended
internal windows of freestanding pnc-Si membranes (one, three, six,
or nine windows of 200.times.200 .mu.m or two slits of 2
mm.times.100 .mu.m for experimental chips and four windows of
100.times.100 .mu.m for imaging chips). A three-layer 20-nm
SiO.sub.2/15- or 30-nm amorphous Si/20-nm SiO.sub.2 stack was
sputtered onto patterned wafers via rf magnetron sputtering. The
wafers were annealed at 1000.degree. C. at a rate of 100.degree.
C/s to induce crystallization and form nanopores in the reorganized
silicon film. The bulk patterned silicon was anisotropically etched
with ethylene diamine pyrocatechol, and protective oxide layers
were removed with buffered oxide etchant. Pore distributions were
obtained from TEM micrographs using an open-source MATLAB (The
MathWorks) image processing program (http ://nanomembranes
.org/resources/software/).
[0062] FIG. 3 shows pnc-Si chips with one, three, six, or nine
200.times.200 .mu.m windows of freestanding membrane. FIG. 3 shows
the active area (area of freestanding membrane) above each chip. A
15-nm-thick pnc-Si membrane extends over each window on the silicon
chips, as shown schematically by FIG. 4.
[0063] FIG. 5 shows a TEM of a pnc-Si membrane. In FIG. 5, white
spots are pores and black regions are diffracting nanocrystals.
FIG. 6 graphically illustrates pore diameters as determined by
MATLAB image processing of a 1.7.times.1.1-.mu.m TEM image of the
membrane depicted in FIG. 5.
[0064] Plasma Oxidation and Aminosilanization: for some of the
below described studies, pnc-Si chips were oxidized using a 1224-P
Yield Engineering Systems chemical vapor deposition (CVD) system
with plasma capabilities. pnc-Si chips were placed in the
150.degree. C. chamber and a vacuum of 0.3 Torr was drawn. A plasma
of 0.198 kV was struck in the chamber with a 20 standard cubic
centimeters per min flow of oxygen for 5 min.
[0065] Aminosilanization was performed in the CVD system with a
process temperature of 150.degree. C. The chips were first
dehydrated with two pump/purge cycles of the chamber with
high-purity nitrogen. An oxygen plasma cleaning was then performed
using the procedure described above. The surface was then
rehydrated by injection of water vapor at a pressure of 0.5 Ton and
soaked for 5 min. Then, 1 mL of APTES was vaporized and injected
into the chamber at a pressure of 1.4 Ton and allowed to soak for 5
min. Spectroscopic ellipsometry measurements on SiO2-coated
reference chips indicate that a highly reproducible 0.5-nm-thick
silane layer is deposited with this process.
EXAMPLE 1
Electroosmosis Flow Rates
[0066] pnc-Si membrane chips with different amounts of freestanding
membrane (one, three, six, or nine 200.times.200-.mu.m windows)
were fabricated as described in Methods (see FIG. 3).
Characterization by electron microscopy determined that membranes
had an average pore size of 19.5 nm and a porosity of 5.7% (see
FIGS. 5 and 6).
[0067] An electroosmosis testing device was built by milling
vertical wells into two pieces of polyethylene terephthalate (PET)
(See FIG. 7). Access points were drilled into the side of the two
PET blocks, each with a recessed ledge to hold an O-ring. pnc-Si
membranes were placed between viton O-rings at the two access
points and the devices were sealed using screws with wing nuts.
Experiments were performed with 100 mM KCl, as some (although not
all) embodiments of the present invention are envisioned as a pump
for microfluidic chips and molecules that may in at least some
instances require physiological salt concentrations. A Hewlett
Packard E3612A dc power supply was used to apply a constant voltage
of 20 V, and the volume of aqueous KCl passed into the receiving
chamber was measured on a balance at specific time intervals. The
supply chamber was continuously replenished so that pressure
gradients between the two chambers were negligible. The chamber was
open to atmosphere to prevent trapping of bubbles at the membrane
caused by electrolysis at the platinum electrodes. Control
experiments with solid silicon chips confirmed that the chambers
were well sealed with no leakage current. Control experiments using
chips with freestanding membranes removed did not exhibit any flow
(See FIG. 8), indicating that the pores in the material are
necessary for electroosmosis in some embodiments.
