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Novel Polybenzimidazole (PBI) Nanofiltration Membranes for the Separation of Sulfate and Chromate from High Alkalinity Brine To Facilitate the Chlor-Alkali Process Kai Yu Wang, Tai-Shung Chung,* and Raj Rajagopalan Department of Chemical & Biomolecular Engineering, National UniVersity of Singapore, 4 Engineering DriVe 4, Singapore 117576
The potential of employing nanofiltration for the removal of sulfate from concentrated chlor-alkali brine has been investigated. Polybenzimidazole (PBI) was chosen to fabricate nanofiltration hollow-fiber membranes through the dry-jet wet phase-inversion technique because of its robust mechanical strength and excellent chemical stability. The feed solution was a concentrated brine consisting of 253.3 g L-1 NaCl, 9.7 g L-1 Na2SO4, and 9.5 g L-1 Na2CrO4 with a pH value greater than 12.65. The PBI membranes showed high sulfate rejection (up to 98.4% at pH 13.25 and 25 bar) and low chloride rejection (less than 4.0%), thus simultaneously obtaining an extremely high di-/monovalent anion selectivity. In addition, the sulfate and chromate rejections increased with increasing solution pH and/or operating pressure. The impressive separation performance can be attributed to the unique pore and charge characteristics and superior chemical stability of PBI NF membranes. It was found that the mean effective pore size of PBI membranes is around 0.30 nm in radius, which is close to the sizes of hydrated sulfate and chromate anions but much larger than chloride anion size, which contributes to the high separation of divalent anions through size exclusion under high ionic strengths. Introduction In the chlor-alkali process, the electrolysis of a concentrated brine solution to produce chlorine and caustic soda takes place simultaneously through electrolyzers using ion-exchange membranes. Depending on the nature of the raw materials and the production techniques, the sodium chloride (NaCl) used to prepare the brine for electrolysis generally contains impurities of SO42- and/or CrO42-. As a consequence, sulfate anions, present at low concentrations in the supplementary brine stream, gradually accumulate in the circuit and adversely affect electrolysis, which can cause operating problems as a result of localized precipitation on the membrane. Because sulfate anions have a detrimental and irreversible impact on the life of expensive ion-exchange membranes, sulfate levels must be kept under control.1 A variety of approaches have been proposed for the removal of sulfate, including the induction of chemical precipitation as BaSO4 or CaSO4, ion exchange, crystallization, and purging.2 These methods are capital-intensive and difficult implement effectively in terms of techniques or environmental constraints. The removal of sulfate by means of nanofiltration (NF) has recently emerged as an alternative approach to effectively handle the brine.3 Nanofiltration is a pressure-driven, membrane-based separation technique that has been widely used for the separation of small neutral and charged molecules in aqueous solutions through their active nanoscale pores, with estimated pore sizes of around 0.5-2 nm in diameter.4 Separation mechanisms of nanofiltration involve steric (size-exclusion) effects, electrostatic (Donnan exclusion) partitioning interactions between the membrane and the external solution, and dielectric exclusion.5-8 Nanofiltration has become an effective means of removing heavy metals ions and divalent anions from wastewater.9 The * To whom correspondence should be addressed. E-mail: chencts@ nus.edu.sg. Tel.: (65) 6516-6645. Fax: (65) 6779-1936.
Figure 1. Chemical structure of polybenzimidazole (PBI).
