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Aug 15, 1996 - Hydrodynamic Permeability of Hydrogels Stabilized within Porous ... HemaSure Inc., 140 Locke Drive, Marlborough, Massachusetts 01752...
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Ind. Eng. Chem. Res. 1996, 35, 3179-3185

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Hydrodynamic Permeability of Hydrogels Stabilized within Porous Membranes Vivek Kapur,† John C. Charkoudian,‡ Stephen B. Kessler,§ and John L. Anderson*,| Colloids, Polymers and Surfaces Program, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, Millipore Corporation, 80 Ashby Road, Bedford, Massachusetts 01730, and HemaSure Inc., 140 Locke Drive, Marlborough, Massachusetts 01752

The purpose of this work was to demonstrate that cross-linked polymer gels can be stabilized against mechanical and osmotic forces by confining them in a microporous support. The hydrodynamic (Darcy) permeability was measured for neutral and charged polyacrylamide (PA) gels synthesized in semirigid membranes having a hydraulic mean pore diameter of 0.5 µm and a porosity of 67%. The permeability was determined by measuring the flow rate of aqueous solutions as a function of pressure drop across the membranes. The membrane-supported gels were stable and yielded a constant permeability when the pressure drop was increased to 300 bar/cm. No swelling/deswelling was observed with the charged gels (0.3-0.4 equiv/L) when the ionic strength was varied between 0.01 and 1.0 M, and the permeability was essentially independent of ionic strength. The permeability of the neutral gel varied as φ-3.3 where φ is the polymer volume fraction, whereas literature data for bulk PA gels shows the dependence to be φ-1.4. The permeability of the membrane-supported neutral PA gel was greater than the literature values for the bulk gel at low φ but comparable to the bulk gels when φ > 0.08. Introduction The promise of gels as viable separation devices for large-scale processes rests on the ability to stabilize them in configurations that take advantage of their space-filling capacity yet maintain their integrity. Polymeric gels can be selective media based on molecular size (Gehrke and Cussler, 1986; Tong and Anderson, 1996) and ion exchange (Boschetti et al., 1995; Gehrke et al., 1989). The basic engineering problem is to protect gels against mechanical and osmotic forces. An example of this challenge is chromatography. Highly crosslinked gels have been used for the packing of chromatographic columns; however, the large pressure gradients required to achieve flows through beds of particles less than 0.05 mm diameter can cause deformation and collapse of the gel particles. An approach to overcome the stability problem is to fabricate gels within pores of a rigid matrix such as silica particles (Boschetti, 1994) or a rigid polymer membrane. If the pores are much larger than the effective mesh dimension of the gel, then the gel will control molecular and viscous transport within the pores (Kim and Anderson, 1991). Such “gel in a shell” composite structures offer mechanical strength without sacrificing the functionality of the gel (Boschetti et al., 1995); that is, the gel network can be optimized with respect to chemistry, charge, and cross-linking. An important property of gels is their hydrodynamic (Darcy) permeability, k, which is defined by Darcy’s law:

v)-

k ∇P η

(1)

* Author to whom correspondence should be addressed: Phone: (412)268-6986. Fax: (412)268-7139. E-mail: jlacheme [email protected]. † Present address: E. I. duPont de Nemours and Co., Experimental Station, Wilmington, DE 19880. ‡ Millipore Corporation. § HemaSure Inc. | Carnegie Mellon University.

