Controlled Permeability and Ion Exclusion in Microporous Membranes

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Controlled Permeability and Ion Exclusion in Microporous Membranes Functionalized with Poly(L-glutamic acid) Aaron M. Hollman and D. Bhattacharyya* Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky 40506-0046 Received February 25, 2002. In Final Form: May 23, 2002 The functionalization of materials with polyamino acids provides opportunities where electrostatic and conformational properties can be utilized for selective separations and controlled transport applications. The influence of covalently attached poly(L-glutamic acid) (PLGA) on the performance characteristics of a microporous cellulosic support has been investigated to determine its effect on the transport of water and charged solutes. The presence of these charged multifunctional groups promotes electrostatic interactions with ionic species far removed from the pore surface. This allows for nonsteric ion exclusion involving membrane materials that offer less resistance to solvent (water) transport. In addition, the helix-coil transitions of this polypeptide and “core leakage” effects have been shown to affect both the permeability and solute retention in a reversible fashion upon variations in the solution pH. Following PLGA attachment, the permeability could be adjusted from 50 to 90% of the value of the base support matrix (∼3-6 × 10-4 cm3/cm2 s bar). Experiments were performed on single and mixed electrolyte systems using model inorganic and organic solutes. Solute rejection values as high as 73% were reported for dilute Na2SO4 solutions using membranes with pore sizes ranging from 0.05 to 0.21 µm.

1. Introduction

2. Background and Related Work

The development of functionalized materials with tunable properties resulting from charge and macromolecular conformational changes provides an exciting approach for applications ranging from separations to controlled transport. The separation of ionic solutes by conventional nanofiltration (NF) relies primarily on electrostatic interactions and steric hindrance effects. Charge exclusion is enabled due to the presence of acidic or basic functional groups incorporated within the relatively dense polymer matrix (pore size < 2 nm) associated with NF. The effectiveness of these monomeric functionalities in inhibiting ionic transport is significantly reduced at much larger pore sizes. The separation principles of nanofiltration can be extended to membranes with microporous structures through functionalization involving charged polypeptides. Furthermore, the immobilization of these macromolecules can allow for the controlled transport of both neutral and charged molecules. This reversible process is the result of changes in the secondary structure of the attached polyamino acid brought about by slight variations in its surrounding chemical environment. In our previous studies, the interaction between metals and these macromolecules was investigated to establish their potential as high-capacity sorbent materials.1,2 The versatility of this particular type of functionalization technique also allows for the development of highly permeable (low pressure) ion selective membranes. The overall objective of this study is to establish the role of helix-coil transitions, electrostatic interactions, and convective transport of both water and ionic solutes in microporous supports (cellulosic nanofibers) functionalized with poly(L-glutamic acid) (PLGA).

The modification of polymeric materials by surface grafting and other functionalization techniques has allowed for the development of membrane platforms with tailor-made properties.1-13 The ability to manipulate the properties of a membrane such as its water permeability, selectivity, or surface hydrophobicity could certainly be useful in the development of controlled-release systems.4-7,9,10 This tunability is enabled through the attachment of molecules that are sensitive to easily controlled environmental parameters such as pH,4-8 temperature,9-11 and ionic strength.12,13 For instance, polypeptides, such as PLGA, have been shown to undergo a conformational transition from a random coil to a compact helix based on changes in the properties of its contacting solution.4,14-16 The morphology and charge density of this macromolecule are highly dependent on the degree of protonation of the functional groups present along its backbone.2,15 Upon immobilization, this response can be utilized to tune the separation properties of membrane materials.

* Corresponding author. D. Bhattacharyya, Alumni Professor. Phone: 859-257-2794. Fax: 859-323-1929. E-mail: [email protected]. (1) Bhattacharyya, D.; Hestekin, J. A.; Brushaber, P.; Cullen, L.; Bachas, L. G.; Sikdar, S. K. J. Membr. Sci. 1998, 141, 121. (2) Ritchie, S. M. C.; Bachas, L. G.; Olin, T.; Sikdar, S. K.; Bhattacharyya, D. Langmuir 1999, 15, 6346.

