J. Phys. Chem. B 2008, 112, 9389–9399
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Transport Properties of Highly Ordered Heterogeneous Ion-Exchange Membranes V. Shapiro, V. Freger, C. Linder, and Y. Oren* Department for Desalination and Water Treatment, Zuckerberg Institute for Water Research, and Unit of EnVironmental Engineering, Ben-Gurion UniVersity, P.O. Box 653, Beer-SheVa 84105, Israel ReceiVed: NoVember 25, 2007; ReVised Manuscript ReceiVed: April 11, 2008
Model “ordered” heterogeneous ion exchange membranes are made with ion exchange particles heaving ion exchange capacity in the range 3 to 2.5 meq/gr (dry basis) and diameters ranging from 37 to 7 µm and 2 component room-temperature vulcanizing silicon rubber as a polymeric matrix, by applying an electric field normal to the membrane surface during preparation. These membranes were shown to have an improved ionic conductivity compared with “nonordered” membranes based on the same ion exchange content (for instance, at 10% resin content “nonordered” membranes show 95-97% of the expected (theoretical) were obtained with dilute solutions. Two cation-exchange membranes were placed on both sides of the tested membrane (RALEX-CMH produced in MEGA a.s. Strazpod Ralskem). The membrane between the positive electrode compartment and the second compartment was an anion exchange membrane (RALEX-AMH produced in MEGA a.s. Strazpod Ralskem). By placing the tested RTV membrane between two commercial cation-exchange membranes, it was ensured that the solution concentrations on both sides of the tested membrane remain constant. The cathode and the anode of the membrane cell were connected to an EG&G 236 potentiostat (Princeton Applied Instruments) operated with an M270 software. The potentiostat was used to apply linear DC voltage changes at the range 8 or 4 V and a sweep rate of 1 mV/sec across the membrane cell. Two data-loggers (Extech Instruments, model Multipro 530) connected to a PC were used to acquire the current and the membrane potential readings. Figure 2 also shows a scheme of the setup used to attain these measurements. The current measurements were taken by connecting an ampere meter in series with the membrane cell. During the experiments, the voltmeter and the ampere-meter readings were recorded simultaneously every 10 s, and the information was saved in a file for data processing.
Figure 3. Cell for measuring the electrical conductance of the ion exchange resins.
2.4. Resin Conductivity. For purposes outlined below the electrical conductivity of the ion exchange material used in this study had to be determined. This was based on the procedure developed by Sauer et al.21 using an apparatus shown in Figure 3. Two platinum electrodes were installed in a glass burette (1.0 cm diameter) equipped with a Teflon stopcock. The lower platinum electrode was kept stationary, while the height of the upper electrode was adjustable. Conductivity meter (El-Hamma Instruments, Israel, Model TH-2300) was used for these measurements. The cell constant was determined by filling the burette with a KCl solution of known concentration, and comparing the measured conductance value to that of a commercial electrode with a known cell constant. A well washed, K+ form ionexchange resin was equilibrated with different KCl solutions (in the range 0.0025 to 0.6 N), and the mixture was poured into the burette. The ion exchanger was then left to settle in the burette. Once the resin became close-packed in the burette (typically after 8-10 h), the upper platinum electrode’s height was adjusted to become in full contact with the resin with a minimum pressure applied to the particles. The clear indication for contact was a sharp rise of the measured conductivity. The conductance and the height of the resin column were then recorded. In addition, the specific conductivity of the solution that was in equilibrium with the saturated resin was documented. 3. Results and Discussion 3.1. Morphology of Ordered and Nonordered Membranes. Cross sections of ordered and nonordered RTV-based ion exchange membranes are shown in Figure 4. It is clearly seen that under the influence of an electric field the randomly distributed ion-exchange particles become organized in long continuous chains aligned along the electric field. Most of the particles in the ordered form are actually in contact. If not, they are, on average, in a much closer proximity, as compared with the situation in the nonordered samples. The close contact between the particles can also be wellobserved in Figure 5, in which surfaces of 10 wt % resin RTV membranes were photographed after equilibration in methylene blue solution. Since the RTV is a transparent material, the photographs show the dyed particles inside the membrane and on its surface. Although both membranes contained the same amount of ion-exchange resin, the ordered membrane captured more of the cationic dye. In the ordered membranes, the methylene blue penetrated the membrane and many more
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Figure 4. Light microscopy photographs of cross sections in RTV membranes containing 5 wt % of ion-exchange resin with an average particle diameter of 37 µm. Right: ordered membrane prepared under an electric field of 1500 [V/cm]. Left: a nonordered membrane.