S0888-5885(96)00015-2 CCC: $12.00

where v is the superficial solvent velocity through the gel, η is the solvent viscosity, and P is the pressure. The above equation assumes the gel is isotropic. The hydrodynamic screening length, xk, is a measure of the mean spacing between the fibers (polymer chains) forming the gel network. Darcy’s law is valid at distances greater than xk from boundaries where a noslip velocity condition is imposed; within distances of about xk, Brinkman’s equation (Brinkman, 1947; Howells, 1974) describes the velocity field. Measurements of k for gels are valuable for two reasons. First, k depends on the the microstructure of the gel, and hence its measurement gives insight into the microstructure; and second, k along with solute diffusion coefficients must be known to model molecular transport within gels (Johnson et al., 1996; Tong and Anderson, 1996). However, experimental determination of k for bulk gels is difficult because of their compressibility. Often a plot of superficial velocity versus applied pressure across a thin film of gel is nonlinear because the gel compresses and k decreases as pressure increases. There are two objectives of this work: first, to demonstrate that a cross-linked gel can be stabilized with respect to mechanical (pressure) and osmotic forces by synthesizing it in a porous membrane; second, to compare the hydrodynamic permeability of membranesupported gels with bulk gels. We report experimental results for the permeability of cross-linked polyacrylamide (PA) and derivatized (charged) PA gels that were formed within the pores of poly(vinylidene fluoride) membranes. The data are broken into two sets, one for the neutral gels and the other for the charged gels. With the neutral gels, we are interested in the variation of permeability with polymer volume fraction of the gel and how our results compare with literature data for the permeability of bulk gels (Tokita, 1993; White, 1960) as well as the stability (i.e., the constancy of the permeability) at large pressure gradients. With the charged gels, our focus is on the ability of the porous © 1996 American Chemical Society

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membrane to stabilize the gel when the ionic strength of the solution changes. Experimental Section A summary of materials and methods is given below. More details are available elsewhere (Kapur, 1995). Synthesis of Gel-Pore Composite Membranes. The neutral PA gel membranes were made at the Millipore Corporation (Bedford, MA). A poly(vinylidene fluoride) (PVDF) membrane (Durapore, Millipore Corp.) of nominal pore diameter 0.22 µm was used as the support. These membranes can be obtained in two forms: with a thin polyacrylate coating to make them hydrophilic (Steuck, 1986) or without any coating (hydrophobic). The hydrophilic membranes were used for synthesis of the neutral PA gels. The membrane was first soaked for 2 min in a degassed aqueous solution of acrylamide monomer plus the cross-linking agent (N,Nmethylenebisacrylamide) and photo-initiator (tradename Darocur 2959 ) 4-(2-hydroxyethoxy)phenyl-(2propyl) ketone, Ciba Geigy, Inc.). The membrane was then removed from the solution and placed between two thin polyethylene sheets. Excess solution was removed by gentle application of a rubberized roll bar. Polymerization was accomplished by transporting the sandwich through a Fusion Systems UV (H bulb) unit at 12 ft/min. After UV curing, the membrane was immersed in deionized/filtered water (MilliQ purified). The membranes were stored in buffered solutions at pH 5.9 or pH 8.5. The cross-link density (CL), which is defined as the ratio of (mass of bisacrylamide)/(mass of acrylamide), was 6% for all the data reported here. The UV energy was too low to expect any significant covalent binding of the PA to either the PVDF surface or the thin polyacrylate coating. The charged membrane-supported gels were made at BioSepra Inc. (Marlborough, MA). Hydrophobic Durapore membranes (i.e., no coating on the PVDF) of 0.22 µm nominal pore diameter were used as the support. Gels based on monomers carrying either positive (Q, quaternary amine) or negative (S, sulfonate) groups were synthesized using methods similar to those described by Girot and Boschetti (1993, 1995), which result in substantially homogeneous, clear gels of low CL. The two referenced patents pertain to the formation of such gels within porous mineral oxide particles. To form the same gels within microporous PVDF membranes, the following procedure was used. The internal surfaces of the membranes were treated using methods similar to those described in the above referenced patents. Working inside a nitrogen-purged glovebag, each membrane sample was placed inside an individual polyethylene pouch. Solution containing monomers, cross-linkers, and polymerization catalyst was applied to each membrane using a microliter syringe. Each pouch was then sealed, and the glovebag was heated to 85 °C for 1.5 h to effect polymerization. The resulting gel-filled membranes were washed in deionized water and stored in appropriate buffers. The charge density based on the pore volume was 0.4 mequiv/cm3 for the Q form and 0.3 mequiv/cm3 for the S form. The volume fraction (φ) of polymer (monomer plus cross-linking agent) in the neutral PA gel membranes was determined in two ways. The first method was based on the weight of the dry membrane before synthesis of the gel (wm) and the weight of the dry membrane after the gel was formed (wm+g). The gel volume fraction was computed from

Figure 1. Apparatus for measuring Darcy permeability of the membrane: km ) ηvm/(-∆P/L) where L is the membrane thickness (0.125 mm), η is the viscosity of the aqueous solution, and vm ) Q/Am.