(3) Belfer, S.; Fainchtain, R.; Purinson, Y.; Kedem, O. J. Membr. Sci. 2000, 172, 113. (4) Ito, Y.; Park, Y. S.; Imanishi, Y. Langmuir 2000, 16, 5376. (5) Mika, A. M.; Childs, R. F.; Dickson, J. M. J. Membr. Sci. 2001, 191, 225. (6) Childs, R. F.; Mika, A. M.; Pandey, A. K.; McCrory, C.; Mouton, S.; Dickson, J. M. Sep. Purif. Technol. 2001, 22-23, 507. (7) Lee, S. B.; Martin, C. R. Anal. Chem. 2001, 73, 768. (8) Turner, J. S.; Cheng, Y. J. Membr. Sci. 1998, 148, 207. (9) Choi, Y.; Yamuguchi, T.; Nakao, S. Ind. Eng. Chem. Res. 2000, 39, 2491. (10) Yamaguchi, T.; Ito, T.; Sato, T.; Shinbo, T.; Nakao, S. J. Am. Chem. Soc. 1999, 121, 4078. (11) Iwata, H.; Odeate, M.; Uyama, Y.; Memiya, H.; Ikada, Y. J. Membr. Sci. 1991, 55, 119. (12) Ito, Y.; Ochiai, Y.; Park, Y. S.; Imanishi, Y. J. Am. Chem. Soc. 1997, 119, 1619. (13) Kontturi, K.; Mafe, S.; Manzanares, J. A.; Svarfvar, B. L.; Viinikka, P. Macromolecules 1996, 29, 5740. (14) Zhang, W.; Nilsson, S. Macromolecules 1993, 26, 2866. (15) Nilsson, S.; Zhang, W. Macromolecules 1990, 23, 5234. (16) Huh, Y.; Inamura, T.; Satoh, M.; Komiyama, J. Polymer 1992, 33, 3262.

10.1021/la025662b CCC: $22.00 © 2002 American Chemical Society Published on Web 06/26/2002

Membranes Functionalized with Poly(L-glutamic acid)

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A different approach to linear biomolecule attachment has been the use of stimuli-responsive hydrogels, such as cross-linked poly(4-vinylpyridine),5,6 poly(acrylic acid),6,13 and poly(N-isopropylacrylamide).9,10 Anderson et al. demonstrated that the integrity of cross-linked polymer gels could be stabilized against mechanical forces through immobilization in microporous supports.17 Mika and Childs displayed NF-type performance and pH-sensitive gating using charged gels anchored within porous hydrophobic supports prepared via in situ polymerization.5,6 They attributed changes in permeability and selectivity to reversible microphase separation in the pore-immobilized gel.5 Although cross-linking provides mechanical stability, it also severely restricts chain mobility and thus limits possible gains in membrane permeability over conventional NF. On the other hand, our approach deals with single-point covalent attachment of a polypeptide in a highly hydrophilic, cellulosic domain. A comprehensive comparison between polyamino acid functionalization and cross-linked gel filled membranes is given in the Supporting Information. The transport of electrolytes in charged media has been a well-discussed topic in the literature.18-32 Models based on the extended Nernst-Planck (N-P) equation have gained wide acceptance because they encompass all three modes of electrolyte transport, namely, diffusion, convection, and electromigration. The ionic flux, Jx,i, in the direction of flow (x) for dilute solutions is described by

Jx,i ) -Di

DiziCiF ∂Φ ∂Ci + vmCi ∂x RT ∂x

(1)

