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Enhanced Water Permeation of Reverse Osmosis through MFI-Type Zeolite Membranes with High Aluminum Contents Liangxiong Li,*,† Ning Liu,† Brian McPherson,†,‡ and Robert Lee† Petroleum RecoVery Research Center, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801, and Department of CiVil and EnVironmental Engineering, UniVersity of Utah, Salt Lake City, Utah 84112
MFI-type zeolite membranes with different Si/Al ratios were synthesized by seeding and secondary growth. Several factors including alkalinity, synthesis time, and Si/Al ratio were varied to optimize the synthesis conditions. Ion separation of 0.10 M NaCl solution by zeolite membranes was investigated through a crossflow reverse osmosis system. The aluminum content was found to play an important role in zeolite growth and reverse osmosis separation performance afterward. Membrane hydrophilicity and surface charge measured by the contact angle and particle ζ-potential were found to be strongly dependent on the aluminum composition of the membranes. Both water flux and ion rejection increased considerably as aluminum ions were incorporated into the zeolite framework with a water flux increase from 0.112 to 1.129 kg/m2‚h and ion rejection improvement from 90.6% to 92.9%. The enhancement in ion separation and water flux for high aluminum ZSM-5 membranes was further analyzed by enhanced water affinity on the membrane surface and restricted ion permeation in confined spaces. 1. Introduction Reverse osmosis (RO) ion separation by zeolite membranes1,2 was reported recently for application in wastewater purification in harsh environments where conventional polymeric membranes cannot be applied due to chemical and mechanical instabilities.3,4 Pore network and surface chemistry are the principal properties by which a membrane controls the permeability of different species and achieves separation. Zeolites are crystalline aluminosilicate materials with well-defined pore structures. Ions could be separated from aqueous solution by zeolite membranes, particularly those with a small pore size, such as A-type and MFI-type zeolites (silicalite or ZSM-5), with a mechanism of size exclusion and electric restriction.5,6 The material chemistry (i.e., Si/Al ratio) plays an important role in the membrane charge and surface wettability and thus water permeation because water transport in confined spaces, such as micropores, whose pore sizes are in the range of intermolecular forces, is strongly dependent on the surface wettability and pore wall roughness.7,8 The understanding of the dynamics of ion and water entrance into zeolite pores and the interaction between ion and water in zeolite micropores will be crucial to tailoring the membrane structure for enhanced water flux and ion separation efficiency. Water wettability on a zeolite surface is mainly determined by the aluminum content of the zeolite framework and extraframework counterions.9 Zeolite membranes with high Si/Al ratios, such as pure silicalite-1 membranes, exhibit hydrophobic separation behavior.10,11 As aluminum ions are incorporated into the zeolite framework, more hydroxyl groups form on the membrane surface,12,13 resulting in a higher tendency to adsorb water molecules.14 Also, the substitution of Si4+ by Al3+ in the zeolite framework creates a large-density surface charge, which is usually balanced by small cations (i.e., Na+ and Ca2+).14 The extraframework cations present in the pores can coordinate with * To whom correspondence should be addressed. Tel.: (505) 8356507. Fax: (505) 835-6031. E-mail:
[email protected]. † New Mexico Institute of Mining and Technology. ‡ University of Utah.