desirable NF membranes for liquid separation must have a robust mechanical strength to withstand high pressures and necessary chemical stability during the operation. This article discusses the fabrication of polybenzimidazole (PBI) NF hollow-fiber membranes with robust mechanical stability to sustain higher transmembrane pressures and necessary chemical resistance to sustain high alkalinity and investigate their ion separation performance under high ionic strength for the removal of sulfate and chromate from concentrated brines. PBIs are a class of heterocyclic polymers that have been commercially developed by the Celanese Corporation in 1983,10,11 whose chemical structure as shown in Figure 1. Moreover, PBI membranes have been fabricated for use in reverse osmosis, desalination, and fuel cells for their excellent chemical and thermal stability.12-15 Within the basic imidazole group of polybenzimidazole molecules, the heterocycle ring has two nitrogen atoms, with the one attached to the hydrogen atom being a hydrogen-bond donor (-NH-) while the nitrogen with the lone pair is more likely a proton acceptor (-N ¨ d).16 This unique characteristic makes it possible for both inter- and intramolecular hydrogen bonding to occur between PBI molecules. As a result, PBI can become self-charged in aqueous environments because the adjacent benzene ring delocalizes the proton of the imidazole group.17 Previous work by our group verified that polybenzimidazole nanofiltration membranes can separate SO42- from Cl- anions in neutral NaCl/Na2SO4 binary salt solution18 and separate chromate CrO42- from high-alkalinity solutions.19 Because the hollow-fiber configuration has the advantage of
10.1021/ie061435j CCC: $37.00 © 2007 American Chemical Society Published on Web 02/08/2007
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007 1573 Table 1. Diffusivities and Stokes Radii of Neutral Solutes and Ions in Aqueous Solutions (at 25 °C) solute/ion
MW (g mol-1)
diffusivity D (10-9 m s-2)
Stokes radius rp (nm)
glycerol glucose saccharose raffinose Na+ ClSO42CrO42-
92 180 342 504 23 35.5 96 116
0.79 0.58 0.44 0.36 1.35 2.06 1.09 1.14
0.26 0.37 0.47 0.58 0.19 0.12 0.23 0.22
Table 2. Spinning Conditions of PBI Nanofiltration Hollow-Fiber Membranes PBI dope solution (wt %) dope flow rate (mL/min) bore fluid composition (wt %) bore fluid flow rate (mL/min) air gap (mm) take-up speed (m/min) external coagulant dope temperature (°C) bore fluid temperature (°C) room humidity dimensions of spinneret (mm)
PBI/DMAc/LiCl (22.6:75.6:1.8) 3.0 DMAc/ethylene glycol (50:50) 1.0 12 45.4 (PBI-A), 35.5 (PBI-B) tap water, 26 ( 1 °C 26 ( 1 26 ( 1 65-70% o.d./i.d. ) 1.3/0.5
self-support and provides a higher ratio of membrane area to module volume,20 fabricating PBI NF hollow-fiber membranes might have greater potential in the removal of SO42- from chloralkali brine with high productivity. Moreover, the relatively low cost of fabricating hollow fibers make such membranes of interest for large-scale industrial applications.
(TOC ASI-5000A, Shimadzu Corporation, Kyoto, Japan). Ion concentrations in aqueous solutions were measured with an ion chromatograph (Metrohm 792 Basic IC, Herisau, Switzerland). The solution pH was measured with a pH meter (Orion PerpHect pH meter 370). The model feed brine solution was supplied by Aker Kvaerner Chemetics, Vancouver, BC, Canada, and had a composition of 253.3 g L-1 NaCl, 9.7 g L-1 Na2SO4, and 9.5 g L-1 Na2CrO4. Nanofiltration Separation Procedure. Nanofiltration experiments were conducted in a laboratory-scale circulating filtration unit, as described elsewhere.22 Each testing module had a filtration area of about 100 cm2. Because the outer surface of the hollow fibers was a selective layer, the feed was pumped into the shell side, with the permeate exiting from the lumen side of hollow fibers. The feed velocity, uf, across the membrane surface was about 1.2 m s-1, which was high enough to minimize the effect of concentration polarization (Re > 8000). The fabricated PBI hollow-fiber membranes were first conditioned at a pressure of 25 bar. Then, each membrane sample was subjected to a pure-water permeation experiment to measure the pure-water permeability, Pw (L m-2 bar-1 h-1). Subsequently, the membrane samples were subjected to solute separation experiments by filtering different solutions that contained neutral solutes or brine samples with different pH values. The mean effective pore size and the pore size distribution can be obtained according to the solute-transport approach.23 The effective solute rejection coefficient, RT (%), was calculated using the equation