where Di is the diffusivity of ion i, vm is the solution velocity across the membrane, zi is the ion valency, R is the gas constant, Ci is the ion concentration, F is the Faraday constant, and Φ is the total electrostatic potential within the membrane pore. In the current study, Φ is dependent on the degree of attachment, the packing density, and the degree of ionization of the attached polypeptide (PLGA). 3. Experimental Methods 3.1. Materials. The microporous supports used in this study were made from pure bacterial cellulose fibers with a high aspect ratio (fiber diameter ∼ 30 nm by scanning electron microscopy). Amine-terminated poly(L-glutamic acid) (Na form) was obtained from Sigma. Two molecular weight types of PLGA were used: 17 500 (lot 128H5903) and 36 400 (lot 79H5918) as determined by light scattering. Monomeric L-glutamic acid and poly(Larginine) (MW ∼ 52,000 LALLS, lot 11K5100) were also obtained from Sigma. All metal salts used in this study (Na2SO4, NaCl, (17) Kapur, V.; Charkoudian, J. C.; Kessler, S. B.; Anderson, J. L. 1996, 35, 3179. (18) Kedem, O.; Katchalsky, A. Trans. Faraday Soc. 1963, 59, 1918. (19) Spiegler, K. S.; Kedem, O. Desalination 1966, 1, 311. (20) Hoffer, E.; Kedem, O. Desalination 1967, 2, 25. (21) Transport Phenomena in Membranes; Lakshminarayanaiah, N., Ed.; Academic Press: New York, 1969. (22) Gilron, J.; Gara, N.; Kedem, O. J. Membr. Sci. 2001, 185, 223. (23) Dresner, L. Desalination 1972, 10, 27. (24) Tsuru, T.; Nakao, S.; Kimura, S. J. Chem. Eng. Jpn. 1991, 24, 511. (25) Wang, X.; Tsuru, T.; Nakao, S.; Kimura, S. J. Membr. Sci. 1995, 103, 117. (26) Bowen, W. R.; Mukhtar, H. J. Membr. Sci. 1996, 112, 263. (27) Wang, X.; Tsuru, T.; Nakao, S.; Kimura, S. J. Membr. Sci. 1997, 135, 19. (28) Garba, Y.; Taha, S.; Gondrexon, N.; Dorange, G. J. Membr. Sci. 1999, 160, 187. (29) Afonso, M.; de Pinho, M. Ind. Eng. Chem. Res. 1998, 37, 4118. (30) Afonso, M.; de Pinho, M. J. Membr. Sci. 2000, 179, 137. (31) Schaep, J.; Vandecasteele, C.; Mohammed, A.; Bowen, W. R. Sep. Purif. Technol. 2001, 22-23, 169. (32) Soltanieh, M.; Mousavi, M. J. Membr. Sci. 1999, 154, 53.

Figure 1. Scanning electron micrographs of the (a) cross section and (b) surface of the bacterial cellulose support matrixes used in this study. Cd(NO3)2) unless otherwise mentioned were reagent grade and supplied by Fischer Scientific. Sodium oxalate (ACS) was obtained from Alfa Aesar. Dextran (lot 111K1647) with an average molecular weight of 482 000, used for membrane characterization, was obtained from Sigma. Aldehyde quantification was determined using p-aminobenzoic acid (PABA) obtained from Acros Organics. 3.2. Membrane Support Preparation. Synthesis of the functionalized bacterial cellulose membranes used in this study consisted of two steps, aldehyde derivatization followed by polyamino acid attachment. The formation of aldehyde groups within the support material began by dispersing approximately 10 g of bacterial cellulose in water. Oxidation of the cellulosic slurry was then performed at room temperature by allowing a 2-4% ozone/oxygen mixture to bubble through the dispersed phase for approximately 1 h using a Welsbach T-816 laboratory ozonator. A detailed description of the effects of oxidation on this type of cellulosic membrane is given in previous work.33 After oxidation, the fibers were dried by vacuum filtration. The filter cake was then redispersed in isopropyl alcohol and placed into an evaporating dish where it was allowed to dry for approximately 2 days. The thickness of the resulting microporous supports ranged from 127 to 270 µm. A scanning electron microscope (SEM) image of the cross section of the support material, shown in Figure 1a, reveals the lamellar structure characteristic of this type of evaporative fabrication technique. The approximate pore size for these membranes was estimated, using SEM images of the surface as shown in Figure 1b, to range from 0.05 to 0.21 µm. The void space between adjacent cellulosic fibers constitutes the membrane pore and the subsequent path for convective flow. The internal surface area (using N2 at 77 K) of these materials was 120 m2/g as determined in previous studies using a Micromeritics ASAP 2000 Brunauer-Emmett-Teller (BET) surface area analyzer.33 The degree of aldehyde functionality imparted to the cellulosic support was determined by analysis with PABA. This compound contains an amine that reacts with the aldehyde groups present within the membrane and gives a reliable estimation of the groups accessible for polyamino acid attachment. Standard PABA analysis consists of permeating a 80 mg/L solution at pH > 8 in 5 × 10-2 M phosphate buffer at a rate of 0.5 mL/min for approximately 80 min. The feed and permeate solutions were analyzed by UV spectroscopy at a wavelength of 264 nm. Aldehyde contents ranged from (0.18 to 3.68) × 10-22 mmol/nm2 (based on the internal surface area of the support matrix). 3.3. PLGA Functionalization. Polyamino acid attachment was performed by permeating aqueous PLGA solutions through the support matrix at pH levels of 9.2-9.8. The concentration of the feed solutions ranged from (5.8 to 69.2) × 10-4 mM dependent on the aldehyde content of the cellulosic support. Functionalization involves the reaction of the terminal amine group present on PLGA with the aldehyde groups present in the support. The result of this Schiff base reaction is the single-point attachment of PLGA macromolecules to the support matrix. The (33) Hestekin, J.; Bachas, L. G.; Bhattacharyya, D. Ind. Eng. Chem. Res. 2001, 40, 2668.