Figure 5. Light microscopy photographs. Surfaces of methylene blue dyed RTV membranes with 10 wt % resin, with an average particle diameter of 37 µm. Right: ordered membrane prepared under an electric field of 1500 [V/cm]. Left: nonordered membrane.
particles were colored compared with the nonordered membrane. This indicates a better contact between the particles aligned within the membrane. 3.2. Membrane Ionic Conductivity. Effect of Field Strength. The effect of the electric field on the specific conductivity of the membranes at constant resin content is depicted in Figure 6. It is clear that under the experimental conditions described above the specific conductivity does not considerably change at electric fields higher than 440 [V/cm]. Accordingly, all of the experiments were conducted at electric fields higher than this value. Effect of Resin Content. The dramatic effect of ordering the ion-exchange resin particles on the specific conductivity of the membranes is evident from Figure 7. The percolation threshold decreases significantly under the influence of the electric field: The nonordered membranes become conductive above resin content of 30 wt %, whereas the ordered membranes conductivity is measurable even at 5 wt % resin. Furthermore, over a particle concentration range of 10 to 30 wt %, the oriented membranes are 105 times more conductive than membranes prepared in the absence of the electric field. The difference in conductivity between ordered and nonordered membranes becomes less distinct as the resin content increases.
Figure 6. Specific conductivity of RTV membranes as a function of the applied electric field; 30 wt % ion-exchange resin, average particle diameter of 37 µm.
The reduced difference is explained based on Figure 4 and Figure 8. When the resin content of the membrane is low, ordering the membrane has a greater effect since the randomly
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εp - εc εp + 2εc
(4)
σp - σc σp + 2σc
(5)
βdielec ) βcond ) τ ) ε0
Figure 7. Specific conductivity vs resin content, in RTV membranes containing 37 µm diameter cation exchange resin. The ordered membranes were prepared under an AC electric field of 900-1500 [V/cm].
dispersed particles that are not in contact, get in touch with each other when aligned (Figure 4). However, as the resin content increases, the homogenously dispersed particles in the nonordered membrane are in greater proximity, and the contact between them becomes more efficient (Figure 8). At these concentrations, the effect of the electric field on improving the contact between the particles becomes much smaller though not negligible. (It should be emphasized that the data in Figure 7 is presented on a semilogarithmic scale. At resin concentrations 50-60 wt %, the conductivity of the ordered membranes is twice as high as that of the nonordered membranes). Effect of Field Frequency. Figure 9 shows the specific conductivity of membranes that were prepared with constant resin concentration under the same electric field strength but at different fabrication frequencies, at the range 17.5 to 10 000 [Hz]. It is evident that no significant trend with frequency can be observed. Nevertheless, membranes that were prepared under a DC electric field of 900 [V/cm], turned out to be nonconductive, apparently due to electrophoresis of the particles toward the electrodes. According to the Maxwell-Wagner polarization model,9,22,23 particle polarization and interparticle interactions at DC and low frequency AC electric fields are controlled by the conductivities of the particle and the surrounding medium. At high frequencies, mobile charges respond slowly to the electric field, leading to polarization dominated solely by the permittivities. At intermediate frequencies, both permittivity and conductivity play a role. In the Maxwell-Wagner theory, the permittivities and conductivities of the individual phases are assumed independent of frequency. According to the pointdipole approximation model,9 the interaction force, F, between two spheres in an AC electric field is proportional to the square of the electric field strength (E0), namely: 2 F ∝ βeff E20
(2)
where βeff, the effective relative polarizability, is a function of the field frequency, ω, according to9 2 βeff )
where
β2dielecω2τ2 + β2cond 1 + ω2τ2
(3)
εp + 2εc σp + 2σc
(6)
Here, εp, εc, σp, and σc are the dielectric constants and conductivities of the particles (p) and the continuous medium (c), respectively, 0 is the vacuum permittivity, and τ is the Maxwell-Wagner relaxation time. For particles with surface conductivity λs, the particles conductivity is given as σp + 2λs/ a, with a presenting the average particle surface area. For ion exchange particles, it is safe to assume that the contribution of the surface conductivity is negligible with respect to that of the bulk ionic conductivity. The components of the Maxwell-Wagner polarization (eqs 4-6) followed by βeff (eq 3) were calculated for the RTV matrix and the cation-exchange resin particles (with mean diameter of 37 µm). The values assigned for the parameters of the RTVresin system are presented in Table 3. RTV dielectric constant was obtained from the manufacturer’s catalog, and its electrical conductivity was