Permeation Characteristics of Electrolytes and Neutral Solutes through

Apr 20, 2010 - from r100 to 150 °C at a ramping rate of 5 °C/min. 2.3. Nanofiltration Experiments. Nanofiltration experi- ments were carried out usi...
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Permeation Characteristics of Electrolytes and Neutral Solutes through Titania Nanofiltration Membranes at High Temperatures Toshinori Tsuru,* Kazuhisa Ogawa, Masakoto Kanezashi, and Tomohisa Yoshioka Department of Chemical Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan Received February 24, 2010. Revised Manuscript Received April 5, 2010 Nanoporous titania membranes with controlled pore sizes ranging from 0.7 to 2.5 nm, which had molecular weight cutoffs (MWCO) ranging from 500 to 2000, were successfully prepared by sol-gel processing, and the transport characteristics were evaluated across a temperature range of 30-80 °C. With increasing temperature, the permeate flux increased 2- to 3-fold, depending on the pore size. The water permeation mechanism was found to be different from viscous flow and was explained by the state of the water (free water/bound water/nonfreezing water) inside confined pores. The rejection of neutral solutes such as raffinose, the separation mechanism of which is molecular sieving (steric hindrance), decreased with temperature whereas that of electrolytes (MgCl2 and NaCl), the separation mechanism of which is the charge effect (Donnan exclusion), was approximately constant. The temperature dependence of neutral and electrolyte solutes was analyzed using the Spiegler-Kedem equation by combining the Arrhenius equations for diffusivity and viscosity, which we obtained ΔEm, the activation energy of diffusion, after eliminating the effect of viscosity. For large ΔEm, which corresponds to the rejection of neutral solutes on the basis of molecular sieving, rejection decreased with temperature but remained unchanged for small ΔEm, which corresponds to the rejection of electrolytes based on the charge effect.

1. Introduction Liquid-phase separation membranes have been categorized into reverse osmosis (RO), nanofiltration (NF), ultrafiltration (UF), and microfiltration (MF) membranes according to their pore sizes and molecular weight cutoffs.1-5 The boundaries of RO and NF, NF and UF, and UF and MF are typically 1, 2, and 100 nm, respectively. Most commercially available RO and NF membranes are manufactured by the interfacial polymerization of polyamides, including fully aromatic polyamide on polysulfone UF membranes. RO membranes, which show a high rejection of all solutes dissolved in water, have been applied to the desalination of seawater and the regeneration of wastewater. However, NF membranes, which have larger pore sizes than RO and MWCOs, ranging from 200 to 2000, have been applied to the production of ultrapure water at lower operation pressures. Because polyamide is prepared by the interfacial polymerization of acids such as trimesoyl chloride and amines such as m-phenylenediamine, most NF membranes are negatively or positively charged because of unreacted charged functional groups such as carboxylic acids and amines. Therefore, the transport mechanism of NFs is based on molecular sieving and the charge effect.3,4,6,7 Although ROs and NFs are conventionally operated at ambient temperature for water treatment such as desalination and purification of land water, a rapid increase in membrane *Corresponding author. E-mail: [email protected]. (1) Baker, R. W. Membrane Technology and Applications, 2nd ed.; John Wiley: New York, 2004. (2) Mulder, M. Basic Principles of Membrane Technology, 2nd ed.,; Kluwer Academic Publishers: Boston, 1996. (3) Sch€afer, A. I., Fane, A. G., Waite, T. D., Eds. Nanofiltration: Principles and Applications; Elsevier Advanced Technology: New York, 2005. (4) Tsuru, T. Sep. Purif. Methods 2001, 30, 191–220. (5) Tsuru, T. J. Sol-Gel Sci. Technol. 2008, 46, 349–361. (6) Tsuru, T; Nakao, S; Kimura, S. J. Chem. Eng. Jpn. 1991, 24, 511–517. (7) Tsuru, T.; Urairi, M.; Nakao, S.; Kimura, S. J. Chem. Eng. Jpn. 1991, 24, 518–524.

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applications has expanded the operation of ROs and NFs at high temperatures. Proposed applications include water treatment in the sugar and textile industries and purification of condensate water from power generators.8,9 The transport characteristics through microporous membranes with a pore size of less than several nanometers in the liquid phase at high temperatures are quite interesting from the viewpoints of theoretical interest in transport phenomena and their importance in practical applications. Commercially available polymeric nanofiltration and reverse osmosis membranes were used to evaluate the permeation performance, such as permeate flux and the rejection of neutral and electrolyte solutes at high temperature typically ranging from 5 to 40 °C.8-19 All of these studies reported that the permeate volume flux increased with temperature because of the lower viscosity of feed solutions, but the viscosity alone in bulk solution cannot explain the temperature dependence due to the contribution of nonviscous flow and/or structural changes in network pores of the polymeric membranes.11,12 However, there is a discrepancy in terms of the temperature dependence of rejection, although the general trend is decreased rejection as the temperature increases. (8) Snow, M.; de Winter, D.; Buckingham, R.; Campbell, J.; Wagner, J. Desalination 1996, 105, 57–61. (9) M€antt€ari, M.; Pihlajam€aki, A.; Kaipainen, E.; Nystr€om, M. Desalination 2002, 145, 81–86. (10) Jin, X.; Jawor, A.; Kim, S.; Hoek, E. Desalination 2009, 239, 346–359. (11) Amar, N. B.; Saidani, H.; Deratani, A.; Palmeri, J. Langmuir 2007, 23, 2937–2952. (12) Sharma, R. R.; Agrawal, R.; Chellam, S. J. Membr. Sci. 2003, 223, 69–87. (13) Sharma, R. R.; Chellam, S. Environ. Sci. Technol. 2005, 39, 5022–5030. (14) Sharma, R. R.; Chellam, S. J. Colloid Interface Sci. 2006, 298, 327–340. (15) Liang, C. H. J. Membr. Sci. 2005, 246, 127–135. (16) Goosen, M.; Sablani, S.; Al-Maskari, S.; Al-Belushi, R.; Wilf, M. Desalination 2002, 144, 367–372. (17) Shaep, J; Van der Bruggen, B.; Uytterhoeven, S.; Croux, R.; Vandecasteele, C.; Wilms, D.; van Houtte, E.; Vanlerberghe, F. Desalination 1998, 119, 295–302. (18) Amar, N. B.; Saidani, H.; Palmeri, J.; Deratani, A. Desalination 2009, 246, 294–303. (19) Saidani, H.; Ben Amar, N.; Palmeri, J.; Deratani, A. Langmuir 2010, 26, 2574–2583.