water molecules and enhance the water affinity on the zeolite surface.14 The high surface charge created by ion substitution will form a strong surface potential when in contact with aqueous solution. A double layer will form and overlap in the intercrystalline pore region, showing a restriction on ion entering and permeation and enhance the ion separation efficiency. In the work described in this paper, MFI-type zeolite membranes with large variations in Si/Al ratio were synthesized on porous R-alumina supports by seeding and secondary growth. The influence of chemical composition on the surface zeta (ζ) potential and water wettability as well as on RO separation was investigated. The water permeation behavior in confined spaces (i.e., zeolite micropores) was further analyzed. 2. Experimental Section 2.1. Membrane Preparation. ZSM-5 membranes were synthesized by seeding and secondary growth on disk-shaped R-Al2O3 substrates. The substrates were made in the laboratory from commercial R-alumina powder (diameter ) 0.44 µm, Alcoa), with a diameter of 28 mm and thickness of 4 mm. The substrate surface for seed coating was polished with 600-mesh sandpaper. Coating the substrate surface with a layer of silicalite seeds of about 120 nm was carried out by dipping the substrate into a seed suspension containing 0.5% silicalite and 0.05% hydroxypropyl cellulose (HPC, MW ) 100 000, Aldrich) for 3 s. The pH of the coating suspension was adjusted to ∼3 by adding 0.1 M HNO3 by drops. The seeded substrates were dried at 45 °C for 2 days and calcinated at 450 °C for 6 h to remove the organic template. The seeding process was repeated one time to obtain better surface coverage. The nanosized silicalite seeds were synthesized from a solution containing 0.35 g of NaOH pellets (>99.99%, Aldrich), 5.0 g of fumed SiO2 (particle size 0.014 µm, Aldrich), and 25 mL of 1.0 M tetrapropylammonium hydroxide (TPAOH, Aldrich) at 60 °C for 14 days.15 Following the substrate seeding, a secondary growth was performed to form a continuous zeolite layer on the seeded substrate. The second growth synthesis solution was prepared by dissolving fumed silica and NaOH pellets in deionized water
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at 80 °C. When a clear solution was obtained, a measured amount of Al2(SO4)3‚18H2O (>98%, Aldrich) was added and stirred at room temperature for 12 h. The seeded substrate was placed in a Teflon-lined autoclave with the coated surface facing down, and the synthesis solution was poured in to immerse the substrate. The autoclave was sealed and moved to a preheated oven at 180 °C for 6 h. After synthesis, the membranes were rinsed with deionized water and dried at 150 °C for the RO permeation test. 2.2. Membrane Characterization. The MFI type of zeolite and crystallinity were determined by X-ray diffraction (XRD, Rigaku Geigerflex diffractometer using Cu KR radiation). Zeolite morphology and membrane thickness were investigated by a scanning electron microscope (SEM, JEOL 5800LV). The chemical composition of the zeolite membranes was verified by a microscope (Cameca SX-100 with SPARC-5 workstation). The surface hydrophilicity of the zeolite membranes with different Si/Al ratios was determined by contact angle measurement (OCA 30, FDS Inc.) using sessile and captive drop methods. The surface charges of the zeolite membranes were estimated from the ζ-potential measurement of zeolite particles synthesized from the same solution. Zeolite particles with an average particle size of 120 nm were diluted to ∼0.05% in a 0.01 M NaCl solution, and the ζ-potential was measured by DELSA 440SX (Coulter). 2.3. Ion Permeation Tests. Ion separations were performed with a cross-flow RO permeation setup, which was described in our previous work.2 The feed side was connected to a pressurized solution tank containing NaCl solutions; the desired transmembrane pressure was maintained by a high-pressure nitrogen cylinder. A constant feed flow rate of 1.0 mL/min was controlled through a needle valve located at the concentrate side. The permeate, defined as the solution transport across the membrane, was collected every 12 h and stored at 5 °C for further composition analysis. The NaCl concentrations in both the feed and permeate sides were analyzed by an ion chromatograph (IC, DX120, Dionex). Each RO test lasted ∼80 h for achievement of stabilized water flux and ion rejection. Water flux (Fw) and ion rejection (ri) are two important parameters in the RO membrane process. The water/ion flux is defined as the molar of permeate water/ion produced per unit membrane area per unit time. Ion rejection is related to the ratio of ion concentration in the permeate to that in the feed with the definition
ri )
Ci,f - Ci,p Ci,f
(1)
where Ci,f and Ci,p are concentrations in the feed and permeate, respectively (mol/m3). 3. Results and Discussion 3.1. Membrane Preparation. Figure 1 gives the SEM image of a silicalite seeding layer on porous R-alumina support. Random surface searching of SEM images indicated that the whole surface was covered by zeolite crystals with diameters of ∼120 nm. However, high densities of interparticle pores and a domelike structure of the coating layer were observed due to random packing of the zeolite crystals on the porous support. After the template was removed by calcination at 450 °C for 6 h, the seeded substrate was immersed in a synthesis solution containing 1.0SiO2 + 41.5H2O + 0.38NaOH + 0.0076Al2O3 for secondary growth. The crystallization time was varied to
Figure 1. SEM image of a coated zeolite seed layer on R-alumina support.