assumed negligible. The dry resin conductivity was obtained by calculating the ratio between the specific conductivities of wet and those of the dried ordered membranes, followed by dividing the wet resin specific conductance (determined by the procedure described in the Experimental) by this ratio. Resin permittivity was calculated from measurements of the electric capacitance of several ordered dry membranes as follows: assuming that within the ordered heterogeneous membranes all of the particles are arranged in separated chains, each having a length equal to the membranes thickness; the measured electric capacitance is then considered a result of two capacitors connected in parallel, one carrying a dielectric constant of the polymeric matrix and the other, that of the dry resin phase. Consequently, the dielectric constant of the dry resin particles p was calculated by using the expression
εp )
εmemb - (εc × Vp) Vc
(7)
where Vp and Vc are the volume fractions of the resin particles and the RTV matrix, respectively. The results for these calculations gave an average value of 13 ( 5 for the resin permittivity. It should be pointed out that determining the dielectric constant and conductivity of the dry resin particles were necessary since none of these values could be tracked in the literature. The permittivity mismatch was found smaller than the conductivity mismatch. Thus, the particle interactions in the RTV/resin system should decrease with increasing field frequency,9 and the ordering of the particles in the membrane is expected to decline in high frequencies. Figure 9 shows the effective relative polarizability squared, calculated by taking into account the values in Table 3 and eq 3, as well as the measured membrane conductivities as a function of field frequency. As shown in Figure 9, the conductivities do not change at the measured frequency range, in complete correlation to the behavior of calculated βeff. This predicts that ordering extent of the particles within the membrane and thus its conductivity are expected to start declining only when field frequency exceeds values of 104 [Hz]. As the maximum frequency of the AC power source in this study is 104 [Hz], this range could not be reached.
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Figure 8. SEM photographs, of cross section in RTV membranes containing 40 wt % of ion-exchange resin with an average particle diameter of 37 µm. Left: ordered membrane that was prepared under an electric field of 1500 [V/cm]. Right: Nonordered membrane.
Figure 9. Specific conductivity of RTV ordered membranes with 20 wt % of ion-exchange resin, average particle diameter 37 µm, and effective relative polarizability square, βeff2, (continuous curve) calculated for the RTV matrix and the polystyrene-co-DVB resin particles, as a function of the fabrication frequency.
TABLE 3: Dielectric Constants and Conductivities of the Particles and Medium Used for Calculating the Effective Relative Polarizability (βeff) property
RTV-polymeric matrix
cation-exchange resin (dry)
dielectric constant specific conductivity [mS/cm]
εc ) 3 σc ∼ 0
εp ) 13 σp ) 10-6
Effect of Particle Size. In order to determine the influence of the particle size on the conductivity of ordered membrane, commercial cation-exchange resins of three specified particle diameter ranges but with the same ionic capacity were used. The data shown in Figure 10 reveals that, in the size range studied, there seems to be no significant trend of the membrane conductivity with respect to particle’s size. It should be noted that the specific conductivities obtained with these particles are smaller than those shown, for example, in Figure 7. This difference is attributed to the lower ion exchange capacity of the presently used resins. It was suggested by Oren et al.6 that the conductivity of an ordered membrane reach an optimum when all of the particles
Figure 10. Specific conductivity of 20 wt % resin (PRP-X400 by Hamilton) RTV ordered (electric field of 1500 [V/cm]) and nonordered membranes as a function of the mean particle diameter.
are in close contact and arranged in chains extending between the two membranes faces. Under ideal conditions, membrane conductivity is proportional just to the volume fraction of the particles in the membrane and to their specific ionic conductivity. The results above show that, under the experimental conditions used in this study, the majority of the particles indeed contribute to membrane conductivity via a close contact chain arrangement. However, it should be noted that various authors point to some important effects that particle’s shape and size have in electrorheology and membrane preparation. For instance, it was shown by Lenga´lova´ et al.24 that not only the polarizability of suspended particles but also the particle shape and size are important for the extent of particle’s alignment in electrorheological fluids. Sugimoto25 used ion-exchange resins as the dispersed phase in electroviscous fluids and showed that ionexchange resin with smaller particle diameter develops larger induced shear stress. In other studies (e.g., Jordan and Shaw26), it was claimed that large particles are more prone to sedimentation and to slow electrorheological response.