[0068] Representative volume vs. time curves are plotted in FIG. 8
for the four chips with different active membrane areas. Volumetric
electroosmotic flow rates were determined from the slope of these
curves. As shown in FIG. 9, the relationship between volumetric
flow rate and active area in this particular instance is linear. In
this non-limiting example, because an increase in active area
results in a proportional increase in the number of pores,
maximizing the active membrane area occupying a channel
cross-section will maximize flow rates. Although the active areas
are small compared with other EOPs, this active area is scalable
using photolithography techniques and can be fabricated to match
channel dimensions in non-limiting embodiments of the present
invention. In various non-limiting embodiments, the active area
will be at least 25%, at least 50%, at least 75% or 100% of the
cross-sectional area of the fluid channel or channels associated
with the EOP. Even in the small size formats shown in FIG. 3,
pnc-Si membranes achieved flow rates up to 10 .mu.L/min with an
active area of 0.36 mm.sup.2.
EXAMPLE 2
Theoretical Comparison
[0069] The following is a comparison of our experimental results
from the above experiment to Rice--Whitehead theory for
electroosmosis in narrow pores. Volumetric electroosmotic flow, V,
through a narrow capillary in the absence of an external pressure
gradient may be described by the following:
V = - .epsilon..zeta. E z A c .eta. [ 1 - 2 I 1 ( .kappa. a )
.kappa. aI 0 ( .kappa. a ) ] , [ 1 ] ##EQU00001##
where .epsilon. is the product of the dielectric constant of the
solution and the permittivity of free space, .xi. the zeta
potential of the capillary walls, E.sub.z the electric field
through the capillary, A.sub.c the cross-sectional area of the
capillary, .eta. the viscosity, a the capillary radius, and I.sub.0
and I.sub.1 modified Bessel functions of the zeroth- and first
order, respectively. K is the reciprocal of the Debye length and is
found using
.kappa. - 1 = .epsilon. kT 2 q 2 N A c , [ 2 ] ##EQU00002##
where k is the Boltzmann constant, T the temperature, q the charge
of an ion in a symmetrical salt, N.sub.A Avogadro's number, and c
the concentration of the counterion (in mol/m.sup.3). The
multiplier on the right-hand side of Eq. 1 takes into account the
reduction in electroosmotic velocity of the region within the
diffuse layer at the edge of the pore wall, although if
.kappa..sup.-1<<a, this term vanishes and the equation
reduces to the classical Helmholtz--Smoluchowski description of
electroosmosis. In our case, the nanopores within the membrane are
similar in dimension to the Debye length and we consider this
scaling factor. As this theory is developed using the
Debye--Hiickel approximation, it is applicable for zeta potentials
of up to 50 mV, and EOPs with higher zeta potentials require
alternate solutions. As shown below, the magnitude of zeta
potential for this embodiment of pnc-Si is less than 30 mV and so
the Debye-Huckel approximation is valid for this embodiment.
[0070] Volumetric electroosmotic flow through a porous medium can
be determined by expanding Eq. 1 to describe a bundle of
capillaries in a manner similar to the use of Darcy's law for
pressurized flow. Because we can obtain pore distributions from TEM
images that are representative of the entire membrane area, we can
sum Eq. 1 over all of the pores in the image and scale by the ratio
of membrane area to image area, A.sub.tot/A.sub.im, to obtain a
total volumetric flow,
V tot = A tot A im .epsilon. .zeta. E z .eta. i = 1 # of pores .pi.
a i 2 [ 1 - 2 I 1 ( .kappa. a i ) .kappa. a i I 0 ( .kappa. a i ) ]
. [ 3 ] ##EQU00003##
[0071] Rice-Whitehead theory gives the following expression for
current I in a system with electroosmotic flow but lacking
pressurized flow:
I = E z A c .lamda. { 1 - .beta. [ 1 - 2 I 1 ( .kappa. a i )
.kappa. a i I 0 ( .kappa. a i ) - I 1 2 ( .kappa. a i ) I 0 2 (
.kappa. a i ) ] } , [ 4 ] ##EQU00004##
[0072] where .beta. is
(.epsilon..sup.2.xi..sup.2.kappa..sup.2)/(16.pi..sup.2.eta..lamda.).