Published on Web 04/20/2010

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M€antt€ari et al.9 reported that with increasing temperature the rejection of uncharged substances, which was measured as the total amount of dissolved carbon (TDC), decreased but the conductivity was not significantly affected. These authors attributed the decreased rejection of neutral solutes with temperature change to increased diffusivity, and the rejection of electrolytes remained approximately constant because of the charge exclusion mechanism. Schaep et al.17 reported that the rejection of NaCl decreased with temperature whereas that of divalent ions increased slightly with temperature. Only a limited number of papers have quantitatively discussed the effect of temperature on permeation characteristics on the basis of a transport model. Sharma and Chellam12-14 studied the temperature dependence of neutral and electrolyte solutes using two types of polyamide membranes: DL (Osmonics, MWCO = 200-300) and TFCS (Koch Fluid Systems, MWCO=160-200). After analyzing the rejection dependence on the permeate solute flux at different temperatures (5-41 °C), they concluded that with increasing temperature the average pore size increased and the pore density decreased because of the thermal expansion of the polymer constituting the active layer of thin-film composite membranes. Amar et al.11,18 also concluded that one of the major reasons explaining the decrease in rejection with increasing temperature is thermal pore dilation, that is, increased pore size with temperature, based on the hindered transport model. To date, the effect of temperature has been investigated using commercially available polymeric NF membranes. Although operating temperatures above 50 °C are expected, the transport properties of polymeric nanofiltration membranes, which are mainly prepared from polyamide, have been reported in a limited range of temperature from 5 to 50 °C. M€antt€arie et al.9 examined 14 types of polymeric NF membranes and found that only a few NFs withstood a temperature of 65 °C without a significant change in performance. Differential scanning calorimetry (DSC) of the separation layer of seven NF membranes revealed that the glass-transition temperature, Tg, which is reported to be in the range of 32-56 °C, is the limiting parameter for high-temperature applications.19 Ceramic membranes show thermal stability as well as chemical resistance and have been applied in various fields of application such as gas separation at high temperatures. Ceramic NF membranes were prepared from titania20-22 and silica-zirconia23 by sol-gel processing and were applied to water treatment. Titania membranes show excellent stability, can be used at both acidic and basic pH, and have great potential as materials for water treatment. The temperature dependence of the rejection of neutral solutes was discussed using silica-zirconia nanofiltration membranes at temperatures ranging from 20 to 60 °C. Recently, zeolite membranes were applied to the desalination of water in reverse osmosis and pervaporation, and the transport mechanism was discussed.24-26 The state of solvents inside nanosized pores is an important part of the permeation mechanism for nanoporous membranes. (20) Puhlf€urss, P.; Voigt, A.; Weber, R.; Morbe, M. J. Membr. Sci. 2000, 174, 123–133. (21) Van Gestel, T.; Vandecasteele, C.; Buekenhoudt, A.; Dotremont, C.; Luyten, J; Van der Bruggen, B. G.; Maes, G. J. Membr. Sci. 2003, 214, 3–10. (22) Tsuru, T.; Hironaka, D.; Yoshioka, T.; Asaeda, M. Desalination 2005, 147, 213–216. (23) Tsuru, T.; Izumi, S.; Yoshioka, T.; Asaeda, M. AIChE J. 2000, 46, 565–574. (24) Li, L.; Liu, N.; McPherson, B.; Lee, R. Ind. Eng. Chem. Res. 2007, 46, 1584–1589. (25) Li, L.; Liu, N.; McPherson, B.; Lee, R. Deslination 2008, 228, 217–225. (26) Duke, M; O’Brien-Abraham, J.; Milne, N.; Zhu, B.; Lin, J.; daCosta, J. Sep. Purif. Technol. 2009, 68, 343–350.

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The state of water in porous materials can be categorized as free, bound, or nonfreezing as determined by differential scanning calorimetry (DSC) analysis. It is reported that water confined in smaller pores melts at a lower temperature because of greater interaction.27,28 According to the temperature dependence of the membrane permeation of water23 and other solvents,29-32 the viscosity in nanosized pores reportedly had a different temperature dependence than in the bulk. Ceramic membranes present a great advantage in the investigation of the transport mechanism through nanosized pores by eliminating the effect of thermal expansion, which is always encountered with polymeric membranes. In this article, nanoporous titania membranes with controlled pore sizes in the range of 1-3 nm were successfully prepared by sol-gel processing and their transport performance was evaluated in the temperature range from 30 to 80 °C. The temperature dependence of pure water permeability was examined using three TiO2 membranes with different pore sizes and was discussed on the basis of the measurement of the state of water in micro/nanoporous TiO2 powders. Moreover, the temperature dependence of solute permeability and the reflection coefficients of solutes were investigated for neutral solutes and electrolytes.