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Ilim )
Figure 11. Current-voltage curves for RTV ordered membrane with 30 wt % ion-exchange resin, average particle diameter of 37 µm, prepared at 1500 [V/cm]. NaCl concentration in compartment 3 in Figure 2 is noted adjacent to each plot.
zDi Fcb δ(t m - t b)
(8)
In eq 8, F is the faraday constant, Di is the diffusion coefficient of ion i, δ is the boundary layer thickness, tm is the counterion transport number within the membrane, z is the ion valence, and tb is the transport number in the solution at the boundary region. It is assumed that D, δ, tm, and tb are independent of the solution concentration. Effect of Resin Concentration and Particle Ordering on Limiting Current Densities. Limiting current densities were determined for ordered and nonordered membranes for following the influence of ordering on the transport properties of the membranes. It should be noted that only the nonordered membranes with resin concentrations exceeding the percolation threshold with respect to membrane conductivity could be measured. The results presented in Figures 13 and 14 show that the limiting current density increases with increase of the resin content for both ordered and nonordered membranes. In addition, it is evident from Figure 14 that limiting current densities for the ordered membranes are significantly higher compared with those for the nonordered membranes made with the same resin concentration.
Figure 12. Limiting current densities as a function of the bulk NaCl concentration for an ordered RTV membrane containing 30 wt % ionexchange resin, average particle diameter of 37 µm, prepared under an electric field of 1500 [V/cm].
Heterogeneous cation exchange membranes that were prepared with polyvinyl chloride as a binder for a cation exchange resin particles showed reduced mechanical strength and lower specific conductivities with decreased particle sizes.27 3.3. Current-Voltage Characteristics. Figure 11 presents a set of typical current-voltage curves taken with an ordered membrane for different concentrations in compartment 3 of the cell shown in Figure 2. The three well-known regions of the current-voltage curve can be clearly distinguished in all plots:11,18,20,28,29 the Ohmic region at low current densities (region I), changing into a current plateau due to diffusion controlled processes (region II), and then to the overlimiting current region (III) as the voltage is increased further. As discussed above, it is well-established today that region III in cation exchange membranesisduetoenhancediontransportviaelectroconvection.28,29 Curves such as those shown in Figure 11 are treated following the procedure suggested by Cowan and Brown19 in order to determine the limiting current densities. According to this method, V/I is drawn as a function of I-1, resulting in an inflection in the plot at Ilim-1. A clear linear behavior of Ilim versus the concentration of ions, Cb in the entering side of the membrane, is shown in Figure 12, as predicted by eq 8 derived from Fick’s law,30
Figure 13. Current-voltage curves of RTV ordered membranes with different resin content. Average particle diameter of 37 µm; Electric field is 1500 [V/cm]. In all cases, solution in compartment 3 of the cell shown in Figure 2 is 0.050 [N] NaCl.
Figure 14. Limiting current densities of RTV ordered and nonordered membranes as a function of the bulk NaCl solution concentration. E stands for the ordered membranes. Average particle diameter of 37 µm; electric field is 1500 [V/cm].
Highly Ordered Heterogeneous Ion-Exchange Membranes
Figure 15. % Atomic fraction of K+ (as the counterion) on the surface of ordered and nonorderd membranes determined by EDS, as a function of resin concentration; average particle 37 µm; ordered membranes prepared under an electric field of 1500 [V/cm].