improve the intergrowth and surface coverage for achievement of high separation performance. Figure 2 shows top-view SEM images of ZSM-5 membranes synthesized from 6 to 12 h. All zeolite membranes synthesized at 180 °C for 6 h or longer show good surface coverage. As synthesis time increased, large crystals formed and embedded in the growing zeolite layer, resulting in higher surface roughness as shown in Figure 2b,c. Crystal growth of MFItype zeolite crystals during secondary growth was confirmed by X-ray study as shown in Figure 3. Alkalinity in the synthesis solution is crucial for zeolite nucleation and growth, especially in the absence of the organic template, because Na+ essentially functions as the structuredirecting agent.16 Also, the alkalinity will affect the dissolution of SiO2 species in the synthesis solution and thus the zeolite crystallinity during zeolite crystallization.17 In this study, zeolite membranes with good surface coverage were synthesized from solutions having a wide range of alkalinity. Figure 4 shows the surface images of zeolite membranes synthesized from solutions having NaOH:SiO2 ratios (x) of 0.32 and 0.48, respectively. Comparing these to the SEM image shown in Figure 3a (x ) 0.38), it can be seen that increasing solution alkalinity promotes the zeolite crystal growth and forms large zeolite crystals and a rough membrane surface. Figure 5 gives SEM images of the surface of zeolite membranes synthesized from solutions containing different Si/ Al ratios. The presence of aluminum ions in the synthesis solution affects the membrane morphology and crystal shape. Membranes synthesized from an aluminum-free solution preserve the characteristic coffin shape of zeolite crystals (Figure 5a). However, the pure silicalite membrane synthesized by secondary growth was found to have a high density of pinholes between crystal boundaries and to show poor separation performance. As aluminum ions were incorporated into the zeolite framework, considerable twinning growth was observed as shown in Figure 5b,c. The twinning growth eliminates most of the pinholes by promoting the intercrystalline growth. Such an observation was reinforced by xylene isomer (p-xylene and o-xylene) separation, which indicated that zeolite membranes synthesized from solutions containing aluminum ions with Si/ Al ratios ranging from 50 to 65 would show molecular sieving on xylene isomers (Rp-xylene/o-xylene ∼ 2.3). The xylene isomer separation was carried out at 300 °C with a procedure described in the literature.18
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Figure 2. Effect of synthesis time on membrane morphology.
Figure 3. XRD patterns of zeolite films formed by seeding and secondary growth.
Figure 4. SEM images of ZSM-5 membranes synthesized from solutions with different alkalinities (1.0SiO2 + 41.5H2O + xNaOH + 0.0076Al2O3).