2. Experimental Section 2.1. Membrane Preparation. Two types of titania sol solutions were prepared for the fabrication of nanoporous membranes: colloidal and polymeric. In the polymeric sol route, hydrolysis and condensation reactions of titanium tetra-isoproxide (TTIP, Ti(OC3H7)4) were carried out with a small amount of water in isopropanol (IPA) solutions with HCl catalysts.22 TTIP, IPA, H2O, and HCl were mixed to give a molar ratio of 1:140:4:0.4. The hydrolysis and condensation reactions were carried out for 1 h in an ice bath, and then the sol solutions were aged at temperatures from 20 to 50 °C for more than 10 h. Titania sol diameters, which were measured by laser light scattering (ELS8000, Otsuka Electric, Japan), were controlled by the temperature of the aging process. In the peptization method, an excess amount of water was added in the hydrolysis step at 60-70 °C, resulting in milky aggregated sol solutions. After complete hydrolysis for an additional 30 min, nitric acid was added to the sols with TTIP, IPA, H2O, and HNO3 in a molar ratio of 1:20:1000:1-3, followed by boiling for 8 h. During the boiling process, the milky sol was peptized to colloidal sol solutions, which were transparent and bluish. Colloidal sizes produced by the peptization method were controlled by acid concentrations ranging from 20 to 50 nm. Titania sols were coated onto R-alumina capillary supports (pore size 150 nm, outer diameter 3 mm, thickness 0.36 mm, length 55 mm, effective membrane area 5.18 cm2; NOK Corp., Japan) and fired from 350 to 650 °C. 2.2. Characterization. The pore size distribution of nanoporous titania membranes was evaluated by the nanopermporometry technique (NPP) using a NanoPerm porometer (Seika Sangyo, Japan). The basic principle of NPP is based on the capillary condensation of a vapor inside nanopores and its ability to block the permeation of a noncondensable gas when a mixture of a noncondensable, such as nitrogen, and a condensable vapor, (27) Ishikiriyama, K.; Todoki, M.; Motomura, K. J. Colloid Interface Sci. 1995, 171, 92–102. (28) Ishikiriyama, K.; Todoki, M. J. Colloid Interface Sci. 1995, 171, 103–111. (29) Tsuru, T.; Sudoh, T.; Kawahara, S.; Yoshioka, T.; Asaeda, M. J. Colloid Interface Sci. 2000, 228, 292–296. (30) Tsuru, T.; Kondo, H.; Yoshioka, T.; Asaeda, M. AIChE J. 2004, 50, 1080-1087. (31) Tsuru, T.; Miyawaki, M.; Yoshioka, T.; Asaeda, M. AIChE J. 2006, 520, 522-531. (32) Dobrak, A.; Verrecht, B.; Van den Dungen, H.; Buekenhoudt, A.; Vankelecom, I. F. J.; Van der Bruggen, B. J. Membr. Sci. 2001, 186, 344–352.

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Figure 1. SEM images of cross sections with an overall thickness and a top layer of the outer surface (magnification: (left) 200 and (right) 10 000). such as hexane and water vapor, is fed into the porous membrane.33 In the present study, the permeance of nitrogen was measured as a function of the vapor pressure of hexane in a mixture of nitrogen and hexane at 40 °C. N2 permeance normalized with dry N2, the dimensionless permeance of nitrogen (DPN), was plotted as a function of the Kelvin diameter converted from the vapor pressure of hexane. Water in confined pores was measured by differential scanning calorimetry (DSC, Shimadzu). Three types of titania powders were prepared: dry peptized sols and polymeric sols aged at 50 and 20 °C and by firing at 450 °C. The titania powers, which were wet with a small amount of water for more than 1 day, were cooled by liquid nitrogen and were then subjected to DSC measurement from -100 to 150 °C at a ramping rate of 5 °C/min. 2.3. Nanofiltration Experiments. Nanofiltration experiments were carried out using a stirred cell made of polycarbonate resin for the smallest dissolution of metal ions in the feed liquid, similar to our previous study.23 The feed solution, pressurized using a plunger pump in the range from 0.2 to 0.5 MPa, was agitated using a magnetic stirrer at 600 rpm and was recycled to the feed tank at an approximate flow rate of 7 cm3 min-1. The permeation temperature was controlled from 30 to 80 °C using a rubber heater winding on the permeation cell. MWCOs were evaluated using organic solutes (i.e., sugars (maltose (MW=342) and raffinose (MW=504)) and poly(ethylene glycol) of different molecular weights. The feed concentrations were controlled at 500 ppm for negligible osmotic pressure and fouling. The electrolytes used were sodium chloride as a mono-monovalent (1-1) electrolyte, sodium sulfate (1-2), and magnesium chloride (2-1) at a feed concentration of 3 mol 3 m-3. Electrolyte concentrations were determined using an electrical conductivity meter. The pH of the feed solutions was adjusted from 3 to 10 using acid or alkali solutions having the same ions as the filtrated electrolytes.