Figure 16. Schematic view of the current line distribution close to a heterogeneous membrane surface taken from Volodina et al.31
As a step toward elucidating the phenomena shown above, energy dispersion spectrometry (EDS) measurements were made with both types of membranes. These made possible estimating the concentration of cation exchange groups on the membrane surface. The results from the EDS measurements presented as the percent atomic fraction of K+ (as the counterion) on the membrane surface as a function of resin concentration within the membranes are shown in Figure 15. These clearly demonstrate that the surface concentration of ion-exchange groups is significantly higher for the ordered membrane as compared with that for nonordered membranes. These results provide a possible explanation for the higher limiting currents found for the ordered membranes. According to Volodina et al.,31 the membrane surface morphology has the main effect on the transport properties. When a direct electric current is applied to a smooth and uniform membrane with electrodes parallel to the membrane surface, assuming a lateral uniform diffusion layer, the current density lines are uniformly distributed normal to the surface. If, however, the membrane surface is not homogeneous, such as the case with heterogeneous ion exchange membranes, the current lines deviate from uniformity as shown schematically in Figure 16, namely, the local current density is higher in the regions with high conductivity. The diffusion of electrolyte from the bulk solution to the heterogeneous surface occurs both normal to the surface and tangentially.13,31 The latter takes place in the solution along the nonconducting areas. The lengthening of the diffusion path is equivalent, in essence, to an increase in the effective thickness
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Figure 17. Limiting current densities of ordered membranes as a function of the bulk NaCl solution concentration. Membranes contain 20 wt % ion-exchange resin, average particle diameter 37 µm, prepared with an AC electric field of 1500 [V/cm] and frequencies at the range 17.5 to 5000 Hz.
of the diffusion layer, if the whole membrane surface is assumed available for ion exchange. Thus, for membrane surfaces containing more conducting domains, the nonconducting areas are smaller and the distortion of the current lines is less pronounced resulting in higher average current densities as in the case of the ordered membranes. In addition to the above, it is well-established that the thickness of the diffusion boundary layer is determined by the hydrodynamic conditions at the membrane-electrolyte interface. Since all current-voltage curves in this study were attained under the same hydrodynamic conditions, it is expected that the boundary layer thickness would have the same value. Thus, the morphology of the membrane surface should have the most effect on transport properties. It is possible that the ordered configuration of the particles in the membrane “pushes” more particles to the surface, creating higher concentration of ion exchange particles on the membrane surface. In this situation, the local current density at each ion exchange domain on the membrane surface is smaller for the ordered membranes as compared with that for the nonordered membranes, leading to reduced polarization and higher limiting current densities for the former. Effect of Frequency on the Limiting Current Density of Ordered Membranes. Limiting current densities were determined for ordered membranes with constant resin content, prepared under the same electric field strength but at different frequencies. Each experimental point depicted in Figure 17 is obtained from membrane duplicates, and the error bars are determined from the standard error of the mean. The results show that in essence there is no significant difference between the limiting current densities of these membranes. This suggests that the ordering process was not influenced by the different frequencies of the AC electric field at the range used in this study. This conclusion is supported by the conductivity measurements of these membranes as discussed above. Effect of Particle Diameter. A typical behavior of the current-voltage curves taken for membranes with constant PRPX400 resin content of 20 wt %. and a constant solution concentration but with different particle sizes is shown in Figure 18. Two points of interest should be emphasized: First, a limiting current plateau is not noticeable with any of the particle sizes, and second, the current density becomes larger as the particles are smaller.
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Figure 19. Schematic view of the current line distribution at heterogeneous conductive surfaces. Both surfaces contain the same fraction of conducting domains.
Figure 18. Current-voltage curves in 0.050 N NaCl and voltage sweep rate of 1 mV/cm for ordered membranes containing 20 wt % PRPX400 Hamilton resins with different particle diameter (indicated adjacent to the plots). Electric field for membrane preparation, 1500 [V/cm].