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imine bond produced in this reaction was subsequently reduced with sodium borohydride treatment to enhance acid resistance. This treatment consists of permeating a 50-100 mL solution of 2 mg/mL sodium borohydride in phosphate buffer at pH 8 for approximately 1 h. Following this step, the membrane was rinsed by permeating 250 mL of distilled water at near neutral conditions. Cadmium adsorption studies were performed on each functionalized membrane to estimate the degree of PLGA attachment. Standard procedure consists of permeating 300 mL of a 0.27 mM Cd solution at pH 6. Breakthrough curves were established by measuring the cadmium concentration in the permeate as a function of time. These concentrations were measured using a Varian SpectAA 220FS atomic absorption spectrometer. Three readings were taken for each sample with standard deviations less than 2.2% for all reported concentrations. It was assumed that each mole of Cd2+ adsorbed by the membrane occupied 2 mol of carboxylic acid groups present on the attached macromolecules. By further assuming a uniform polymer distribution and that all available carboxylic acid groups were complexed with cadmium, a maximum fixed charge associated with the membrane was estimated. 3.4. Analysis of Membrane Performance Characteristics. Characterization of these membranes began with the determination of the hydraulic permeability. These values prior to functionalization ranged from (2.91 to 5.70) × 10-4 cm3/cm2 s bar. Following PLGA attachment, permeation studies were then performed using distilled water at various pH levels. Some comparison experiments were also conducted with commercial (Osmonics, Inc.), negatively charged nanofiltration membranes (designated as YK-NF). The NF membranes are thin-film (skin thickness < 1 µm) composite membranes, whereas our PLGAfunctionalized membranes are about 200 times thicker. Solute rejection studies involving aqueous systems were investigated using a SEPA ST membrane cell provided by Osmonics. Rejection is defined as 1 - (Cpermeate/Cfeed), where C refers to solute concentration. This apparatus has a membrane cross-sectional area of 13.2 cm2 and is equipped with a magnetic stirring device placed in intimate contact with the feed solutionmembrane interface to minimize concentration polarization. Dilute solutions of NaCl, Na2SO4, and Na2C2O4 were used to determine the salt separation capabilities of the functionalized membranes. For single inorganic salt systems, sodium concentrations in the feed and permeate were determined by atomic absorption measurements. This was used to calculate solute rejection. Once again, three readings were taken for each sample with standard deviations less than 2.2%. The concentration of the organic compounds, sodium oxalate and dextran, in the feed and permeate streams was determined using a TOC 5000A total organic carbon analyzer. Experimental error for TOC analysis in the range of 10-40 mg of carbon per liter was less than 5%. In mixed NaCl/Na2SO4 electrolyte systems, total Na+ concentrations, [Na+], were determined using atomic absorption. Chloride concentrations, [Cl-], were then measured using an Orion model 96-17B chloride selective electrode. From a simple charge balance,

[Na+] ) [Cl-] + 2[SO42-]

(2)

the concentration of sulfate ions, [SO42-], was determined allowing for calculation of the rejection associated with each solute type.

4. Results and Discussion The attachment of high molecular weight (17 500 and 36 400) poly(L-glutamic acid) within the structure of a microporous cellulosic support allows for the controlled transport of both water and charged solutes in dilute systems. This level of tunability regarding water permeation and ion exclusion is brought about due to the conformational transitions of the attached polypeptide from a helical to a random-coil formation. PLGA has a repeat unit length of 0.15 nm in the helical form and 0.35 nm in the random-coil form with molecular diameters of

Figure 2. Normalized permeate flux as a function of pH for both PLGA-functionalized bacterial cellulose (∆P ) 2.1 bar) and track-etched polycarbonate membranes.