3. Results and Discussion 3.1. TiO2 Nanofiltration Membranes. Figure 1a,b shows the cross section of a TiO2 membrane at magnifications of 200 and 10 000, respectively. An R-alumina substrate, which was prepared from alumina particles that were 300-400 nm in size, showed an overall thickness of 360  10-6 m. Fingerlike voids, which would be preferred for the reduction of the resistance of water permeation, were observed. The TiO2 layer, which was fabricated on the outer surface of the substrate, had an approximate thickness of 200-300 nm. Figure 2 shows the pore size distribution (PSD) curves of three membranes, as measured by nanopermporometry: M-2.5, M-1.0, and M-1.0.33 The dimensionless permeance of nitrogen, which was obtained by normalizing nitrogen permeance for a specific feed humidity with dry nitrogen permeance, was plotted as a function of the Kelvin diameter, which was calculated by assuming a contact angle of zero in the Kelvin equation. TiO2 membrane M-2.5, which was prepared using colloidal sols (peptized) and was fired at 450 °C, has an average pore size, defined at 50% of the dimensionless permeance of nitrogen, of 2.5 nm. M-0.7 (33) Tsuru, T.; Hino, T.; Yoshioka, T.; Asaeda, M. J. Membr. Sci. 2001, 186, 257–265.

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Figure 2. Pore size distribution of nanoporous TiO2 membranes measured by nanopermporometry (M0.7, M1.0, and M2.5).

Figure 3. Molecular weight cutoff curves of TiO2 membranes having average pore sizes of 0.7, 1.0, and 2.5 nm.

and M-1.0, which had average pore sizes of 0.7 and 1.0 nm, were prepared from TiO2 polymeric sols aged at 25 and 50 °C, respectively. It should be noted that larger polymeric sols were obtained by aging at higher temperatures, resulting in TiO2 membranes with larger pore sizes. Figure 3 shows the MWCO curves of the three membranes determined by the nanofiltration experiment using neutral solutes. Rejection increased with an increase in the molecular weight of solutes and reached almost complete rejection, indicating a small number of pinholes in the TiO2 membranes. The MWCOs, defined at 90% rejection, of M-0.7, M-1.0, and M-2.5 were 600, 1000, and 2000, respectively, and the pure water permeability, Lp, defined as the water permeation rate (m3/s) per unit membrane area (m2) per pressure difference across a membrane (Pa), which is the driving force for water permeation, was in the range of (1-20)  10-11 m3 m-2 s-1 Pa-1. A comparison, as summarized in Table 1, indicates a consistent order between the average pore sizes determined by NPP and MWCOs; the smaller the pore size, the smaller the MWCO, confirming that the separation mechanism is molecular sieving. It should be noted that the pore size distribution determined by nanopermporometry has several limitations. First, strictly speaking, the Kelvin equation cannot be applied to pore sizes smaller than 2 nm because the Kelvin equation is based on macroscopic thermodynamics. Second, a zero contact angle was assumed with no experimental evidence. Finally, the adsorption layer was not considered. However, if membranes prepared from the same materials are measured, then nanopermporometry PSD DOI: 10.1021/la100791j

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Tsuru et al. Table 1. Characterization of Nanoporous TiO2 Membranes membrane

M0.7 (0.7 nm)

M1.0 (1.0 nm)

types of sol average pore size (nm) MWCO (g mol-1) pure water permeability, Lp (m3m-2 s-1 Pa-1)

polymeric sol aged at 25 °C 0.7 600 1.1  10-11

polymeric sol aged at 50 °C 1.0 1000 5.2  10-11

M2.5 (2.5 nm) colloidal sol 2.5 2000 1.7  10-10

Figure 4. Rejection and permeate flux of electrolyte solutions at different pH values (M1.0; solutes: NaCl, MgCl2, and Na2SO4).

curves can offer criteria for the evaluation of the pore size distribution. We reported that the pore sizes of porous membranes estimated from nanopermporometry showed an adequate correlation with nanofiltration separation ability (pore size 1-3 nm) as well as with gas separation (pore size 0.3-1.0 nm).33 Figure 4 shows the rejection of electrolytes of different valence types (NaCl, Na2SO4, and MgCl2) as a function of the pH of the feed solution. Although membrane M-1.0 had an approximate pore size of 1 nm and allowed the permeation of solutes smaller than 1000 g/mol (MWCO), electrolytes with molecualr weights in the range of 58-90 g/mol were rejected and the rejection was highly dependent on pH. The rejection of the three solutes was approximately zero at pH 7. In the acidic pH range, the order of rejction was MgCl2 > NaCl > Na2SO4 whereas the order was Na2SO4 >NaCl>MgCl2 in the alkaline pH range. This can be explained by the surface charge, which is dependent on the pH of the feed solution. We reported that the rejection of electrolytes of different valence types, such as NaCl as a 1-1 valence, MgCl2 as a 2-1, and Na2SO4 as a 2-1, could be successfully explained by the extended Nernst-Planck model6,7 using parameters related to membrane stucture (pore size, thickness, and porocity) and membrane charge (polarity and charge density). On the basis of the concept of the extended Nernst-Planck model, the rejection dependence can be quantitatively explained as follows. TiO2 has its isoelectric point at approximately pH 7 (pI 7). Therefore, in the acidic pH range, TiO2, which is positively charged, exerts a larger repulsive force on the Mg2þ divalent cation than on the Naþ monovalent cation because of the Donnan exclusion, which leads to a higher rejection of MgCl2 than of NaCl. However, the SO42divalent anion, which received a larger attractive force from positively charged TiO2 than the Cl- monovalent anaion, could easily enter the TiO2 membrane, leading to a lower rejection of Na2SO4 than of NaCl. In the alkaline pH range, the tendency was the opposite. However, no rejection was observed at neutral pH because no electric repulsion was generated by the neutral surface charge (pI ∼7). In addition, electrolyes, the molecular weight of which ranged from 58 to 90 g/mol, were too small to be rejected by M-1.0, with a molecular weight cutoff that was approximately 1000 g/mol on the basis of the molecular sieving mechanism. 10900 DOI: 10.1021/la100791j

Figure 5. Temperature dependence of water permeability, Lp, and viscosity-corrected water permeability, Lpμ, for TiO2 membranes with different pore sizes.