Figure 6 gives the cross-sectional SEM images of the seeded substrate before and after the secondary growth. To increase the surface coverage, dip coating was repeated once and the seeding layer formed therein had a thickness of 0.5-1.0 µm. The second growth was carried out at 180 °C for 6 h. The membrane synthesized in that condition had an overall zeolite thickness of ∼2.5 µm, giving an effective membrane thickness of ∼2 µm. 3.2. Reverse Osmosis Separation. Table 1 gives the RO separation results for 0.10 M NaCl solution on ZSM-5 membranes synthesized from solutions with Si/Al ratios ranging from 40 to 65. For comparison, RO permeation of 0.10 M NaCl solution on a pure silicalite membrane is also given in Table 1. The silicalite membrane was synthesized by in situ crystallization with a procedure reported in our previous report.2 Pure silicalite membrane synthesized by in situ crystallization gives an ion rejection of 90.6% and water flux of 0.112 kg/ m2‚h at an operating pressure of 2.76 MPa. Both water flux
and ion rejection increase considerably as small amounts of aluminum ions were substituted into the zeolite structure, with water flux increase from 0.112 to 1.129 kg/m2‚h and ion rejection enhancement from 90.6% to 92.9%. As aluminum content increased further (i.e., Si/Al ) 40), a sharp drop in ion rejection to 81.8% was observed. Such a decline in ion rejection is explained by the enlarged intercrystalline pores and poor zeolite crystallinity.11,19 As revealed by SEM images and xylene isomer separations, the presence of appropriate aluminum contents (Si/Al ) 50-65) during the secondary growth is necessary to synthesize defect-free zeolite membranes by promoting the twinning growth. Zeolite membranes synthesized from a solution containing low aluminum contents (i.e., Si/Al > 65) have a random packing of coffin-shaped crystal structure and large density of pinholes, and thus poor separation performance. On the other hand, high aluminum contents in the synthesis solution will result in precipitation of amorphous aluminum silicate in the intercrystalline space, resulting in a considerable decline in ion rejection. The nearly 1-fold increase in water flux of ZSM-5 membranes is attributed to the reduced membrane thickness and enhanced surface hydrophilicity.13 As trivalent cations (Al3+) are progressively incorporated into the zeolite framework, a high density of hydroxyl groups forms and enhances the affinity of water molecules with the membrane surface.9 Also, extraframework counterions (i.e., Na+ and Ca2+) can coordinate to water molecules, enhancing the water affinity on the membrane surface. The thickness-independent permeabilities calculated in Table 1 clearly show the enhancement in water permeation for high aluminum ZSM-5 membranes. The water affinity on the membrane surface was qualitatively studied by contact angle measurements. The membrane samples were tested as received to simulate the actual membrane preparation process. Because water droplets spread rapidly on the membrane surface, the images were taken 30 s after the water droplet touched the membrane surface. Figure 7 gives the contact angle measurement results of zeolite membranes with increasing aluminum contents. The pure silicalite membrane shows a weak hydrophilic property with a contact angle of ∼30°, which is consistent with the literature result.20 The hydrophilic property of pure silicalite membranes is explained by the dissolution of trace aluminum elements from the R-alumina substrate in the strong basic synthesis solution and their incorporation into the zeolite structure.11 As small amounts of aluminum ions were used in the synthesis solution, the contact angles of zeolite membranes were below 5° as shown in Figure 7b,c, indicating strong hydrophilic characteristics of the membranes. Zeolite membranes synthesized from a wide range of aluminum contents by secondary growth show high ion rejection
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Figure 5. Effect of Si/Al ratio on zeolite membrane morphology (1.0SiO2 + 41.5H2O + 0.38NaOH + xAl2O3).
Figure 6. SEM images of cross section of seeded substrates before and after secondary growth (Si/Al ) 65).