It is likely that the absence of the limiting current plateau in the plots is due to the relatively large ohmic resistance of these membranes. It should be recalled that the ion exchange capacity of the PRP-X400 resins is nearly twice as low as that for the 37 µm particles. Therefore, their conductivity should be much lower and so is the conductivity of the membranes prepared with them. By comparing, for instance, the I-V curve for 20 wt % resin content in Figure 13 (mean particle diameter 37µm) with that of the 30-50 µm in Figure 18, it is evident that in both cases the plateau is not visible. However, in Figure 13, the plateau becomes evident as the resin content increases to 30 wt % and more. It should be concluded therefore that in the two cases the I-V curves contain a large ohmic component, dominating the contribution of other important features such as the limiting current plateau. In the case of Figure 13, it is due to the low resin content, while in the case of Figure 18, it is due to both the low resin content and its lower ionic conductivity. The increasing current densities with the decreasing of particle size imply that the membranes with the smaller particles are less polarizing. In conjunction with the discussion above, this should be attributed to more homogeneously distributed ionic flux on the membrane surface as the ion conductive domains are getting smaller. If a model of a perfectly ordered membrane is assumed in which the spherical particles form cylindrical channels of identical volume across the membrane, each having a length equal to the membrane thickness, then it can be easily shown that for a specific resin content the conducting area on the membrane surface should be independent of the channel (particle) diameter. Analysis of the potassium surface atomic percent (similar to that in Figure 15) on ordered membranes prepared with particles of different diameters and the same concentration shows that the surface concentration of cation exchange groups is higher for membranes with smaller particles. These results are inconsistent with the above model, indicating that the ordering process is more efficient for the smaller particles (smaller particles are more easily suspended in the polymeric matrix and less affected by gravity and friction with the polymeric matrix while moving under the influence of the electric field).
By following the discussion above and on the basis of Volodina et al.,31 the effect of the particle size on the I-V characteristics can be ascribed to the higher concentration of cation-exchange groups on the membrane surface. Figure 19 is an extension suggested to the model presented in Figure 16. This figure shows an illustration of two heterogeneous membranes containing the same fraction of conducting domains on the membrane surface but with different dimensions. At the smaller conducting domains, the distortion of the current lines is less significant; in this case, the effective thickness of the diffusion layer decreases and the average current density is higher. Conclusions The electrorheological concept applied in this study to heterogeneous ion exchange membranes presents an interesting and a new valuable approach in preparing these membranes for electrodialysis and fuel cell applications. Nevertheless, presently, it seems that a large scale application is far from feasibile because of the many technological hurdles that have to be overcome. However, controlling the extent of orientation of ion exchange domains within a polymeric matrix, finally resulting in the form of heterogeneous ion exchange membrane barriers, has important implications in understanding ionic transport mechanisms through these ion selective membranes. Three distinct consequences of orienting the ion exchange domains into chains spanning along the ion conductance lines within the membrane should be highlighted: First, the percolation threshold of the ion exchange capacity toward ionic conductivity is significantly reduced, leading to high enough ionic conductivity but with less swelling; Second, because of an increase of surface concentration of the ion conductive domains, resulting in a more homogeneous characteristic of the membrane surface, concentration polarization is reduced, leading to higher limiting current densities; Third, oriented membranes with reduced sizes of the ion conductive domains are less polarizing because of the increase of their surface concentration. These properties render the membranes better than nonordered membranes with respect to their stability and resistance to ion transport. Acknowledgment. The authors are indebted to the FleisherCoppersmith and the Tessler Funds for supporting this study. Appendix List of Symbols a ) Average particle surface area [cm2] dair )Thicknesses of the air gap [cm] Cb ) Bulk concentration [M]
Highly Ordered Heterogeneous Ion-Exchange Membranes dmemb ) Thicknesses of membrane [cm] Ememb ) Effective electric field on membrane [volt cm-1] F ) Interaction force between two spheres [dyne] V0 ) Applied total voltage [V] E0 ) Electric field strength between two spheres [volt cm-1] Vp ) Volume fraction of the resin particles Vc ) Volume fraction of the RTV matrix V ) Total voltage across the membrane [V] Vmem ) Membrane potential [V] RS ) Electrical resistance of the solutions between the electrodes [Ω] Ilim ) Limiting current density [A cm-2] I ) Current density [A cm-2] F ) The faraday constant [coulomb equivalent-1] Di ) Diffusion coefficient of ion i [cm2 s-1] tm ) Counter ion transport number within the membrane tb ) Transport number in the solution at the boundary region z ) Ion valence air ) Air gap dielectric constant memb ) Membrane dielectric constant βeff ) Effective relative polarizability εp ) Particle dielectric constant εc ) Dielectric constant of the continuous medium σp ) Conductivity of particles [S cm-1] σc ) Conductivity of the continuous medium [S cm-1] 0 ) Vacuum permittivity [s2coul2cm-3g-1] τ ) Maxwell-Wagner relaxation time [s] λs ) Surface conductivity [S cm] δ ) Boundary layer thickness [cm] Abbreviations ASTM RTV
American Society for Testing and Materials Room-Temperature Vulcanizing
References and Notes (1) Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962. (2) Shah, B. G.; Shahi, V. K.; Thampy, S. K.; Rangarajan, R.; Ghosh, P. K. Desalination 2005, 172, 257. (3) Strathmann, H. Ion-Exchange Membrane Separation Processes; Elsevier: Amsterdam, 2004. (4) Klimova, Z. V.; Saldadze, G. K. Zhurnal Prikladnoi Khimii (SanktPeterburg, Russian Federation) 1985, 58, 524.