At the physiological salt concentrations used in the experiments,
.beta. is very small and the electric field for the porous membrane
is
E z = I A tot .chi..lamda. , [ 5 ] ##EQU00005##
where .chi. is the membrane porosity and .lamda. is the
conductivity of the solution. Experimental currents were found
using a TEK DMM252 multimeter (Tektronix). Conductivity was
measured with a CONE conductivity meter (Oakton Instruments) in
bulk solution. We note that this measurement for the conductivity
is an approximation, as the conductivity inside the nanopores could
potentially deviate from the bulk solution. The results indicate
electric fields of 8.times.10.sup.5 V/m across the membranes. These
high electric fields are likely obtained for relatively low applied
voltages because pnc-Si is only 15 nm thick. Because electroosmotic
flow rates increase in proportion to the electric field strength
(Eq. 1), high electric fields across the membrane enhance pump
performance in this example. The benefit of using thin materials
for electroosmosis in some instances is further examined in our
following comparison with other EOPs.
[0073] The zeta potential of the pore walls was determined from
streaming potential measurements. In these experiments, pnc-Si
chips were inserted into the polycarbonate streaming potential
device in FIG. 10 and were sealed by threading the two chambers
together and compressing two O-rings. Ag/AgCl electrodes were
prepared using the method of Burns and Zydney (described in Burns D
B, Zydney A L (2000) Buffer effects on the zeta potential of
ultrafiltration membranes. J Member Sci 172(1):39-48) and sealed
into the device with silicon cord compressed with a polycarbonate
screw. The chamber was filled with 100 mM KCl and pressurized with
N.sub.2 through an entry port fitted with Tygon tubing. For each
measurement the pressure was allowed to stabilize for 30 s, as
displayed by a VWR digital manometer, and the potential difference
across the membrane was measured with a multimeter.
[0074] Streaming potential can be described using Rice--Whitehead
theory, and if .beta. once again is very small, we can use the
expression
E s P = .epsilon. .zeta. .eta. .lamda. [ 1 - 2 I 1 ( .kappa. a )
.kappa. a I 0 ( .kappa. a ) ] , [ 6 ] ##EQU00006##
where E.sub.s is the streaming potential measured at zero current
and P is the applied pressure through the membrane. In Eq. 6 the
pore size a is taken to be the average pore size. The slope of a
streaming potential versus pressure plot can be substituted for the
left-hand side of Eq. 6, allowing for the determination of the zeta
potential (see FIG. 12). By this method we find that the zeta
potential of untreated pnc-Si membranes is -13.9 mV in this
particular example, consistent with a native oxide surface.
[0075] Theoretical flow rates for each experiment were calculated
using the electric field (Eq. 5), average zeta potential (Eq. 6),
and pore characteristics as obtained from image processing of TEM
micrographs. The theoretical flow rates are very similar to the
experimental flow rates, indicating that theory developed for
infinitely long pores also holds for pore radii that are on the
same order as their length. If entrance and exit effects exist for
electroosmosis in short nanopores, they were not observable by our
methods in this particular example.
EXAMPLE 3
Surface Modifications
[0076] Modifying the surface of a material can in some instances
change the zeta potential and alter the rate of electroosmotic
flow. To investigate the ability to change the rate of
electroosmosis through surface modifications, we treated pnc-Si
membranes with both plasma oxidation and aminosilanization (see
FIG. 13). Oxidation increased flow rates by about two times over
the untreated samples, whereas aminosilanization reduced the flow
rates almost to zero.
[0077] The effects of plasma oxidation can be understood as an
enhancement of the intrinsic negative charge of pnc-Si. pnc-Si is
expected to grow a negatively charged native oxide as silicon
surfaces typically do in many instances in the presence of oxygen.
This expectation is consistent with the negative zeta potential of
untreated pnc-Si and the fact that electroosmostic flow is directed
toward the negative electrode. Plasma oxidation, a treatment that
is commonly used to remove carbonaceous substances from inorganic
surfaces, has been previously shown to slow the diffusion of
negatively charged molecules, indicating a stronger negative charge
than untreated membranes. Treatment in oxygen plasma has been shown
to create negatively charged silanol groups on the surface of poly
(dimethyl siloxane) microfluidic channels, thereby allowing them to
generate electroosmotic flow. In the pnc-Si membranes used in this
example, plasma oxidation resulted in a larger measured zeta
potential compared with untreated membranes (see FIG. 14),
suggesting that the oxide layer formed during this process is
denser than the native oxide layer.