for 0.10 M NaCl solution (ri > 90%). The xylene isomer separations have indicated that the pure silicalite membranes synthesized by in situ crystallization give a higher separation efficiency (Rp-xylene/o-xylene ) ∼8.9) than that on the zeolite membranes synthesized by secondary growth from solutions having Si/Al ratios from 40 to 65. Similar influences of aluminum contents on the intercrystalline structure of zeolite membranes were also reported in the literature.21 It is more likely that the enhancement in ion rejection for ZSM-5 membranes is caused by a strong surface charge rather than molecular sieving.14 The surface charge of zeolite membranes was estimated from ζ-potential measurement of zeolite nanoparticles synthesized from the same solution as that of the membranes. Figure 8 gives the ζ-potential of nanocrystalline zeolite particles as a function of aluminum content. The trace element of
aluminum ions (Si/Al ) 200) resulted in a high increase in surface ζ-potential, from -4.7 to -49.2 mV. As aluminum content increased further (i.e., Si/Al ) 65), surface ζ-potential increased gradually to -54.7 mV. The further increase of aluminum contents (Si/Al ) 50) resulted in a leap in ζ-potential to -76.2 mV. In contacting with aqueous solution, a double layer will develop and overlap in the intercrystalline pore region and restrict ion entrance and transport. The double layer thickness monotonically increases with increase of surface potential,22 with the result that more intercrystalline pores are permselective when high concentrations of aluminum ions are incorporated into a zeolite framework. Figures 9 and 10 give the pressure-dependent water flux and ion rejection of zeolite membranes with Si/Al ratios ranging from 50 to infinity (pure silicalite). Increasing operation pressure leads to a linear increase in water flux. Ion rejection, on the other hand, increases initially and then levels off with an increase in operating pressure. Ions permeate through zeolite membranes by two mechanisms: (1) surface diffusion and (2) transport through intercrystalline pores where the double layer cannot overlap.6 In a micropore with a structure similar to that of pure silicalite zeolite membranes, ions and water prefer to stay in the center of the microchannels and ion permeation by surface diffusion is negligible.23 When aluminum ions are incorporated into a zeolite structure, the framework is anionic with its charge balanced by extraframework cations. Such changes in zeolite structure will enhance ion permeation through surface diffusion while hindering ion transport from intercrystalline pores because of the high ion surface coverage and increased double layer
Figure 7. Contact angle measurement of zeolite film on porous support: (a) silicalite; (b) Si/Al ) 65; (c) Si/Al ) 50. Table 1. RO Permeation of 0.10 M NaCl Solution on MFI Zeolite Membranes with Different Si/Al Ratios (P ) 2.76 MPa) membrane M-1 M-2 M-3 M-4
Si/Al ratio 40 50 65 ∼∞
membrane thickness, µm ∼2 ∼2 ∼2 ∼3
Na+ rejection, % 81.8 92.9 91.5 90.6
water flux, kg/m2‚h 1.416 1.129 0.527 0.112
permeability, mol/(m‚h‚kPa) 10-8
5.70 × 4.55 × 10-8 2.12 × 10-8 6.76 × 10-9
remarks 2th growth 2th growth 2th growth in situ
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Figure 8. Zeta-potential of zeolite particles with different Si/Al ratios at 0.01 M NaCl solution.
Figure 11. Enhanced ion flux by water transport in zeolite membranes.
permeation in zeolite-like pores is not a single-file movement; they need to overcome a high-energy profile to pass each other.23,29 Enhanced water permeation under increased operating pressure facilitates the diffusion of ions due to the “dragging effect” of water molecules on large and slow ions.28 This results in a monotonic increase of ion flux with increase of water flux, as shown in Figure 11. The enhanced diffusion of large species by small and fast molecules was widely observed in zeolite membranes.30 4. Conclusions
Figure 9. Water flux of zeolite membranes as a function of operating pressure.
Thin ZSM-5 membranes (∼2 µm) with high aluminum contents were synthesized from template-free solution by seeding and secondary growth. Solution alkalinity, aluminum content, and synthesis time were found to play important roles in membrane morphology, surface roughness, and zeolite intercrystalline growth. Defect-free ZSM-5 membranes were synthesized from synthesis solutions containing 1.0SiO2 + 41.5H2O + 0.38NaOH + (0.0076-0.01)Al2O3. Considerable enhancement in water flux was observed when aluminum ions were incorporated into the zeolite framework. The water flux increased from 0.112 to 1.129 kg/m2‚h and ion rejection increased from 90.6% to 92.9% as 2.0 mol % Si4+ in zeolite framework was substituted by Al3+ ions. The enhancement in water flux and ion rejection is attributed to high surface charge and strong water affinity on aluminum-containing zeolite membrane surfaces. Acknowledgment
Figure 10. Ion rejection as a function of operating pressure for zeolite membranes with different Si/Al ratios.