J. Phys. Chem. B, Vol. 112, No. 31, 2008 9399 (5) Strathmann, H. Electrodialysis; In Membrane Handbook; Ho, W.S.W., Sirkar, K.K., Eds.; Chapman and Hall: New York, 1992; pp 219262. (6) Oren, Y.; Freger, V.; Linder, C. J. Membr. Sci. 2004, 239, 17. (7) Dassanayake, U. M.; Offner, S. S. R.; Hu, Y. Phys. ReV. E 2004, 69, 021507. (8) Kanu, R. C.; Shaw, M. T. J. Rheol. 1998, 42, 657. (9) Parthasarathy, M.; Klingenberg, D. J. Mater. Sci. Eng., R 1996, 17, 57. (10) Krol, J. J.; Wessling, M.; Strathmann, H. J. Membr. Sci. 1999, 162, 145. (11) Mulder, M. Basic Principles of Membrane Technology, 2nd ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996. (12) Simons, R. Desalination 1979, 28, 41. (13) Choi, J.-H.; Park, J.-S.; Moon, S.-H. J. Colloid Interface Sci. 2002, 251, 311. (14) Rubinstein, I.; Shtilman, L. J. Chem. Soc., Faraday Trans. II 1979, 75, 231. (15) Rubinstein, I. Physics of Fluids A 1991, 3, 2301. (16) Rubinstein, I.; Maletzki, F. J. Chem. Soc., Faraday Trans. 1991, 87, 2079. (17) Rubinstein, I.; Zaltzman, B. Phys. ReV. E 2000, 62 (2), 2238. (18) Barragan, V. M.; Ruız Bauza, C. J. Colloid Interface Sci. 2002, 247, 138. (19) Cowan, D. A.; Brown, J. H. Journal of Industrial and Engineering Chemistry 1959, 51, 1445. (20) Tanaka, Y. J. Membr. Sci. 2003, 216, 149. (21) Sauer, M. C., Jr.; Southwick, P. F.; Spiegler, K. S.; Wyllie, M. R. J. Journal of Industrial and Engineering Chemistry 1955, 47, 2187. (22) Espin, M. J.; Delgado, A. V.; Dura´n, J. D. G. J. Colloid Interface Sci. 2005, 287, 351. (23) Liu, B.; Shaw, M. T. J. Rheol. 2001, 45, 641. (24) Lenga´lova´, A.; Pavl’ınek, V.; Sa´ha, P.; Quadrat, O.; Stejskal, J. Colloids and Surfaces A: Physicochemical and Engineering Aspects 2003, 227, 1. (25) Sugimoto, N. Bulletin of JSME. 1977, 20, 1476. (26) Jordan, T. C.; Shaw, M. T. IEEE Trans. Electric Insul. 1989, 24 (5), 849. (27) Vyas, P. V.; Shah, B. G.; Trivedi, G. S.; Ray, P.; Adhikary, S. K.; Rangarajan, R. ReactiVe and Functional Polymers 2000, 44, 101. (28) Ibanez, R.; Stamatialis, D. F.; Wessling, M. J. Membr. Sci. 2004, 239, 119. (29) Balster, J.; Yildirim, M. H.; Stamatialis, D. F.; Ibanez, R.; Lammertink, R. G. H.; Jordan, V.; Wessling, M. J. Phys. Chem. B 2007, 111, 2152. (30) Krol, J. J. Monopolar and Bipolar Ion Exchange Membranes. Mass Transport Limitations. Ph.D. Thesis, Twente University Press: Enschede, 1997. (31) Volodina, E.; Pismenskaya, N.; Nikonenko, V.; Larchet, C.; Pourcelly, G. J. Colloid Interface Sci. 2005, 285, 247.
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