( )
RT ) 1 -
Cp × 100 Cf
(1)
Experimental Section Materials. The PBI dope was purchased from Hoechst Celanese Corporation, Chatham, NJ, with the composition of 25.6 wt % PBI, 72.4 wt % DMAc, and 2.0 wt % LiCl. N-Dimethylacetimide (DMAc), ethylene glycol, sodium chloride (NaCl), sodium sulfate (Na2SO4), sodium chromate (Na2CrO4), and sodium hydroxide (NaOH) were obtained from Merck, Darmstadt, Germany. The uncharged neutral solutes glycerol, glucose, saccharose, and raffinose were supplied by Aldrich (Milwaukee, WI). The molecular weights, diffusivities, and Stokes radii of neutral solutes and ions21 are listed in Table 1. All chemicals were used as received. Deionized water (MilliQ, 18.0 MΩ cm) was used for the preparation of solutions. Fabrication of PBI Nanofiltration Hollow-Fiber and FlatSheet Membranes. The polymer dope of PBI/DMAc/LiCl (22.6/75.6/1.8 wt %) was prepared by diluting the supplied PBI solution with DMAc. The hollow-fiber spinning conditions are listed in Table 2, and a detailed procedure is provided elsewhere.18 After being immersed in tap water for 3 days to remove the residual DMAc and LiCl, the fabricated hollowfiber membranes were soaked in a 50 wt % aqueous glycerol solution for 48 h and then air-dried at room temperature. The dried hollow fibers with a length of 20 cm were assembled in a stainless steel tube, and the two ends of the bundle of fibers were sealed with solidified epoxy resin to form a membrane module. The PBI hollow fibers were dried with a freeze-dryer (ModulyoD, Thermo Electron Corporation), fractured in liquid nitrogen, and then subjected to platinum sputtering by a Jeol JFC-1100E ion sputtering device. The cross-sectional morphologies were observed with a field-emission scanning electronic microscope (FESEM, JEOL JSM-6700). Chemical Analysis. Concentrations of the neutral solute solutions were measured with a total organic carbon analyzer
where Cp and Cf are the solute concentrations in the permeate and feed solutions, respectively. Results and Discussions Morphology Studies of PBI Hollow-Fiber Membranes. Figure 2 illustrates the membrane microstructure, which consists of four types of morphologies, namely, an asymmetric outer selective skin layer, fingerlike macrovoids, a spongelike substructure, and a porous inner skin layer. During PBI hollowfiber spinning, water was applied as the external coagulant to form the nanoporous outer selective layer. The fingerlike macrovoids are very close to the outer layer, indicating that their origin is possibly from capillary convection and waterinduced intrusion during the phase inversion.24,25 The spongelike substructure near the inner skin is due to delayed phase separation induced by the solvent-enriched bore fluid consisting of a DMAc/ethylene glycol mixture. This kind of microstructure can help hollow fibers sustain high transmembrane pressures and subsequently obtain high productivity. Membrane Characterization. The pure-water permeabilities of two PBI hollow fibers were determined to be 0.19 and 0.17 L m-2 bar-1 h-1. In our previous work, we verified that the pure-water permeability increases but the mean pore size decreases with increasing elongational drawing during PBI hollow-fiber spinning.18 As a result, the membrane characteristics can be finely controlled through the spinning process. The newly developed PBI NF membranes have molecular-size pores throughout their selective layer that determine the permeate flux and separation performance, which can be characterized by means of the solute-transport method to obtain the mean effective pore size and pore size distribution. The solute rejection is expressed by a log-normal probability function of solute
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Figure 2. Morphology of asymmetric PBI-A nanofiltration hollow-fiber membrane.
size,26,27 i.e.