thickness.24 At low operating pressures, zeolite membranes with higher aluminum contents show lower ion rejection because of the large contribution of ion permeation through surface diffusion. As the transmembrane pressure increases, water permeation increases faster than ion permeation,25 resulting in enhanced ion rejection efficiency. The increase in ion rejection with operating pressure is more significant when high aluminum ions are incorporated into the zeolite framework, as shown in Figure 10. Conventional reverse osmosis theory suggests that water permeation in RO membranes increases linearly with the transmembrane pressure,26 while ion transport is pressure independent.27 These theories cannot easily explain the transport behavior of water and ions in zeolite membranes because the permeation of ions and water in confined spaces, i.e., zeolite pores, is strongly pressure dependent.23,28 Ion and water
This research was sponsored by the U.S. Department of Energy through the National Energy Technology Laboratory (Grant DE-FC26-04NT15548) and Southwest Carbon Sequestration Partnership (Grant DE-FC26-05NT42591). The authors would like to thank Ms. Liz Bustamante for editing the manuscript. Literature Cited (1) Lin, J.; Murad, S. A computer simulation study of the separation of aqueous solutions using thin zeolite membranes. Mol. Phys. 2001, 99, 1175. (2) Li, L. X.; Dong, J. H.; Nenoff, T. M.; Lee, R. Desalination by reverse osmosis using MFI zeolite membranes. J. Membr. Sci. 2004, 243, 401. (3) Bostick, D. T.; DePaoli, S. M.; Guo, B. Treatment of low-level radioactive wastewaters with IONSIV (TM) IE-911 and chabazite zeolite. Sep. Sci. Technol. 2001, 36, 975. (4) Sommer, S.; Melin, T. Performance evaluation of microporous inorganic membranes in the dehydration of industrial solvents. Chem. Eng. Process. 2005, 44, 1138. (5) Kumakiri, I.; Yamaguchi, T.; NaKao, S. Application of a zeolite A membrane to Reverse Osmosis Process. J. Chem. Eng. Jpn. 2000, 33, 333.
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007 1589 (6) Li, L. X.; Dong, J. H.; Nenoff, T. M.; Lee, R. Reverse osmosis of ionic aqueous solutions on a MFI zeolite membrane. Desalination 2004, 170, 309. (7) Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J. Enhanced Flow in Carbon Nanotubes. Nature 2005, 438, 44. (8) Holt, J. K.; Park, G.; Wang, Y.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Fast Mass Transport Through Sub-2-Nanometer Carbon Nanotubes. Science 2006, 19, 1034. (9) Olson, D. H.; Haag, W. O.; Borghard, W. S. Use of water as a probe of zeolitic properties: interaction of water with HZSM-5. Microporous Mesoporous Mater. 2000, 35-36, 435. (10) Coronas, J.; Falconer, J. L.; Noble, R. D. Characterization and permeation properties of ZSM-5 tubular membranes. AIChE J. 1997, 43, 1797. (11) Noack, M.; Kolsch, P.; Caro, J.; Schneider, M.; Toussaint, P.; Sieber, I. MFI membranes of different Si/Al ratios for pervaporation and steam permeation. Microporous Mesoporous Mater. 2000, 35-36, 253. (12) Jareman, F.; Hedlund, J.; Sterte, J. Effects of aluminum content on the separation properties of MFI membranes. Sep. Purif. Technol. 