φ)

vp(wm+g - wm) πRm2L

(2)

where Rm is the radius (2.35 cm), L the thickness (0.125 mm),  the porosity of the membrane (0.67), and vp the partial specific volume of PA (0.7 cm3/gm (Munk et al., 1980)). The second method was based on determination of the nitrogen content of the membrane (Desert Analytics, Tucson, AZ). The nitrogen determination was converted into PA content per unit volume of membrane, from which φ was calculated (Kapur, 1995). The values of φ by these two methods were in good agreement in all cases. The nitrogen-based analysis was probably more accurate, so its result was used for φ except for the two lowest values of φ for which the nitrogen analysis was not available. The polymer volume fraction of the charged PA gels was determined by the gravimetric method only. Equation 2 was used, and the specific volume was assumed to be the value for PA (0.7 gm/cm3). From representative samples of the membrane-supported gels, we found that φ ) 0.12 ( 0.01 for the Q form and φ ) 0.16 ( 0.01 for the S form. Measurement of Hydrodynamic Permeability. The membrane hydraulic permeability (km) is defined by

km )

ηvm (-∆P/L)

(3)

where vm is the water flow rate (Q) divided by the available membrane area (Am ) 5.07 cm2). The apparatus is sketched in Figure 1. The membrane was mounted on a porous stainless steel screen that provided negligible resistance to flow. The low-pressure reservoir was a block of Plexiglas with holes drilled at a converging angle. The total volume of the low-pressure reservoir was 0.35 cm3. Pressurized nitrogen was used to force water through the membrane. The water was obtained from a MilliQ2 system. Buffer solutions of sodium dihydrogen phosphate/sodium hydroxide and sodium chloride (pH ) 5.9) or sodium borate/hydrochloric acid and sodium chloride (pH ) 8.5) were prefiltered in-line with 0.2 and 0.1 µm pore size polyester Nuclepore membranes. Pressure was measured with Validyne DP-15 transducers. The solvent flow rate was measured by following the movement of a bubble in a precision-bore capillary (radius ) 0.275 mm) connected to the low-pressure side of the Plexiglas cell. The hydrodynamic resistance of the membrane without gel in the pores was more than 100

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Pore volume and pore-size distribution of sample hydrophobic membranes were determined by mercury porosimetry (Micrometrics Corporation, Norcross, GA). From these data we found that  ) 0.67 and the mean pore diameter equaled 0.4 µm.  was calculated from the measured specific pore volume (mL/g of solid) and the density of PDVF (1.77 gm/mL). The mean pore diameter was defined as the diameter at 50% volume intrusion. The Darcy permeability of the bare membranes (kmo) was about 2-3 × 10-11 cm2. The Kozeny equation (Happel and Brenner, 1973) relates the permeability to the hydraulic radius (rh ) pore volume/surface area) and porosity () of the porous medium:

rh2 K*

kmo )

Figure 2. Sample data for three gel-filled membranes (neutral PA) with different polymer volume fractions (φ) in the pores. km is the slope of the straight lines.