1.1 and 1.4 nm in the helical and coil forms, respectively.14 The carboxylic acid (γ) side groups present along the polymeric backbone of PLGA have a pKa value of 4.375.15 Unless otherwise noted, all lines appearing in figures represent trends in experimental data. 4.1. Permeation Studies at Varying pH Levels. The effects of PLGA functionalization on the pure water transport through the cellulosic-based membranes used in this study are shown in Figure 2. For purposes of comparison, results reported on a gold-coated polycarbonate microfiltration (MF) (0.2 µm pore diameter) membrane that has been functionalized with PLGA containing a terminal disulfide group are also indicated in Figure 2.34 Flux measurements for both types of membranes were normalized using the permeation rates determined prior to functionalization, Jv0. The flux trend with pH is similar for both functionalization techniques. In the high-pH regime, both membranes displayed a marked decrease in the observed water flux. This significant reduction in flux is a clear indication that PLGA has been successfully attached to the membrane surface. Under these conditions, PLGA exists in a fully extended random-coil formation. The presence of these extended macromolecules within the pore structure hinders water transport resulting in the observed decline in permeability. This can easily be explained by examination of the classical Hagen-Poiseuille equation,

Jv )

φ ∆P 2 r 8µτ ∆x

(3)

where Jv is the water flux, φ is the porosity, µ is the solvent viscosity, τ is the tortuosity, ∆P is the applied pressure gradient, and ∆x is the membrane thickness. By normalizing eq 3 using the flux measurements determined prior to functionalization, Jv0, all terms except for the effective pore radius, r, remain constant. Using this approach, it was estimated that the 51% decrease in Jv/Jv0 shown at high pH conditions was accompanied by a 29.6% decrease in the effective width of the transport corridor (pore radius). The permeability measured at high pH (polypeptide in random coil state) was 2.31 × 10-4 cm3/cm2 s bar. In its ionized form, this would correspond to greater than an order of magnitude increase in permeability over gelfilled MF membranes found in the literature.5 Conversely, at low pH, the pure water flux of both membranes returned (34) Ito, Y. Nanotechnology 1998, 9, 205.

Membranes Functionalized with Poly(L-glutamic acid)

Figure 3. Helix formation of poly(L-glutamic acid) in homogeneous solutions as a function of the ratio between Cd2+ and carboxylic acid side group concentrations (data calculated from ref 35).

to approximately 90% of Jv0. This would correspond to a 5% reduction in the effective pore radius. Therefore, the accurate description of transport in membranes of this type must consider the existence of two distinct solutiondependent regions in the radial direction under all pH conditions. The flux-pressure relationship was linear for our functionalized membranes up to applied pressures of 5 bar. Therefore, flow effects, such as shear-induced deformation of the terminally anchored polymer chains, are minimal. This further substantiates the claim that the adjustable permeability shown (Figure 2) by these supports is due to the helix-coil transitions of the attached biomolecule. The conformational transitions of PLGA can also be induced at pH > 5.5 upon the addition of divalent metal ions, such as Ca2+, Mg2+, or Cd2+. Kurotu et al. monitored this metal ion induced transition using circular dichroism (CD) spectroscopy at 222 nm.35 The effect of a model divalent ion, in this case Cd2+, on the helical content of PLGA is depicted in Figure 3. These results suggest that the secondary structure of PLGA can be adjusted at near neutral conditions. In the absence of divalent metal, PLGA will exist almost exclusively in the random-coil state under these pH conditions. However, complexation with Cd2+ suppresses the ionization of the carboxylate side groups alleviating the intramolecular electrostatic repulsive force. Therefore, as the ratio between Cd2+ and the number of side groups increases, the helical content of the overall macromolecule increases as is shown in Figure 3. This observed phenomenon would be important to consider when modeling water transport and separation behavior involving mixed electrolyte solutions containing divalent cations. 4.2. Solute Rejection Studies. To establish the tunable separation behavior of these PLGA-functionalized cellulosic membranes, a number of solute rejection studies were performed using aqueous solutions containing Na2SO4, NaCl, and sodium oxalate (Na2C2O4). For the dilute concentration range (0-2 mM) studied, the effects of osmotic pressure are negligible. 4.2.1. pH Effects. To illustrate reversible ion exclusion, three separate solute rejection experiments were performed in sequence on a PLGA-functionalized membrane using dilute (0.2 mM) sodium sulfate solutions. The cellulosic support used in this particular set of experiments had an average pore size of approximately 210 nm and (35) Kurotu, T. Inorg. Chim. Acta 1991, 191, 141.