[0078] Aminosilanization treatment causes a reduction of
electroosmotic flow by reducing the native surface charges on
pnc-Si. Silanization, a chemical reaction that enables a
silicon-containing organic compound (or silane) to be covalently
bonded to a silica surface, allows for a myriad of
functionalization possibilities due to the abundance of silanes.
Previous work with capillary electrophoresis and microfluidic chips
has shown that surface modification with various silanes reduces
the electroosmotic flow rates and the zeta potential of silica. In
this example, we have grafted aminopropyltriethoxysilane (APTES) to
the surface of the plasma-oxidized pnc-Si membranes. This
modification results in a terminal amino group on the surface that
carries a positive charge at neutral pH. The aminosilanization
treatment greatly reduced the rate of electroosmosis, but did not
change the direction of fluid flow or reverse the sign of the zeta
potential (see FIGS. 13 and 14). This suggests that the positive
amino groups in this example reduced the net surface charge within
the pores, but that the modification was not complete enough to
invert the native negative charge.
[0079] Note that in this example we calculated zeta potential from
streaming potential (Eq. 6) and electroosmosis measurements (Eq.
3). Streaming potential measurements are a common form of zeta
potential calculation, although we include electroosmotic
calculations for comparison. pH changes induced by electrolysis at
the electrodes and the effects of ion migration through the device
can influence the zeta potential in some instances as calculated
from electroosmosis. In this example, we do see an agreement in the
trend of the zeta potentials as calculated by the different methods
for the treated membranes, although electroosmosis calculations
lead to lower zeta potentials for all membrane types in many
instances.
EXAMPLE 4
Intrinsic Electroosmotic Flow Rate
[0080] pnc-Si may be in some instances more than 100 times thinner
than other membrane materials used for dc electroosmotic pumping,
and it may be expected that thinner materials in at least some
instances would result in higher electroosmotic flow rates.
However, the test devices used in this example were not optimized
and thus do not take advantage of the intrinsic rate of
electroosmosis for this material. Here, we calculate this potential
rate by normalizing the flow rate by active area and transmembrane
voltage. Note that only a small portion of the applied voltage
V.sub.app falls across the membrane. One method to determine the
transmembrane voltage V.sub.TM is through the electrical resistance
in the system,
V.sub.app=V.sub.dec+(2R.sub.b+R.sub.c+R.sub.m)I. [7]
[0081] The resistance R.sub.b occurs within the bulk fluid in the
chambers, R.sub.c is the resistance of the orifice within the
silicon chip, and R.sub.m is the resistance of the membrane.
V.sub.dec is the decomposition potential, or the voltage required
to initiate electrolysis at the Pt electrodes. The transmembrane
voltage is the product of the membrane resistance and current:
V.sub.TM=R.sub.mI. Current-voltage (I-V) curves (see FIG. 15,
inset) can be used to determine the parameters in Eq. 7; the slope
of an I-V curve of a system with an intact membrane gives
(2R.sub.b+R.sub.c+R.sub.m) and the slope of an I-V curve using an
equivalent geometry chip in which the membrane was removed gives
(2R.sub.b+R.sub.c). Thus, the difference in resistances calculated
in these two cases is attributed to the membrane itself
(R.sub.m).
[0082] FIG. 15 illustrates the resistances as calculated from I-V
curves for different active area chips both with and without
membranes. In each case the difference is within the SE of the
measurements (.about.60.OMEGA.), indicating that the transmembrane
voltage is no greater than 600 mV given experimental currents of 10
mA in this particular example. However, the actual transmembrane
voltage appears to be much smaller than this estimate. The electric
field strength (8.times.10.sup.5 V/m) and a 15-nm-thick membrane
require a transmembrane voltage of only 12 mV. Low membrane
resistance compared with all other resistances in the system has
been observed for diffusive transport through pnc-Si. In some
studies, the ultrathin dimension of the membrane results in a
transmembrane resistance to diffusion that can be neglected
compared with bulk resistances. Analogously, the low electrical
resistance of pnc-Si in electroosmosis experiments follows from the
ultrathin quality of the membrane, as other resistances in the
system are much higher by comparison. It is striking that the
insertion of a vanishingly thin membrane is necessary to generate
microscale flow, yet does not significantly alter the current or
power consumed by the system.