times the sum of the resistances of all other components in the system. The membrane permeability was determined by measuring Q versus ∆P, correcting η for the temperature during the experiment (20-25, ( 0.5 °C during an experiment), and then using eq 3 to compute km. Sample data for three gel-filled membranes are plotted in Figure 2. With some of the gel-filled membranes at low φ there was a very slight curvature to the plot of vm versus ∆P. The values of km reported here are the extrapolations to zero pressure. The reduction in km in going from the lowest to the highest pressure (-∆Pmax ≈ 3 bar) was always less than 7% of the extrapolated zero-pressure value of km. Since cross-linked gels are elastic media, it is important to recognize elastic relaxation in making pressureflow measurements. Scherer (1989) modeled the time course of compression of a elastic thin film that is supported by a plane on the low-pressure side. If time zero is defined when the pressure drop is first impressed across the film, then the time required before the stress in the film becomes essentially linear is given by

τe )

L2η Mk

(4)

where M is the uniaxial elastic modulus of the film. For polymeric gels with φ ) 0.1, the osmotic modulus is of order 1 bar and increases as φ2.3 (Sellen, 1987). Taking this value for the elastic modulus, a bulk gel film of thickness comparable to our membranes (≈0.1 mm) would have τe ≈ 100 s; steady-state flow would only be expected for times longer than this. The times for a flow measurement at one pressure were about 103 s. The system was allowed to equilibrate for 10-60 min before the flow rate was recorded. Moreover, two repeatable measurments were taken for each increment in pressure. Characterization of Bare Durapore Membranes. The Durapore membranes had a nominal pore diameter of 0.22 µm. We measured the porosity of sample membranes by gravimetric methods and found  ) 0.67 ( 0.02. The nominal thickness of the membranes was 0.125 mm; this value was confirmed by our measurements. These characterizations were done with hydrophilic membranes.

(5)

where K* is the Kozeny constant, which equals 2 for parallel capillary-type pores of circular cross section and 25/6 for consolidated structures (for example, packed beds) with  less than 0.5. The value of K* increases as  increases and is about 5 for  ≈ 2/3. Taking the equivalent pore diameter to be 4rh and using the value 2 × 10-11 cm2 for the Darcy permeability, we estimate the hydraulic mean pore diameter to be 0.5 µm, which falls between the values obtained by electron microscopy (0.6 µm) (Allegrezza and Kazan, 1993) and the porosimetry data (0.4 µm). Conversion of measurements of km to the permeability of the gel itself (k) requires knowledge of /τ where τ is the “tortuosity factor”:

(τ)

-1

k)

km

(6)

The ratio /τ can be experimentally determined by measuring the diffusion rate (M) of a solute through a bare Durapore membrane as a function of concentration difference:

M ) kD(-∆C) kD0 ) lim kD ) ωf∞

 DoAo τ L

(7a) (7b)

where Do is the diffusion coefficient of the solute, Ao is the membrane area for these diffusion experiments (2.9 cm2), and ω is the rotation rate (rad/s) of the stirring bars. A diaphragm diffusion cell with rotating stirring bars oriented parallel to the membrane surface on both sides was used. Extrapolation of the experimental kD to infinite stirring speed, as shown in Figure 3, allows the determination of the intrinsic membrane coefficient kDo (Malone and Anderson, 1977). The two solutes were ribonuclease A and bovine serum albumin. Because both solutes are 2 orders of magnitude smaller than the mean pore size of the membrane, Do essentially equals the diffusion coefficient in solution. The mean value of /τ for the two solutes is 0.29. Given that the porosity of the bare membranes was 0.67, we have τ ) 2.3, which is consistent with the value derived from the Kozeny constant (K*/2 ) 2.5). If Darcy’s law (eq 1) is valid in the gel phase of the membrane, then the pressure obeys Laplace’s equation in the gel-filled pore spaces because ∇‚v ) 0. Note that the solute (protein) concentration within the gel-free pore spaces of the bare membrane also obeys Laplace’s equation during diffusion. The mathematical analogy

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Figure 3. Diffusion of proteins across a bare (no gel) membrane to determine /τ. kD is the overall mass transfer coefficient (cm3/s) defined by eq 7a, where kDo is mass transfer coefficient for Durapore membrane (ω f ∞) defined by eq 7b, ω is the angular velocity (rad/s) of the stirrers in the diffusion cell, and Do is the diffusion coefficient (19 °C) of the protein in solution (cm2/s). /τ is computed from the intercept of the best-fit straight lines and eq 7b. The values are 0.31 for ribonuclease A and 0.26 for bovine serum albumin; error estimates on each determination are ( 0.03.