Figure 6. Normalized Lpμ for TiO2 membranes with different pore sizes as a function of temperature (M0.7, M1.0, and M2.5).

It can therefore be concluded that the mechanism of rejection of electrolytes was based on the charge effect (i.e., the Donnan exclusion). 3.2. Temperature Dependence of Pure Water Permeability. Figure 5 shows the temperature dependence of water permeability, Lp. With an increase in the permeation temperature from 30 to 70 °C, the water permeability of the three TiO2 membranes with different pore sizes increased 2- to 3-fold, depending on the membrane pore sizes. According to the viscous flow mechanism, permeability through a porous membrane consisting of capillaries (pore size, rp; length, Δx; and porosity, Ak) is formulated as the following Hagen-Poiseuille equation.23 Lp μ ¼

r p 2 Ak ¼ const 8Δx

ð1Þ

If the permeation mechanism of nanosized pores is the viscous flow mechanism, then corrected water permeability, Lpμ, defined as water permeability (Lp) multiplied by the viscosity of Langmuir 2010, 26(13), 10897–10905

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bulk water (μ), should be constant irrespective of the permeation temperature because the right side of eq 1 consists of the structural parameters of a membrane, which should be independent of the permeation temperature. As shown in Figure 5, Lpμ of the three membranes was not constant and clearly increased with permeation temperature. In Figure 6, Lpμ is shown as a function of temperature when normalized by that at 30 °C for TiO2 membranes with different pore sizes. It should be noted that normalized Lpμ should be unity if the transport mechanism is subjected to the viscous flow mechanism. However, normalized Lpμ increased as the permeation temperature increased, and a TiO2 membrane with a smaller pore size has a larger slope. As summarized in Table 2, the activation energy of Lp and Lpμ, obtained by the following Arrhenius equation increased for membranes with smaller pore sizes. Therefore, it can be concluded that the water permeation mechanism through nanoporous membranes is different from viscous flow. Possible reasons include the following: (1) water permeation is an activated process in which water molecules permeate through smaller pores via a repulsive force from the pore wall; (2) the thickness of the adsorbed water decreases with temperature, resulting in larger effective pores for water permeation; and (3) the viscosity of water in small pores shows a different temperature dependence from that in the bulk.23 Although a similar temperature dependence for water permeability was reported for polymeric membranes, this has been attributed to increased pore size due to thermal expansion at high temperatures. Here, with the help of ceramic membranes with negligible thermal Table 2. Activation Energy of Lp and Lpμ for M-0.7, M-1.0, and M-2.5 membrane

M-0.7

M-1.0

M-2.5

viscous flowb

ΔE(Lp) (kJ/mol)a 22.7 19.7 18.0 14.5 8.2 5.1 3.5 0 ΔE(Lpμ) (kJ/mol)a a Activation energies ΔE(Lp) and ΔE(Lpμ) were obtained using Lp = (Lp)0 exp(-ΔE(Lp)/RT) and Lpμ = (Lpμ)0 exp(-ΔE(Lpμ)/RT) with a pre-exponential constant of (Lp)0. bActivation energy of the viscous flow mechanism calculated from the temperature dependence of the water viscosity, μ, in the bulk assuming a constant Lpμ.

Figure 7. DSC curves of TiO2 powders prepared using anatase colloidal, peptized, and polymeric sols.

expansion, we have clearly shown that thermal expansion is not the only reason for the temperature dependence. Another important point is that with nanoporous ceramic membranes an increased Lpμ was also observed for nonaqueous solutions such as alcohols.29-32 An approximately constant Lpμ was found with hydrophobic membranes,30,32 which had small interactions between the membrane surface and permeating molecules. Therefore, the interaction between the membrane surface and the permeating molecules is thought to be responsible for the difference in the temperature dependence compared with that in the bulk. Figure 7 shows DSC curves that were collected at a ramping rate of 5 °C/min from -100 to 20 °C after cooling in liquid nitrogen. As summarized in Table 3, TiO2 powders were prepared from TiO2 peptized sols and polymeric sols aged at 50 and 20 °C by drying and firing at 450 °C, which corresponded to M-2.5, M-1.0, and M-0.7, respectively. The powders were pretreated with a small amount of water at least 1 day before the measurement. The state of water in confined pores can be categorized as free water, bound water, and nonfreezing water.27,28 Free water freezes at approximately 0 °C, and bound water freezes at temperatures lower than 0 °C because of interactions with pore surfaces covered with hydrophilic TiOH groups. The melting points of water in TiO2 powders, P-colloidal and P-polymeric50 °C, were observed at -14 and -25 °C, respectively, whereas no melting point was observed for P-polymeric-25 °C. Water is nonfreezing because of strong interactions, even at -100 °C. The amounts of bound water, wbound, and free water, wfree, were obtained from the area of the endothermic peak, which appeared at temperatures lower than 0 °C, ΔQbound, and the heat of melting at approximately 0 °C, ΔQfree. The weight of dry TiO2 powder, Wdry, was obtained after heating to 200 °C. The amount of nonfreezing water was determined by the following equation using the heat of melting, ΔHm. wnonfreezing ¼ 1 -