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was functionalized with 36 400 molecular weight PLGA. The first experiment was conducted at pH 6, ensuring the dissociation of the immobilized polypeptide. For this initial run, the average solute rejection determined was greater than 60%. In adjusting the pH of the feed solution to 4, the observed rejection decreased to approximately 20%. This indicates a dramatic decline in the electric potential established by the attached macromolecule. Under these conditions, a high degree of protonation reduces the overall charge of the polypeptide and thus limits electrostatic interaction between the membrane and the permeating co-ions. However in readjusting the feed solution back to pH 6 (run 3), the mechanism of electrostatic exclusion is regained. The percent difference in the solute rejection for the two runs at pH 6 was only 0.41%. Preliminary experiments with cellulosic membranes functionalized with positively charged poly(L-arginine) (MW ∼ 52 000) show no dependence of solute rejection (with 0.2 mM CaCl2 solutions) on pH. The guanadino side group of this residue has a pKa of 12.5. Thus, poly(L-arginine) does not experience a conformational transition under normal solution conditions. This clearly indicates that the stimuliresponsive nature of these PLGA-functionalized membranes is derived from the helix-coil transitions of the attached biomolecule. The separation of ionic solutes with a microporous membrane (0.21 µm) is a significant achievement when considering that the hydrated radius of the sulfate ion is 0.379 nm.36 Similar experiments conducted with neutral dextran (482 000 MW) with a diameter greater than 36 nm showed limited solute rejection (∼16%).37 For this reason, these types of membranes should not be viewed as a physical barrier to solute transport. The separation of sodium sulfate is based entirely on electrostatic interaction between the solute and the membrane. To further illustrate this point, rejection studies were performed under identical conditions using a cellulosic support functionalized with monomeric glutamic acid. The results of these studies showed no rejection of Na2SO4 even under high-pH conditions. Therefore, the observed rejections determined using high molecular weight PLGA can be attributed solely to the extension of the membrane charge into the pore structure. Commercial nanofiltration membranes report asymptotic Na2SO4 rejections anywhere from 95 to 99% for dilute solutions.30 However, NF membranes have pore sizes of about 1-2 nm and typically operate at pressures ranging from 10 to 40 bar. This specific set of experiments involved an applied pressure of 2.1 bar. Ion rejection studies were also performed on organic anions. The effects of pH on the transport of oxalic acid in a PLGA-functionalized membrane are shown in Figure 4. At pH levels above 5.5, there was no apparent change in the observed rejection. This result coincides directly with helix-coil transition theory given in the literature for poly(L-glutamic acid) in aqueous solutions.14,15 PLGA attains its maximum level of dissociation at pH levels around 5.5. Therefore, above this value, the electric potential established by the attached molecule is unchanged and the maximum solute rejection is obtained. For this particular membrane, the maximum rejection determined for sodium sulfate at approximately the same molar concentration and permeate flux was 63.5% (∼16% higher than oxalic acid). In comparing the net charge field around SO42- and dissociated oxalic acid ((COO-)2), one would expect lower rejection of the organic anion because (36) Nightingale, E. J. Am. Chem. Soc. 1959, 73, 1381. (37) Hagel, L. J. Chrom. Library 1988, 40, 119.

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Figure 4. Solute rejection of 0.3 mM sodium oxalate solutions using a PLGA (MW ∼ 17 500; 116 repeat units) functionalized membrane at various levels of pH (∆P ) 3 bar).

Figure 5. Dependence of the solute rejection on the feed concentration of Na2SO4 solutions at pH 6 using a PLGA (MW ∼ 17 500; 116 repeat units) functionalized cellulosic membrane (∆P ) 3 bar).

of its dispersed overall charge. At pH conditions approaching 5, a significant decline in the solute rejection of oxalic acid was observed. This descent is due to the combination of two effects: protonation of the attached polypeptides and oxalic acid ionization (the second pKa of oxalic acid is 4.21). 4.2.2. Effects of Feed Concentration and Anion Valence. The effect of feed concentration on the solute retention of these PLGA-functionalized membranes is shown in Figure 5. The apparent decrease in the solute rejection at higher electrolyte concentrations is brought about due to the saturation or shielding effect of cations on the fixed membrane charge. At higher feed concentrations, this shielding effect is enhanced resulting in a subsequent decrease of the membrane repulsion forces on the co-ions in solution. Higher attachment efficiencies are required to enhance the overall fixed charge associated with the membrane. This would result in the stabilization of its performance over broad concentration ranges. The effect of permeate flux on the rejection ratio of sulfate to chloride, RSO4/RCl,

rejection ratio )

RSO4 RCl

)

Cf,Cl(Cf,SO4 - Cp,SO4) Cf,SO4(Cf,Cl - Cp,Cl)

(4)

(where f and p denote feed and permeate, respectively) for an equimolar (0.25:0.25 mM) mixed electrolyte system is