RT ) erf(y) )
1 x2π
∫-∞y e-(u2/2) du
with y)
ln rs - ln µs (2) ln σg
where RT is the solute rejection; rs is the solute radius; µs is the geometric mean radius of the solute at RT ) 50%; and σg is the geometric standard deviation about µs, defined as the ratio of the rs values at RT ) 84.13% and RT ) 50%. When the solute rejection of a membrane is plotted against solute radius on the log-normal probability coordinates, a straight line is obtained as
F(RT) ) A + B(ln rs)
(3)
By ignoring the influences of the steric and hydrodynamic interactions between the solute and the pores on the solute rejection, the mean effective pore radius (µp) and the geometric standard deviation (σp) can be assumed to be the same as µs and σg, respectively. Therefore, based on µp and σp, the pore size distribution of an NF membrane can be expressed as the probability density function28
[
]
(ln rp - ln µp)2 dRT(rp) 1 ) exp drp 2(ln σp)2 rp ln σpx2π
(4)
where rp is the effective pore radius of the membrane. The values of µp and σp determine the position and sharpness of the distribution curves, respectively.
Solutions (200 ppm) containing glycerol, glucose, saccharose, or raffinose were used to measure the solute rejection (RT) because the relationship between the Stokes radius, rs, and the molecular weight, MW, of these known neutral solutes can be expressed by the equation29
log rs ) -1.4962 + 0.4657 log MW
(5)
where rs is in nanometers and MW is in grams per mole. From this equation, the radius of a hypothetical solute at a given molecular weight can be obtained. The molecular weight cutoff (MWCO), which is referred to as the molecular weight above which 90% of the solute in the feed solution is retained by the membrane, can be obtained from Figure 3. The relationship between solute rejection and the solute Stokes radius is plotted for both sample membranes on a lognormal probability graph to fit eq 3 at a pressure of 20 bar, as illustrated in Figure 3. Linear relationships are obtained with the reasonable high correlation coefficients (r2 > 0.95). The mean effective pore radii, µp, calculated from the plots are listed in Table 3. The two PBI NF hollow-fiber membranes have mean effective pore radii of 0.30 and 0.33 nm in radius; MWCOs of 188 and 287 g mol-1 were calculated from the fitted straight line and eq 5. The pore size distribution probability density curves of the PBI membranes calculated from eq 4 are also presented in Figure 3. It can be seen that the PBI NF membranes have a narrow pore size distribution, which is essential for their ion separation performance. Effect of Pressure on the Separation of Sulfate from Chloride. These two PBI NF membranes show a high rejection to divalent anions and a low rejection to monovalent anions. In addition, the solute rejection increases with increasing trans-
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much less than that of chloride Cl-, and the ion sizes of SO42and CrO42- anions are much larger than that of Cl-. As a result, Cl- anions can preferentially pass through the PBI membrane, whereas SO42- and CrO42- anions are rejected. With an increase in pressure, the rejections of divalent SO42and CrO42- anions increase, and the rejection of Cl- anions also increases. However, the rejection of Cl- anions remains at a very low level (i.e., less than 4.0% at pH 13.25 and 25 bar), and the rejections of SO42- and CrO42- can rise to 98.4% and 97.2%, respectively, under the same conditions, which makes possible the separation of SO42- and CrO42- from brine with high selectivity. Effect of Pressure on the Permeation Volumetric Flux Decrease. The dependence of the water permeation flux on the operating pressure at different solution pH values is plotted in Figure 5. It can be found that the product rate of the PBI membrane is much less than the pure-water permeability. This can be explained by two factors. First, at high pH, the pore surface property of the PBI membrane can be modified by the attachment of -OH- group on the pore surface based on the amphoteric PBI molecules, as shown in Figure 6. Thus, the membrane pore size decreases and subsequently enhances the rejection of divalent anions. However, the permeation flux also decreases because of the narrowed pores with increasing solution pH values, as shown in Figure 5. Second, because of the high rejection of divalent SO42- and CrO42- anions and the low rejection of monovalent Cl- anion, a significant difference in osmotic pressure is produced between the feed and permeate sides. Thus, the different osmotic pressure balances against the driving force of pressure. This can be expressed by the equation30