ΔQbound ΔQfree Wdry ΔHm Wdry ΔHm

ð2Þ

The amounts of nonfreezing water in three TiO2 powders prepared from different sols were found to be in the range of 0.048-0.058 g/g of TiO2. Because the BET surface areas of P-colloidal and P-polymeric-50 °C were 130 and 96 m2/g, respectively, the thickness of nonfreezing water can be calculated to be 0.4-0.6 nm, suggesting approximately one or two water molecules adsorbed onto the TiO2 surface in the form of nonfreezing water. However, the melting point of bound water decreased as the pore size decreased. According to Ishikiriyama et al.,27,28 water confined in smaller pores melted at a lower temperature because of larger interactions. On the basis of the above discussion, it can be concluded that water molecules in nanosized pores are tightly bound to the hydrophilic surface of TiO2 membranes, as confirmed by DSC analysis, as nonfreezing and/or bound water in TiO2 powders and that they have different properties, including the melting point and viscosity, from those in the bulk. Irrespective of approximately the same amount of nonfreezing water for the three powders, M-0.7 had the largest activation

Table 3. Bound Water and Nonfreezing Water of Three TiO2 Powders Based on DSC Analysis bound water

nonfreezing water

TiO2 powder

sol used for powder preparation

freezing temperature (°C)

amount (g/g of TiO2)

amount (g/g of TiO2)

P-colloidal P-polymeric-50 °C P-polymeric-25 °C

colloidal sol (used for M-2.5) polymeric sol aged at 50 °C (used for M-1.0) polymeric sol aged at 25 °C (used for M-0.7)

-14 -25 n.d.

0.053 0.018 n. d.

0.048 0.058 0.048

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Figure 8. (a) Flux and solute rejection as a function of permeation temperature (M-1.0; solutes: raffinose, NaCl (pH 3.5), and MgCl2 (pH3.5); ΔP = 0.2-0.3 MPa). (b) Flux and solute rejection as a function of permeation temperature (M-2.5; solutes: raffinose, NaCl (pH 3.5), and MgCl2 (pH 3.5); ΔP=0.1 MPa).

energies of Lp and Lpμ probably because it had the largest ratio of nonfreezing water to the total amount of water, which would equate to the largest interaction with a membrane surface. It can be concluded that nanoporous membranes showed a temperature dependence that was different from that in the bulk because of the interaction between the membrane pore surface and the permeating molecules. 3.3. Temperature Dependence of Neutral and Electrolyte Solutions. Figures 8 (a) and (b) show rejection and permeate flux normalized with operating pressure as a function of permeating temperature, using M-1.0 and M-2.5, respectively. Electrolytes (NaCl, MgCl2) and neutral solutes (raffinose (M.W.: 594), polyethylene glycol 1000 (PEG1000, M.W.: 1000)) were used for the evaluation of temperature dependence. Permeate flux, which was collected under constant operating pressure, increased with temperature for both electrolytes and neutral solutes. The permeate flux was increased approximately 2-fold by increasing the permeation temperature from 30 to 70 °C. No obvious difference in the temperature dependence was observed between the permeation of pure water and the nanofiltration of solutions. Figure 8a,b shows that the rejection decreased with temperature for neutral solutes, that is, raffinose and PEG1000, respectively. This temperature dependence is also similar to that of polymeric membranes.9-19 As discussed in section 3.2, the increased pore sizes cannot account for the decreased rejection with increasing temperature because inorganic membranes show a negligible thermal expansion in the present temperature range. Interestingly, electrolytes NaCl and MgCl2, which were nanofiltered at pH 3.5 where TiO2 was positively charged, showed approximately constant rejection in the range of 30-70 °C. This tendency was confirmed for two TiO2 membranes, M-1.0 and M-2.5, with different pore sizes (1.0 and 2.5 nm). From the viewpoint of separation efficiency, a high-temperature operation is recommended for the removal of electrolytes because of the higher flux and approximately similar rejection. Figure 9a,b shows the pressure dependence of the permeate flux and rejection for raffinose and MgCl2, respectively. The rejection of raffinose increased with applied pressure, and the rejection at 30 °C was higher that that at 70 °C. However, MgCl2 rejection at 30 °C was approximately the same as that at 70 °C. The temperature dependence, as discussed in Figures 8a,b, was confirmed, as shown in Figure 9a,b. It should be noted that MgCl2 rejection increased only gradually with applied pressure. 3.4. Analysis of the Effect of Temperature on Solute Permeation. From the viewpoint of the transport mechanism 10902 DOI: 10.1021/la100791j

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Figure 9. Pressure dependence of flux and rejection for (a) raffinose and (b) MgCl2 . (M1.0; T=30 and 70 °C; curves are calculated using eqs 3, 5, and 6 with membrane parameters σ, P, and Lp listed in Table 4).

of NF membranes, transport models are based on two mechanisms, the sieving effect and the charge effect. With respect to the charge effect, the electrostatic force between the membrane and ions in the feed solutions can play an important role in rejecting electrolytes because NF membranes have pore diameters in the range of a few nanometers. However, the permeating molecules encounter friction from the pore wall when the transport mechanism is molecular sieving. Although the two mechanisms are quite different from one another, it is widely accepted that the permeation properties of NF and RO can be described using the Spiegler-Kedem equation, which is based on irreversible thermodynamics, for both permeation mechanisms.6,7,12 The NF membrane was initially modeled as a charged-capillary membrane that has uniform pores large enough for negligible molecular sieving for electrolytes and was successfully applied to the analysis of commercially available NF membranes. At present, the transport equations have been extended to include both steric (molecular sieving) and charge effects.34,35 In the present study, only the charge effect was considered in the rejection of electrolytes because the MWCO of TiO2 membranes is large enough, compared with electrolytes. Spiegler-Kedem derived the following transport equation to describe the volume flux, Jv, and solute flux, Js, using three membrane parameters;water permeability, Lp, the reflection coefficient, σ, and solute permeability, P;based on irreversible thermodynamics23 Jv ¼ Lp ðΔP - σΔπÞ Js ¼ - PΔx

d C þ ð1 - σÞCJv dx

ð3Þ ð4Þ

where ΔP, Δπ, and Δx are the pressure difference, the osmotic pressure difference, and the membrane thickness, respectively. Equation 4, where the first and second terms show the contributions of diffusion and convection, respectively, is Fick’s equation for dilute solutions. The solute permeability, P, can be interpreted as Deff/Δx (i.e., effective diffusivity divided by membrane thickness), and the reflection coefficient, σ, can be interpreted as the fraction of solute reflected by the membrane in convective flow. By integration from the feed solution to the permeate stream (34) Bowen, W. R.; Mukhtar, H. J. Membr. Sci. 1996, 112, 263–274. (35) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. J. Chem. Eng. Jpn. 1995, 28, 372–380.