[0083] For this example, we have normalized the electroosmosis flow
rate by the calculated transmembrane voltage and the active area of
the chip to obtain a figure of merit of 260
mLmin.sup.-1cm.sup.-2V.sup.-1. In other non-limiting examples, the
figure of merit may be in the range of 100-600
mLmin.sup.-1cm.sup.-2V .sup.1. FIG. 16 shows that this figure of
merit exceeds low-voltage EOPs fabricated from examples of porous
silicon, alumina, and track-etched polymer by three orders of
magnitude. Normalized flow rates for examples of ultrathin pnc-Si
EOPs are also 20 times higher than carbon nanotube (CNT) EOPs,
which are considered to have unique properties due to a slippery
surface. Recent advances in alternating current (ac) electrode
arrays have enabled the development of ac EOPs. Whereas the flow
rates of ac EOPs increase nonlinearly compared with dc EOPs, at the
low voltages used in this paper the figure of merit for pnc-Si EOPs
exceeds that of an ac EOP by 70 times. In addition, electroosmotic
flow through ac EOPs is hampered by high salt (>10 mM), which
reduces their utility in solutions with physiological ionic
concentrations. pnc-Si EOPs are also inexpensive to fabricate
(.about.$1 per chip), as hundreds of functioning membrane chips can
be produced per 6-inch wafer.
[0084] The low electrical resistances and high electrical fields
achieved across the ultrathin pnc-Si membranes enable the high
normalized flow rate. To realize the full potential of pnc-Si-based
EOPs, in some instances, fluidic channel cross-sections and active
membrane areas may be of similar dimensions. In some instances,
both the fluidic channel and active membrane cross-sectional width
or diameter may be similar and in the range of 1 .mu.m to 1 cm.
Electrodes also could be brought closer to one another (e.g. spaced
approximately 50-500 .mu.m apart) or sputtered directly on the
membrane surface to further minimize the applied voltage. Unlike ac
EOPs, Faradaic reactions in dc EOPs can cause sample or fluid
contamination, and this drawback could be a greater problem for
smaller scale EOPs with electrodes closer to the membrane surface.
By keeping the applied voltages low and using Ag/AgCl electrodes,
we can minimize, in at least some embodiments, electrolysis and
bubble formation within the pores of smaller scale EOPs.
EXAMPLE 5
Development of pnc-Si EOP Prototype
[0085] To demonstrate the applicability of pnc-Si membranes as
pumps in microfluidic systems, we designed and tested an example
prototype of a low-voltage EOP (see FIGS. 17 and 18). Ag/AgCl
electrodes were prepared by coating 200-.mu.m-diameter silver wire
with Ag/AgCl ink (Conductive Compounds), which were allowed to dry
before insertion into the device. The electrodes were sealed in the
polycarbonate enclosure with silicone gaskets, and
500-.mu.m-diameter tubing was connected to the inlet and outlet
ports. The device was filled with 100 mM NaCl under vacuum. A
double-slit pnc-Si membrane was inserted into the device between
two viton O-rings in solution at atmospheric pressure. Once
assembled, the device was left submerged in solution for at least
12 h before testing.
[0086] Both Ag/AgCl electrodes of the EOP were connected to an
Agilent 33220A arbitrary waveform generator, which was used as a
controllable voltage source. The current measurement was performed
by using an Agilent 34410A digital multimeter. Both waveform
generator and digital multimeter were connected to a personal
computer and controlled remotely. This software, written in C/C++,
was developed specifically to provide a constant dc voltage ranging
from -5 V to +5 V and simultaneously record the current readouts
from the multimeter.
[0087] Electroosmosis was visualized by tracking the movement of
the menisci in inlet and outlet capillary tubes under a microscope
equipped with a CCD camera. FIGS. 19-21 show images of the menisci
at three different time points during an experiment in which the
voltage polarity was switched every 40 s. The fluid flowed toward
the negatively charged electrode at a rate of 1 .mu.L/min at an
applied voltage of 2 V (see FIG. 22). With the Ag/AgCl electrodes,
fluid flow through the capillary tubes was achieved at voltages
lower than the hydrolysis of water, and no gases were generated in
the chamber during the experiments.