Jv ) Pf(∆p - RT∆πfeed)
Figure 3. (a) Effective rejection curves (solute rejection versus Stokes radius) plotted on a log-normal probability coordinate system for PBI membranes (20 bar). (b) Pore size distribution probability density curves. Table 3. Mean Effective Pore Size, Molecular Weight Cutoff, and Pure-Water Permeability of PBI Nanofiltration Hollow-Fiber Membranes PBI hollowfiber membrane
mean pore radius, µp (nm)
molecular weight cutoff, MWCO (g mol-1)
pure-water permeability, Pw (L m-2 bar-1 h-1)
PBI-A PBI-B
0.30 0.33
188 287
0.19 0.17
membrane pressure because the water permeate flux increases relatively faster than the solute permeate flux, as shown in Figure 4. However, at low pressures, the PBI membrane exhibits a negative rejection of Cl- anions, so that Cl- is enriched on the permeate side. This is attributed to the high ionic strength of the solution, which balances against the driving force of transmembrane pressure. As a result, the contribution of the convection flow of ions in the pore can be ignored at low pressures. This can be verified by the dramatically decreased permeation volumetric flux at low pressures, as shown in Figure 5. Therefore, the contribution of ion diffusion through the membrane pores controls the membrane rejection. The diffusivities of sulfate (SO42-) and chromate (CrO42-) anions are
(6)
where Jv is the permeation volumetric flux and Pf, ∆p, RT, and ∆πfeed are the water permeability at the same pH as the brine, the pressure drop across the membrane, the rejection of the salts, and the osmotic pressure of the feed, respectively. Here, Pf is less than pure-water permeability; the quantity RT∆πfeed cannot be ignored when there is high rejection to the concentrated solution, so that Jv decreases accordingly. Effect of Solution pH on Separation of Sulfate from Chloride. The solution pH has a dominant effect on the rejection of ions because pH determines the surface charge characteristics of the PBI membrane and the ionization states of the ions. In aqueous solutions, the divalent CrO42- anion predominates as the major Cr(VI) species for pH > 6.5.31 At high pH (with high alkalinity), the PBI membrane is negatively charged. From Figure 4, the PBI membrane shows much higher rejection to divalent SO42- and CrO42- anions but less rejection to Clanion. In addition, the rejection of CrO42- anions is slightly lower than that of SO42- anion because the hydrated ion size of the CrO42- anion is less than that of the SO42- anion. Although the ionic strength of the concentrated brine feed is very high (i.e., with an osmotic pressure of 115.2 bar), which can swamp the effect of electrostatic exclusion on the rejection of ions, the PBI membrane shows a very high rejection to divalent anions. This might be due to the fact that the pore surface structure can be modified by the attachment of -OHgroups on the pore surface based on the amphoteric property of PBI molecules. Therefore, size exclusion makes the dominant contribution to the rejection of divalent anions. Moreover, modification of the pore surface by the attachment of -OHgroup at high pH further decreases the pore size.
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Figure 4. Ion rejections of two PBI membranes as a function of pressure at different pH values. Feed composition: 253.3 g L-1 NaCl, 9.7 g L-1 Na2SO4, and 9.5 g L-1 Na2CrO4.
Figure 5. Product rate as a function of pressure at different pH values.
Over long-time operation at pH 13.25 and 25 bar, the permeation volumetric flux of the PBI hollow-fiber membrane maintains an almost constant product rate. In addition, the purewater permeability of the PBI membrane recovers close to the original value after the membrane is flushed with pure water. This demonstrates the robust mechanical and chemical stability of PBI membranes under high pressures and high solution alkalinity. As a consequence, PBI NF hollow-fiber membranes can be efficiently employed in the removal of sulfate (SO42-) from chloride (Cl-) at high pH values above 13.0 and high ionic strength.
Figure 6. Effect of solution pH on the pore structure of the PBI NF membrane.