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with activation energies Eμ and ED and pre-exponentials μ0 and D0.37

Figure 10. Real rejection as a function of reciprocal flux for (a) M1.0 and (b) M1.1. (Solid and dotted curves are calculated for raffinose and MgCl2, respectively, using eq 5 and membrane parameters in Table 4.)

R ¼ 1-

  Cp ð1 - FÞσ Jv where F ¼ exp ¼ 1 - σF Cm P

ð5Þ

Transport equations given in an excellent review by Deen36 are expressed with similar equations. It should be noted that Cm, which is the concentration at the surface of a membrane, is used to define the real rejection, R. When one of the feed components was rejected, concentration polarization occurred outside of the membrane. Solutes that are rejected by a membrane accumulate on the outer surface of the feed side; therefore, the concentration at the interface (Cm) is higher than the feed concentration (Cb). Two kinds of rejection, that is, observed rejection Robs (= 1 (Cp/Cb)) and real rejection Rreal (= 1 - Cp/Cm), can be defined, and Rreal must be used for the discussion of membrane permeation mechanisms. Rreal under the permeate volume flux, Jv, can be calculated by following the concentration polarization equation   Jv Robs exp k (   ) R¼ Jv -1 1 þ Robs exp k

ð6Þ

with the help of our previously proposed correlation equations for the mass-transfer coefficient, k (Appendix).23 Figure 10a,b shows Rreal as a function of the reciprocal permeate volume flux, 1/Jv. Curves in the Figure are calculated with eq 5 and fitted membrane parameters σ and P summarized in Table 4. Calculated curves for both molecules agreed well with the experimental data, although MgCl2 did not fit as well as raffinose. Reflection coefficients, σ, for both solutes were found to be fitted independently of the permeation temperature, probably because the pore structure of inorganic membranes is stable in the temperature range of the present study, in comparison with polymeric membranes that were reported to change their pore size. However, permeability coefficients (P) of neutral and electrolyte solutes increased with temperature. This is consistent with previous reports regarding the temperature dependence of neutral solutes.9,11,12,23 Viscosity, η, and diffusivity, D, in the bulk can be predicted well by Arrhenius-type viscosity and diffusion equations (36) Deen, W. M. AIChE J. 1987, 33, 1409–1425. (37) Poling, B. R.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2000.

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ð7Þ

D ¼ D0 expð -ED =RTÞ

ð8Þ

The two equations above give the following expression for viscosity and diffusivity, indicating that D is linear with respect to reciprocal viscosity, which can be derived from the StokesEinstein equation D¼

using RO conditions (Js=CpJv), rejection can be expressed by the following Spiegler-Kedem equations.

μ ¼ μ0 expð -Eμ =RTÞ

  ED þ Eμ D0 μ0 f exp ¼ expð - ΔE=RTÞ μ μ RT

ð9Þ

where f is the product of pre-exponentials D0 and μ0 and ΔE (= ED þ Eμ) indicates the activation energy of diffusion after eliminating the temperature dependence of the viscosity. Using diffusivity data estimated with a Wilke-Chang equation37 and the water viscosity data, ΔE was calculated to be 2.5 kJ/mol, or approximately zero, for bulk solutions in the range of 20-70 °C. ΔE corresponds to the kinetic energy required to overcome the potential barrier between a membrane and a solute. In membrane permeation, solute permeability, P, can be interpreted as DmAk/Δxm with surface porosity, Ak, and membrane thickness, Δxm,9,11,12,23 and can be expressed with the activation energy of diffusion, ΔEm, the viscosity in the membrane, μm, and the constant fm (= Dm0μm0). P¼

  Dm Ak f m Ak ΔEm ¼ exp Δxm μm Δxm RT

ð10Þ

As shown in Table 4, the solute permeability for both membranes increased approximately 2-fold for electrolytes and more than 3-fold for neutral solutes. It should be noted that with an increase in temperature from 30 to 70 °C the diffusivity of both neutral and electrolyte solutes in the bulk increased approximately 2-fold so the temperature dependence clearly differed from that in the bulk. As already discussed in section 3.2, the viscosity in nanosized pores is different from that in the bulk and may be related to the pure water permeability, Lp, as shown in eq 1. Therefore, by dividing the solute permeability, P, by the water permeability, Lp, it is possible to discuss the temperature dependence of the solute permeability in nanosized pores by eliminating the effect of viscosity. In other words, the evaluation of permeate flux and solute rejection corresponds to the simultaneous measurement of the viscosity of the solution and the diffusivity of solutes through nanosized pores.23     P fm ΔEm ΔEm µ exp ð11Þ ¼ 2 exp Lp rp RT RT The last two columns in Table 4 show the ratio of P/Lp from 70 to 30 °C and ΔEm, the activation energy of diffusion after eliminating the effect of viscosity. The P/Lp ratio for MgCl2, the separation mechanism of which is the charge effect, was approximately 1 for both M-1.0 and M-1.1, suggesting no activated process in diffusion through TiO2 membrane pores; that is, the diffusivity in the pores increased in the same manner as did the reciprocal viscosity, resulting in no change in rejection with changing temperature. However, the P/Lp ratios for raffinose, the separation mechanism of which is molecular sieving, were 1.4 and 2.4 for M-1.0 and M-1.1, respectively, indicating an activated process for DOI: 10.1021/la100791j