EXAMPLE 6
Thermodynamic Efficiency
[0088] We tested the capability of an EOP to pump against back
pressures supplied by a precision air pressure regulator type 70
(Marsh Bellofram). Electroosmosis flow rates in the presence of
back pressure were measured from the meniscus movement in the inlet
tube (see FIGS. 23-24). Application of pressure linearly reduced
the electroosmotic flow rate for applied voltages of 1,000-1,500 mV
(See FIG. 23). In FIG. 25 we show the maximum flow rate at zero
pressure Q., the maximum pressure at zero flow P., and the power
consumption. Q. and P. can be used to normalize the flow rate and
pressure, respectively, which is plotted in FIG. 24. This data
compares well with the accepted relationship between flow rate and
pressure,
Q Q max = 1 - P P max , [ 8 ] ##EQU00007##
which is plotted as a solid line in FIG. 24.
[0089] The thermodynamic efficiency is the ratio of hydraulic to
electrical power for an EOP, or
.eta. = 1 4 Q max P max IV app . [ 9 ] ##EQU00008##
[0090] Using the data from the back pressure analysis and the
applied voltages, we calculated the thermodynamic efficiencies to
be on the order of 0.00075% in this example. Thermodynamic
efficiency has been shown to range from 0.005% to 2% experimentally
in aqueous buffers. In embodiments of the present invention, the
thermodynamic efficiency could be improved by orders of magnitude
by moving the electrodes to either side of the membrane. The
efficiency may also be improved by increasing the amount of
membrane occupying the channel cross-section (currently 5% or
less). Increasing the active area will raise both the flow rate and
the current, but the current increase is expected to plateau as the
resistance does (see FIG. 15).
[0091] To address whether the low back pressures supported by
pnc-Si EOPs were related to membrane thickness, we conducted
experiments with both 15- and 30-nm membranes. Surprisingly, we
discovered that the 30-nm membranes exhibited lower stall pressures
than the 15-nm membranes (see FIG. 25), indicating that thickness
was not the only variable that determined stall pressures. By
characterizing the pore distributions of the two membranes, we were
able to calculate a significantly higher hydraulic permeability for
the 30-nm membrane (see FIG. 26). Whereas the porosities of the 15-
and 30-nm membranes were similar, it has been shown that larger
pores naturally form in thicker membranes due to looser geometric
constraints. Thus, the low stall pressure seen with pnc-Si may be
directly related to the permeability. Low porosity, rather than
greater thickness, may be the most effective way to improve this
aspect of pnc-Si performance in some instances. Despite a low
thermodynamic efficiency and low stall pressures in some of the
current embodiments described, pnc-Si EOPs were used to produce
flow rates of 1 .mu.L/min through 10 cm of microcapillary tubing in
voltages lower than 2 V. Thus, by installing pnc-Si EOPs in
microfluidic chips with low back pressures, high microfluid flow
rates can be achieved under low applied voltages (e.g. in the range
of 0.02 .mu.L/min-1 mL/min depending on the diameter of the fluid
channel). pnc-Si could therefore find uses as in-line pumps to move
reagents and samples between locations within microfluidic
chips.
Summary of Examples
[0092] Examples of ultrathin pnc-Si membranes have been described
that operate as high-flow-rate EOPs with low applied voltages. In
at least some instances, this may be due to the small electrical
resistance presented by the membrane and high electric fields
across the molecularly thin membrane. The normalized flow rates of
these examples were shown to be 20 times to several orders of
magnitude higher than recent low-voltage EOPs. Pore distributions
of pnc-Si membranes can be imaged via TEM, and we show using
Rice--Whitehead theory that flow rates can be predicted for a given
membrane in at least some instances. Surface modification through
oxidation and silanization techniques may be used to change the
zeta potential of the material and the electro-osmotic flow rates.
The example of a prototype pnc-Si EOP described above has been
shown to produce flow through capillary tubing with applied
voltages as low as 0.25 V, although stalling pressures were in the
range of 1 kPa. In some instances, such an EOP may be optimized by
bringing the electrodes closer to the surface and maximizing active
membrane area to channel dimensions. Due to scalable silicon
fabrication methods, pnc-Si EOPs may be fabricated cheaply in at
least some instances and can be easily integrated on silicon- or
silica-based microfluid chips in at least some instances. pnc-Si
EOPs will potentially enable low-voltage, on-chip electroosmotic
pumping in microfluidic devices.
[0093] It will be appreciated that variants of the above-disclosed
and other features and functions, or alternatives thereof, may be
combined into many other different systems or applications. Various
presently unforeseen or unanticipated alternatives, modifications,
variations, or improvements therein may be subsequently made by
those skilled in the art which are also intended to be encompassed
by the following claims.
* * * * *
References