between pressure in the pressure-flow experiments with gel-filled membranes and protein concentration within the bare membrane in the diffusion experiments means that the tortuosity factor is the same for both processes. Thus, the hydrodynamic permeability of the gel itself (k) is related to the hydrodynamic permeability measured for the membrane (km) by eq 6 with /τ ) 0.29. Results Neutral PA Gels. The experimental values of k for neutral PA gels are plotted against polymer volume fraction of the gel in Figure 4. There was no measurable effect of ionic strength (0.001 f 1.0 M) or pH (3.0 f 9.0) (Kapur, 1995). The straight line is a power law fit to these data, neglecting the values for φ < 0.04:

k ) 4.35 × 10-18φ-3.34 (cm2)

(8)

The exponent on φ is larger than the value 1.5 derived from the theory of deGennes (1979) for entangled polymer networks. Data for the sedimentation of linear polymers in solution above the semidilute concentration yield an exponent near 1.5 (Mijnlieff and Jaspers, 1971; Nystrom and Roots, 1980; Ethier, 1986). Tokita (Tokita, 1993; Tokita and Tanaka, 1991) measured the Darcy permeability of bulk, neutral PA gels that were synthesized as films 1 mm thick. Tokita’s data for 2.2% cross-linked gels are represented by the following empirical expression (Tong, 1995):

k ) 2.64 × 10-16φ-1.42 (CL ) 2.2%)

(9a)

Tokita also measured the effect of cross-link density at φ ≈ 0.035. The following empirical expression fits his data over the range 0.7-24.0% cross-link density (Tong, 1995):

k ) 2.48 × 10-14CL0.295 (φ ≈ 0.035)

(9b)

where CL ) % cross-link density (100 × mass of crosslinker/monomer). The increase in permeability with

Figure 4. Hydrodynamic permeability (k) versus total polymer volume fraction (φ) for PA gels. The symbols are from our experiments (6% CL) with k determined from km using eq 7 and /τ ) 0.29. Literature data for bulk PA gels are represented by the lines: Tokita (1993), eq 9; White (1960), eq 10.

increasing CL implies that more cross-linking causes greater microscopic heterogeneity of the gel structure, as suggested by Weiss et al. (1981). This hypothesis is also consistent with the measured increase in the partitioning of macromolecules with increasing CL (Tong, 1995). White (1960) also measured the permeability of bulk PA gels. At CL ) 5%, he obtained data that are fit by the following empirical expression over the range 0.04 < φ < 0.11:

k ) 1.015 × 10-16φ-1.083 (cm2)

(10)

These permeabilities are an order of magnitude lower than those measured by Tokita. A possible explanation is that the hydraulic permeability of bulk gels is difficult to measure accurately due to their compressibility. Since White’s measurements were performed at 20-fold higher pressures than Tokita’s, greater compression of the gel is to be expected, which would result in lower apparent permeabilities. It is our opinion that Tokita’s results are the most representative of bulk, neutral PA gels. In Figure 4, we compare our data for the membranesupported gels (CL ) 6%) with the data of Tokita (1993) and White (1960). It appears that the membranesupported gels were more permeable than the bulk gels at low φ, but the differences were small when φ g 0.08. In general though, the differences between Tokita’s data and ours are less than the differences in permeability cited for bulk PA gels by different research groups. Charged PA Gels. Figures 5 and 6 display data for the charged gels. Table 1 summarizes the results. The reproducibility between membranes with the same nominal gel composition is excellent; the standard deviation of the measurements is less than 10% of the

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Figure 5. Flowrate data for membranes filled with charged PA gels at 0.05 M ionic strength. The symbols represent different membranes. The straight lines are linear best fits of all the data to eq 3. (a) Q gel: km ) 0.122 × 10-14 cm2; (b) S gel: km ) 0.0435 × 10-14 cm2. Table 1. Results for Hydrodynamic Permeability of Membrane-Supported, Charged PA-Based Gelsa gel type