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Tsuru et al. Table 4. Summary of Membrane Parametersa, the Ratio P/Lp, and the Activation Energy P Lp

membrane

solutes

temperature (°C)

Lp  1011 (m/s Pa)

P  106 (m/s)

30 5 3 70 11.1 6 raffinose 30 4.5 6 70 9.1 17 30 3.2 0.65 M1.1 (MWCO 800) MgCl2 50 5.9 1.1 70 9.9 2.2 raffinose 30 3.1 1.6 70 8 10 80 11.5 16 a Pure water permeability, Lp, the solute water permeability, P, and the reflection coefficient, σ.

M1.0 (MWCO 1000)

MgCl2

(1)

(2)

Figure 11. Schematic of the permeation mechanism of electrolyte and neutral solutes.

diffusion through nanoporous membranes. In other words, ΔEm for neutral solutes is larger than that for electrolytes, leading to decreased rejection with temperature. Molecular sieving is based on the friction between permeating molecules (molecular size approximately 0.5 to 1 nm) and membrane pores (pore size 1 to 2 nm), resulting in an activated process. However, electrolytes are rejected on the basis of an electric repulsive force, which acts over a wide range of several to several tens of nanometers. The Debye length for the concentration of 3 mol m-3 is 5.5 nm, which is much larger than the pore size (1 to 2 nm) of NF membranes. Thus, the electrical potential inside NF membranes can be considered to be uniform by overlapping in both the radial and longitudinal directions, and this tendency was confirmed by the numerical calculation of the Poisson-Boltzmann equation.38 Because the electrorepulsive force is less sensitive to temperature, the temperature dependence of rejection was less than that of the molecular sieving effect. Figure 11 shows a schematic representation of the permeation mechanisms of electrolyte and neutral solutes. In conclusion, the transport mechanisms of neutral and electrolyte solutes, which are molecular sieving and the charge effect, respectively, were found to be responsible for the temperature dependence.

4. Conclusions Nanoporous titania membranes with controlled pore sizes ranging from 0.7 to 2.5 nm, which had MWCOs ranging from 500 to 2000 g/mol, were prepared by sol-gel processing, and the transport characteristics were evaluated in the temperature range of 30-80 °C. (38) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. J. Membr. Sci. 1995, 103, 117–133.

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(3)

σ (-)

P Lp

! !70o C 30o C

ΔEm (kJ/mol)

0.8

0.9

-2.3

0.99

1.4

7.3

0.83

1.1

2.1

0.99

2.4

18.9

With an increase in temperature, the permeate flux increased 2- to 3-fold, depending on the pore size. The water permeation mechanism was found to be different from the viscous flow and was discussed on the basis of the state of the water (free water/bound water/nonfreezing water) inside confined pores, as determined by DSC analysis. Water molecules in nanosized pores were tightly bound to the hydrophilic surfaces of TiO2 membranes, as confirmed by DSC analysis as nonfreezing and/or bound water in TiO2 powders, and had different properties, including melting points and viscosity, from those in the bulk. The rejection of neutral solutes such as raffinose decreased with temperature, and that of electrolytes (MgCl2 and NaCl) was approximately constant. On the basis of analysis using the Spiegler-Kedem equation, the transport mechanisms of neutral and electrolyte solutes, which are molecular sieving and the charge effect, respectively, were found to be responsible for the temperature dependence.

Acknowledgment. This study was supported by The Salt Science Research Foundation (no. 0806) and the Research and Development Grant Program of the Kanto Bureau of Economy, Trade and Industry, Ministry of Economy, Trade and Industry (METI) of Japan.

Appendix: Mass-Transfer Coefficient, k The mass-transfer coefficient, k, can be obtained using the Sherwood number (= NSh), which was correlated with the Reynolds number (= NRe) and the Schmit number (= NSc) 23 NSh ¼ jðNRe Þ0:567 ðNSc Þ0:33 ¼ NRe ¼

kr D

ωr2 ωr2 F ¼ μ ν

NSc ¼

ν μ ¼ D FD

where D is the diffusivity of the solute. r and ω are the radius of a stirring bar and the agitation speed. F and μ are the density and viscosity of feed solutions, respectively. j is an equipment factor and is 0.25 for the present stirring cell.23 Langmuir 2010, 26(13), 10897–10905

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Nomenclature Glossary Ak porosity C concentration (mol/m3) Cp, Cm permeate concentration, membrane surface concentration (mol/m3) D diffusivity (m2/s) Eμ, ED activation energy of viscosity and diffusivity (J/mol) f defined in eq 7 (N) solute flux (mol/(m2 s)) Js permeate volute flux (m3/(m2 s)) Jv k mass-transfer coefficient (m/s) pure water permeability (m3/(m2 s)) Lp

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P solute permeability (m/s) R rejection pore radius (m) rp weight of dry TiO2 powder (kg) Wdry wnonfreezing weight ratio of nonfreezing water (kg of water/kg of TiO2) σ reflection coefficient μ viscosity (Pa s) heat of melting of water (J/kg) ΔHm ΔQbound, ΔQfree melting heat of bound water, melting heat of free water (J) Δx membrane thickness (m) ΔE defined in eq 7 (J mol-1)

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