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Conclusions In conclusion, asymmetric PBI nanofiltration hollow-fiber membranes can be fabricated with a mean effective pore size of around 0.30 nm in radius and a narrow pore size distribution. These PBI membranes exhibit high rejection to divalent sulfate (SO42-) and chromate (CrO42-) anions but low rejection to chloride anions (even negative rejection at low pressure) under high ionic strength and high alkalinity. The size exclusion between the hydrated ions and the molecule-size pores in the membrane might be the main rejection mechanism, rather than electrostatic exclusion under high ionic strength. Therefore, as an environmentally beneficial and economically attractive tool, PBI nanofiltration hollow-fiber membranes offer great potential in effectively separating sulfate and chromate from chlor-alkali brine at high pH without sacrificing the chloride concentration. Acknowledgment The authors thank the National University of Singapore (NUS) and A*star for funding this project under Grants R-279000-165-112 and R-398-000-029-305. Thanks are also due to Aker Kvaerner Chemetics, Vancouver, BC, Canada, for its useful suggestions. Nomenclature Cf ) solute concentration in the feed solution (mol L-1) Cp ) solute concentration in the permeate (mol L-1) D∞ ) solute diffusivity in dilute solution (m s-2) Jv ) permeate flux of solvent (L m-2 h-1) MW ) molecular weight (g mol-1) MWCO ) molecular weight cutoff (g mol-1) Pw ) pure-water permeability (L m-2 bar-1 h-1) Pf ) water permeability (L m-2 bar-1 h-1) rs ) solute Stokes radius (nm] rp ) effective pore radius (nm) RT ) effective solute rejection uf ) linear velocity of feed stream across membrane surface (m s-1) ∆P ) transmembrane pressure drop (bar) µp ) mean effective pore radius (nm) µs ) geometric mean radius of solute at RT ) 50% (nm) π ) osmotic pressure (bar) σg ) geometric standard deviation about µs σp ) geometric standard deviation about µp Literature Cited (1) Maycock, K.; Twardowski, Z.; Ulan, J. A new method to remove sodium sulfate from brine. In Modern Chlor-Alkali Technology; Sealy, S., Ed.; Royal Society of Chemistry: Cambridge, U.K., 1998; Vol. 7, p 213. (2) Scha¨fer, A. I.; Fane, A. G.; Waite, T. D. Nanofiltration: Principles and Applications; Elsevier Advanced Technology: New York, 2005. (3) Twardowski, Z. (Chemetics, Vancouver, Canada). Nanofiltration of concentrated aqueous salt solutions. U.S. Patent 5,587,083 and European Patent 0,821,615, 1996. (4) Raman, L. P.; Cheryan, M.; Rajagopalan, N. Consider nanofiltration for membrane separations. Chem. Eng. Prog. 1994, 90 (3), 68. (5) Donnan, F. G. Theory of membrane equilibria and membrane potentials in the presence of non-dialysing electrolytes. A contribution to physical-chemical physiology. J. Membr. Sci. 1995, 100, 45. (6) Yaroshchuk, A. E. Rejection mechanisms of NF membranes. Membr. Technol. 1998, 100, 9. (7) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. The electrostatic and steric-hindrance model for the transport of charged solutes through nanofiltration membranes. J. Membr. Sci. 1997, 135, 19.