IS (M)

k × 1014 (cm2)

Q Q

0.05 0.01 0.10 1.00 0.05 0.01 1.00

0.420 ( 0.035b 0.342 0.452 0.679 0.150 ( 0.013c 0.152 0.169

S S

a Q form: quaternary amine, pH ) 8.5, charge density ) 0.4 mequiv/cm3 gel, φ ) 0.12 ( 0.01. S form: sulfonate, pH ) 5.9, charge density ) 0.3 mequiv/cm3 gel, φ ) 0.16 ( 0.01. IS means ionic strength of the buffered solution, defined as 1/2∑izi2Ci where zi and Ci are the equivalent valence and concentration of ions of type i. b Six different membranes prepared in the same manner. The ( value is the standard deviation of the data. c Four different membranes prepared in the same manner. The ( value is the standard deviation of the data.

mean for both positive (Q) and negative (S) gels. No hysteresis in the pressure-flowrate measurements was observed when the pressure was first increased and then decreased. The mean values of permeabilty for the Q and S gels at 1.0 M ionic strength are plotted in

Figure 6. Flow versus solution ionic strength (M ) molarity) of charged PA gels. The order of the experiments is given by the order of the symbols in the legend (top ) first). The ionic strength was computed using the standard formula 1/2∑izi2Ci where zi and Ci are the equivalent valence and concentration of ions of type i. Increases in ionic strength were achieved by adding sodium chloride to the buffered solution.

Figure 4 for comparison with the neutral gels. The permeability of the charged gels was approximately the same as the neutral gels for the given values of φ. Figure 6 is interesting in that there is only a small effect of ionic strength on the permeability. The small increase in k in going from 0.01 to 1.0 M can be explained in two ways. First, electroviscous effects that retard flow are damped by increasing the ionic strength. Second, the effective solvent quality for a charged polymer decreases at higher ionic strength; a decrease in solvent quality can result in an increase in the permeability of entangled polymer chains (Mijnlieff and Jaspers, 1971). At higher ionic strengths the charged groups on the PA chains are less repelled so that Brownian fluctuations in local gel volume fraction are greater, leading to a higher permeability. Figure 6 shows that the charged gels in the pores were stable with respect to large osmotic stresses. We found that bulk samples of these gels collapsed to less than 20% of their total volume (φ increased by a factor of 5 or more) when the ionic strength was increased from 0.01 to 1.0 M. It appears that confining the gel in a

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porous matrix minimized such osmotic swelling/deswelling. Furthermore, the recovery of the same value of k when the ionic strength was first increased from 0.01 to 1.0 M and then reduced to 0.01 M (Figure 6a) demonstrates the stability of this system. Discussion Hydrodynamic Theories of Permeability. Because polymeric gels have a chain-like structure, they are often modeled as a network of straight cylinders of radius af. The Darcy permeability is expressed in general as a function of the volume fraction of chains (φ):

k ) af2f(φ)

(11)

where f(φ) depends on the spatial arrangement of the chains. Several models are based on a regular periodic array of cylinders. Sangani and Acrivos (1982) considered a regular square array of cylinders with flow oriented perpendicular to the axes of the cylinders at an angle of 45° with respect to the alignment of the array. They numerically solved the Stokes equations for this alignment and computed the drag on each cylinder. Tsay and Weinbaum (1991) converted the drag per cylinder to a Darcy permeability and obtained the following empirical expression from the calculations of Sangani and Acrivos:

[x ]

f(φ) ) 0.0572

π -2 φ

2.377

(12a)

Drummond and Tahir (1984) also solved the Stokes equations for flow past regular arrays of parallel cylinders. Their results are represented by the following equation:

f(φ) )

1 [-ln φ - 1.476 + 2φ - 1.774φ2 + 4.076φ3] 8φ (12b)