Figure 6. The effects of permeate flux on the rejection ratio (RSO4/RCl) for equimolar NaCl/Na2SO4 (0.25:0.25 mM) mixed electrolyte systems at pH 6 using a PLGA (MW ∼ 17 500; 116 repeat residues) functionalized cellulosic support (maximum RSO4 ) 51.4%, maximum RCl ) 14.7%).

displayed in Figure 6. The observed selectivity is typical of negatively charged membranes and corresponds well with established ion exclusion principles. The charge density associated with sulfate ions is much greater than that of chloride. Therefore, with similar cation charge densities, sulfate ions will always be rejected much more efficiently than chloride due to the magnitude of their electrostatic interaction with the membrane. The prominent decrease in the rejection ratio with permeate flux is a unique characteristic of this type of functionalized membrane. It is the direct result of enhanced solute leakage in the core region of the membrane pore structure. The effects of core leakage will be addressed in great detail in the following paragraphs. 4.2.3. PLGA Attachment Efficiency Effects. Solutemembrane electrostatic interactions are strong functions of polyamino acid loading (fixed membrane charge) and solution pH (helix-coil transition). The fixed membrane charge was calculated from results of cadmium sorption studies. These values ranged from (0.497 to 1.235) × 10-3 mmol COO-/m2 (∼0.003-0.006 PLGA chains/nm2) based on the internal surface area of the membrane support. This would correspond to an approximate mass gain of 1-2%. In contrast, polyelectrolyte gel filled membranes report average mass gains around 190%.5 This alternative architecture shows greater ion exclusion with considerable loss in permeability.5 The low degree of attachment associated with PLGA functionalization can be attributed to a number of factors. It was determined that no more than 4.2% of the total available aldehyde groups reacted with PLGA when using an average molecular weight of 36 400. This number increased to 13.6% using PLGA having a molecular weight average of 17 500. This reveals the importance of chain length on this type of functionalization technique. Obviously, as the number of repeat units within a given macromolecule is increased, the probability that its terminal group will be accessible to reaction is reduced significantly due to steric effects. Another critical factor is that functionalization occurs at pH levels greater than 9.2. This is done to ensure that the terminal amine group is not protonated and therefore will react with aldehyde functionalities. One significant drawback is that under these conditions the polypeptide itself is highly charged. Therefore, the attachment of one PLGA macromolecule within a given region may prevent the attachment of another due to intermolecular electrostatic repulsive forces. The effective charge of a PLGA macro-

Membranes Functionalized with Poly(L-glutamic acid)

Figure 7. Effect of permeate flux on the rejection of 0.2 mM Na2SO4 solutions (pH 6) determined for both a microporous PLGA (MW ∼ 36 400; 241 repeat units) functionalized membrane and for a typical negatively charged, dense NF membrane. Inset: Schematic illustrating a model cylindrical pore functionalized with PLGA.

molecule increases with molecular weight, therefore enhancing this effect at higher degrees of polymerization. 4.2.4. Core Leakage Effects. Even with sparse PLGA loading, these membranes were able to reject various charged species primarily by electrostatic interactions. The dependence of rejection on permeate flux for dilute Na2SO4 solutions at pH 6 is shown in Figure 7. The permeate flux (shown on the x-axis) was varied by changing the transmembrane pressure (1.5-2.7 bar). This behavior contrasts that typically observed for conventional NF processes. To quantitatively establish the performance of these PLGA-functionalized membranes with regard to Na2SO4 rejection, a number of experiments were performed on a commercially available NF membrane at similar permeate flux. Results of these experiments are also given in Figure 7. The model NF membrane used in this study was the YK-NF membrane provided by Osmonics. This thin composite polyamide-based membrane has a hydraulic permeability of approximately 2.4 × 10-4 cm3/cm2 s bar and an asymptotic rejection of Na2SO4 greater than 99%. The observed decrease in solute rejection with decreasing permeation rate for this particular NF membrane follows from the fact that diffusion becomes much more prevalent at lower solution velocities (see eq 1). However, due to its relatively narrow pore size, the electric potential established by its surface functional groups is maintained across the entire pore cross section. Therefore, at high transmembrane pressures where convective transport (second term on the right-hand side of eq 1) is dominant, the rejection of charged species is maintained due to electrostatic hindrance effects. The enhanced water flux coupled with sustained exclusion of charged species results in an increase in the observed rejection at higher applied pressures as is depicted in Figure 7. In contrast, membranes functionalized with PLGA display these characteristics only over a certain portion of the pore cross section. For example, a standard membrane used in this study would have a pore diameter of about 210 nm. At pH conditions greater than 5.5, PLGA with an average molecular weight of 36 400 (241 repeat units, 0.35 nm per unit) that is 90% extended has an approximate length of 75.9 nm. Thus, for a perfectly cylindrical pore with PLGA uniformly attached along its perimeter, 7.7% of the cross section is devoid of the charged macromolecules. A schematic of this cylindrical pore