(8) Van der Bruggen, B.; Schaep, J.; Wilms, D.; Vandecasteele, C. Influence of molecular size, polarity and charge on the retention of organic molecules by Nanofiltration. J. Membr. Sci. 1999, 156, 29. (9) Hafiane, A.; Lemordant, D.; Dhahbi, M. Removal of hexavalent chromium by nanofiltration. Desalination 2000, 130, 305. (10) Choe, E. W.; Choe, D. D. In Polymeric Materials Encyclopedia; Salamone, J. C., Ed.; CRC Press: Boca Raton, FL, 1996; p 5619. (11) Chung, T. S. Polybenzimidazoles. In Handbook of Thermoplastics; Olabisi, O., Ed.; Marcel Dekker: New York, 1997; p 701. (12) Seno, M.; Hara, S.; Taketani, Y. (Teijin Ltd., Osaka, Japan). Selective permeable membranes for reverse osmosis. Jpn. Kokai Tokkyo Koho JP 50001080, 1975. (13) Model, F. S.; Davis, H. J.; Poist, J. E. PBI membrane for reverse osmosis. In ReVerse Osmosis and Synthetic Membranes: Theory, Technology, Engineering; Sourirajan, S., Ed.; National Research Council Canada: Ottawa, Canada, 1977; Chapter 11. (14) Sawyer, L. C.; Jones, R. S. Observations on the structure of first generation polybenzimidazole reverse osmosis membranes. J. Membr. Sci. 1984, 20, 147. (15) Samms, S. R.; Wasmus, S.; Savinell, R. F. Thermal stability of proton conducting acid doped polybenzimidazole in simulated fuel cell environments. J. Electrochem Soc. 1996, 143, 1225. (16) Kreuer, K. D.; Fuchs, A.; Ise, M.; Spaeth, M.; Maier, J. Imidazole and parazole-based proton conducting polymers and liquids. Electrochim. Acta 1998, 43, 1281. (17) Staiti, P.; Lufrano, F.; Arico`, A. S.; Passalacqua, E.; Antonucci, V. Sulfonated polybenzimidazole membranessPreparation and physicochemical characterization. J. Membr. Sci. 2001, 188, 71. (18) Wang, K. Y.; Chung, T. S. Polybenzimidazole nanofiltration hollow fiber for cephalexin separation. AIChE J. 2006, 52 (4), 1363. (19) Wang, K. Y.; Chung, T. S. Fabrication of polybenzimidazole (PBI) nanofiltration hollow fiber membranes for removal of chromate. J. Membr. Sci. 2006, 281, 307. (20) Strathmann, H. Membrane separation processes: Current relevance and future opportunities. AIChE J. 2001, 47 (5), 1077. (21) Bowen, W. R.; Mohammed, A. W.; Hilal, N. Characterization of nanofiltration membranes for predictive purposessUse of salts, uncharged solutes and atomic force microscopy, J. Membr. Sci. 1997, 126, 91. (22) Wang, K. Y.; Chung, T. S. The characterization of flat composite nanofiltration membranes and their applications in the separation of cephalexin. J. Membr. Sci. 2005, 247, 37. (23) Singh, S.; Khulbe, K.; Matsuura, T.; Ramamurthy, P. Membrane characterization by solute transport and atomic force microscopy. J. Membr. Sci. 1998, 142, 111. (24) Levich, V. G.; Krylov, V. S. Surface tension driven phenomena. Annu. ReV. Fluid Mech. 1969, 1, 293. (25) Chung, T. S.; Hu, X. D. Effect of air-gap distance on the morphology and thermal properties of polyethersulfone hollow fibers. J. Appl. Polym. Sci. 1997, 66, 1067. (26) Michaels, A. S. Analysis and prediction of sieving curves for ultrafiltration membranes: A universal correlation. Sep. Sci. Technol. 1980, 15, 1305. (27) Van der Bruggen, B.; Shaep, J.; Wilms, D.; Vandecasteele, C. A comparison of models to describe the maximal retention of organic molecules in nanofiltration. Sep. Sci. Technol. 2000, 35 (2), 169. (28) Aimar, P.; Meireles, M.; Sanchez, V. A contribution to the translation of retention curves into pore size distribution for sieving membranes. J. Membr. Sci. 1990, 54, 321. (29) Bowen, W. R.; Mohammad, A. W. Characterization and prediction of nanofiltration membrane performancesA general assessment. Trans. Inst. Chem. Eng. A 1998, 76, 885. (30) Zhou, W. W.; Song, L. Experimental study of water and salt fluxes through reverse osmosis membranes. EnViron. Sci. Technol. 2005, 39, 3382. (31) Tandon, R. K.; Crisp, P. T.; Ellis, J.; Baker, R. S. Effect of pH on chromium(VI) species in solution. Talanta 1984, 31, 227.
ReceiVed for reView November 8, 2006 ReVised manuscript receiVed December 28, 2006 Accepted January 4, 2007 IE061435J