The difference between the above two expressions is 6% or less for 0.01 < φ < 0.15. Durlofsky and Brady (1987) and Phillips et al. (1989,1990) numerically solved the Stokes equations for flow through networks of chains of spheres (af ) sphere radius) arranged in periodic configurations. Their calculated permeabilities are comparable to those predicted from eq 12. Jackson and James (1986) reviewed experimental data for flow through fibrous media over a large variation of af and found that the following expression, which is semi-empirical in nature, fits much of the data:

f(φ) ) -

3 [ln(φ) + 0.931] 20φ

(13)

Spielman and Goren (1968) modeled a network of straight cylinders by considering it a Brinkman fluid. The result for a random orientation of the cylinders is

[

x2 ) 4φ

]

x2 5x K1(x) + 3 6 K0(x)

(14)

where x ) af/xk and Kn is the modified Bessel function of the second kind. Values of k computed from eq 14 are about 25% higher than from eq 13 over the range 0.01 < φ < 0.15. Note that the algebraic form of eq 14 is less convenient than eq 11. A least-squares fit of eq

13 to the data of Tokita (1993) at 2.2% CL (see eq 9a) gives af ) 5.7 Å, which is comparable to the value (6.5 Å) determined from measurements of the partitioning of globular proteins in bulk gels (Tong and Anderson, 1995). Theoretical models for hydrodynamic permeability do not explicitly account for cross-link density. Tokita’s data (see eq 9b) show an increase in k as CL increases. This trend has also been noted by Weiss et al. (1981). The random network models represented by eq 11 would require af to increase as CL increases if it is applied to gels at different cross-link density. A physical interpretation of this increase in af can be constructed by imagining that an increased cross-link density results in “bundling” of the polymer chains, that is, microsegregation of the polymer. Bulk versus Membrane-Supported Gels. Because the pore size (≈0.5 µm) of our membranes was much greater than the hydrodynamic screening length of the gel (xk < 4 nm), the microstructure of the gel should be the same in the pores as in a bulk gel. Figure 4 suggests that there might be a difference between membrane-supported neutral gels and bulk gels at low φ; however, Tokita’s data could be in error at low φ because of some compression of the bulk gel when subjected to pressure. One might speculate that there were defects in the low φ gels synthesized in the porous membranes, which would explain the higher permeabilities. We believe this was not the case. Measurements of diffusion and filtration of proteins through the same gel-filled membranes that were studied here, when taken together with the hydrodynamic permeability data, show conclusively that the gel substantially filled the porous membranes (Kapur, 1995; Kapur et al., 1996). In aggregate, these experimental results prove that the membrane-supported gels were essentially defect free. One possible explanation for the different permeabilities for the bulk and membrane-supported neutral gels at low φ is that the method of synthesis was different. In the membrane-supported neutral gels, the polymerization was photo-initiated whereas the bulk gels studied by Tokita (1993) were chemically initiated. Righetti et al. (1981) have found that gels synthesized with different initiators and promoters can have different properties. Summary The hydrodynamic permeability of the membranesupported gels was reproducible between membranes for a given cross-link density and polymer volume fraction. Compression of the gel, which would have been indicated by a lack of proportionality between water flow rate and applied pressure, was negligible up to pressure gradients as great as 300 bar/cm. The membrane-supported charged gels were resistant to osmotic deswelling/swelling, and their permeability varied little when the ionic strength was changed from 0.01 to 1.0 M. The permeabilities of the positive (Q) and negative (S) gels were the same as for the neutral gels at the same polymer volume fraction. The important result is that our experiments demonstrate that stable, essentially defect-free and noncompressible gels can be fabricated within microporous supports. Acknowledgment This research was supported by NSF Grant CTS9122573 and by BioSepra, Inc. We greatly appreciate the assistance of Dr. J. Y. Koo of BioSepra, Inc., who

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Received for review January 17, 1996 Revised manuscript received June 18, 1996 Accepted June 22, 1996X IE960015Z

X Abstract published in Advance ACS Abstracts, August 15, 1996.