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Figure 8. Dependence of the overall solute rejection on the ratio between the polyamino acid chain length to the average pore radius for dilute Na2SO4 solutions (0.2 mM, pH ) 6) with a permeate flux of 2.5 × 10-4 cm3/cm2 s.

representation is given in the inset of Figure 7. In this core or inner region, charge interactions can be assumed negligible and thus the established electric potential has no effect on ionic transport. Therefore, the solution composition in this region will be similar to that of the feed solution. At higher operating pressures, the overall flux through the core region (eq 3) will increase, resulting in the observed decrease in the solute rejection. The flux ratio through the core region, fc, can be calculated using laminar flow conditions in the cylindrical membrane pore by solving the following equation:

∫0r vx(r)r dr fc ) r ∫0 vx(r)r dr c

p

(5)

where vx(r) is the parabolic velocity profile, rp is the pore radius, and rc is the distance in the radial direction encompassing the core region (rp - chain length of the attached polypeptide). An estimation of the significance of the core region on the performance of these membranes can be determined through simple calculations to establish the local solute rejection in the region containing the charged macromolecules. A membrane with pore dimensions of 210 nm was used in the experiments shown in Figure 7. At pH conditions around 6, a maximum solute rejection of 62.5% was observed for dilute Na2SO4 solutions. However, if the flow rate of pure feed solution through the core region was taken into account, solute rejection values as high as 73.3% were calculated for the outer region. This value is calculated from a material balance on both regions of the pore cross section. The permeate solute concentration in the outer region, C*,

C* )

Cpermeate - fcCfeed 1 - fc

(6)

where fc can be calculated from eq 5 (with rp ) 210/2 nm and rc ) rp - PLGA chain length of 75.9 nm), is used to calculate the local average solute rejection for the outer region. To further quantify the effects of solute leakage in the core region, similar calculations were performed on membranes functionalized with PLGA of varying lengths. As shown in Figure 8, the observed solute rejection was highly dependent on the ratio of the polyamino acid chain

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Langmuir, Vol. 18, No. 15, 2002

length to the average pore radius. These studies were performed using dilute Na2SO4 solutions under high-pH conditions (>6) with a permeate flux of 2.5 × 10-4 cm3/ cm2 s. The maintenance of constant flux required the adjustment of ∆P as the ratio between chain length to pore radius increased. Using the average solute rejection for the outer region calculated from eqs 5 and 6, the observed overall solute rejection can be predicted for various polymer chain length to pore radius ratios. This figure clearly indicates the importance of limiting the core region on membrane performance. More effective membranes could thus be synthesized by limiting the core region by using polypeptides with a higher degree of polymerization or by slightly reducing the pore diameter. More comprehensive alternatives to the cylindrical pore model proposed in this work must account for pore size distribution and for nonuniform polypeptide attachment. 5. Conclusions Membrane functionalization with polyamino acids, such as PLGA, allows for the simultaneous control of both the hydraulic permeability and ion selectivity of a cellulosic, microporous support. It was shown that separation of very small molecules in dilute solutions can be achieved in an extremely open pore structure. This porous medium offers less resistance to solvent transport, allowing for higher

Hollman and Bhattacharyya

permeation rates at much lower operating pressures. The solute separation due to electrostatic interactions and polypeptide conformational changes was found to depend highly on the type of salt, the feed concentration, and the solution pH. Adequate modeling of ionic transport with this membrane architecture will require a two-dimensional approach to account for radial distributions in the electrostatic potential and solute concentration. The fabrication of much more effective membranes will require much higher polyamino acid loading and the limitation of the core or inner region. Acknowledgment. The authors recognize the NSFIGERT program for the partial support of this research work. Thanks are also due to Dr. Stephen M. C. Ritchie, currently at the University of Alabama, and Noah Scherrer (NSF-REU student) for their help. The authors also acknowledge GlaxoSmithKline for partial support of this work. Supporting Information Available: Comparison of this experimental work with recently published data for microporous membranes containing cross-linked hydrogels. This material is available free of charge via the Internet at http://pubs.acs.org. LA025662B