2003, 32, 159. (13) McDonnell, A., M. P.; Beving, D.; Wang, A.; Chen, W.; Yan, Y. Hydrophilic and Antimicrobial Zeolite Coatings for Gravity-independent Water Separation. AdV. Funct. Mater. 2005, 15, 336. (14) Auerbach, S. M.; Carrado, K. A.; Dutta, P. K. Handbook of Zeolite Science and Technology; Marcel Dekker, Inc.: New York, 2003. (15) Dong, J. H.; Wegner, K.; Lin, Y. S. Synthesis of Submicron Polycrystalline MFI Zeolite Films on Porous Ceramic Supports. J. Membr. Sci. 1998, 148, 233. (16) Uguina, M. A.; Delucas, S.; Ruiz, F.; Serano, D. P. Synthesis of ZSM-5 from ethanol-containing systemssinfluence of the gel composition. Ind. Eng. Chem. Res. 1995, 34, 451. (17) Lai, Re.; Gavalas, G. R. ZSM-5 membrane synthesis with organicfree mixtures. Microporous Mesoporous Mater. 2000, 38, 239. (18) Lai, Z. P.; Bonilla, G.; Diaz, I.; Nery, J. G.; Sujaoti, K.; Amat, M. A.; Kokkoli, E.; Terasaki, O.; Thompson, R. W.; Tsapatsis, M. Microstructural Optimization of a Zeolite Membrane for Organic Vapor Separation. Science 2003, 300, 456. (19) Noack, M.; Kolsch, P.; Seefeld, V.; Toussaint, P.; Georgi, G.; Caro, J.; Influence of the Si/Al-Ratio on the Permeation Properties of MFIMembranes. Microporous Mesoporous Mater. 2005, 79, 329.
(20) Munoz, R. A.; Beving, Do.; Yan, Y. S. Hydrophilic Zeolite Coatings for Improved Heat Transfer. Ind. Eng. Chem. Res. 2005, 44, 4310. (21) Oonkhanond, B.; Mullins, M. E. Electrical double-layer effects on the deposition of zeolite A on surfaces. J. Colloid Interface Sci. 2005, 284, 210. (22) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry, 4th ed.; HarperCollins College Publisher: New York, 1993. (23) Lynden-Bell, R. M.; Rasaiah, J. C. Mobility and Solvation of Ions in Channels. J. Chem. Phys. 1996, 105, 9266. (24) Bandini, S.; Vezzani, D. Nanofiltration Modeling: the Role of Dielectric Exclusion in Membrane Characterization. Chem. Eng. Sci. 2003, 58, 3303. (25) Li, L. X.; Liu, N.; McPherson, B.; Lee, R. Influence of Counter Ions on the Reverse Osmosis through MFI Zeolite Membranes: Implications for Produced Water Desalination. Desalination, in press. (26) Williams, M. E.; Hestekin, J. A.; Smothers, C. N.; Bhattacharyya, D. Separation of Organic Pollutants by Reverse Osmosis and Nanofiltration Membranes: Mathematical Models and Experimental Verification. Ind. Eng. Chem. Res. 1999, 38, 3683. (27) Zhou, W.; Song, L.; Experimental Study of Water and Salt Fluxes through Reverse Osmosis Membranes. EnViron. Sci. Technol. 2005, 39, 3382. (28) Bowen, T. C.; Noble, R. D.; Falconer, J. L. Fundamentals and Applications of Pervaporation through Zeolite Membranes. J. Membr. Sci. 2004, 245, 1. (29) Mon, K. K.; Percus, J. K. Self-diffusion of Fluids in Narrow Cylindrical Pores. J. Chem. Phys. 2002, 117, 2289. (30) Bowen, T. C.; Wyss, J. C.; Noble, R. D.; Falconer, J. L. Inhibition during multicomponent diffusion through ZSM-5 zeolite. Ind. Eng. Chem. Res. 2004, 43, 2598.
ReceiVed for reView October 5, 2006 ReVised manuscript receiVed January 1, 2007 Accepted January 15, 2007 IE0612818
