Ind. Eng. C h e m . R e s . 1988,27,983-987
983
Artificial Membranes from Multiblock Copolymers. 6. Water and Salt Transports through a Charge-Mosaic Membrane Hiroshi Itou,? Masatoshi Toda, Koji Ohkoshi, Minoru Iwata, and Teruo Fujimoto D e p a r t m e n t of Materials Science and Technology, Technological University of Nagaoka, Kamitomioka-cho, Nagaoka 949-54, J a p a n
Yoshiyuki Miyaki* and Toshiya Kataoka Scientific Instrument Division, T O S O H Corporation, 2743-1 Hayakawa, Ayase-shi, Kanagawa 252, J a p a n
Water and salt transports through a charge-mosaic membrane prepared from a pentablock copolymer of the ISBAI type were investigated by using aqueous solutions of KC1. The membrane showed a very high permeability for KC1, pronounced negative osmosis, and piezodialysis. The data were analyzed according to the phenomenological equation by Kedem and Katchalsky. According to the phenomenological theory by Kedem and Katchalsky (1963), a charge-mosaic membrane, which consists of parallel arrays of anion-exchange and cationexchange microelements passing through the membrane, shows an enhanced salt transport and negative osmosis for an aqueous salt solution. Such a transport behavior of a charge-mosaic membrane was first predicted by Sollner (1932) and practically observed by some authors (Neihof and Sollner, 1950,1955; Carr and Sollner, 1964; Weinstein and Caplan, 1968, 1970; Weinstein et al., 1973; Igawa et al., 1985) with model membranes. For example, Weinstein et al. (1973) reported that the membrane prepared by embedding cation- and anion-exchange resin powders in a silicone rubber bed exhibited salt permeability of 50-100 times that of the cation-exchange or anion-exchange control and reflection coefficient of about -1 for dilute KC1 solutions. Recently, we fabricated a charge-mosaic membrane made of a very fine domain structure from pentablock copolymers of the ZXZ'YZ type and have already published the detailed fabrication method (Matsushita et al., 1980; Funabashi et al., 1983; Miyaki et al., 1984a,b;Miyaki and Fujimoto, 1983; Takahashi et al., 1986),brief transport behaviors of salt and water (Fujimoto et al., 1984a,b; Miyaki et al., 1984b), and transport behaviors of various organic and inorganic substances (Hirahara et al., 1986). These reports suggest that our membrane can be made to be of practical use in the field of desalination or separation of organic species even if their molecular weights are low. In this work, in order to reveal the basic characteristics of this charge-mosaic membrane, we study experimentally the salt and water transports for KC1 solutions in detail under the condition where concentration polarization near the membrane surfaces is suppressed as far as possible.
Experimental Section Membrane. The membrane used in this work was fabricated from a four-component pentablock copolymer of the ISBAI type, poly(isoprene-b-styrene-b-butadiene-b(4-vinylbenzyl)dimethylamine-b-isoprene)(TUN 1013), which was synthesized by a sequential anionic polymerization. The molecular characteristics of the pentablock copolymer were shown in the preceding paper (Takahashi et al., 1986). The fabricating method is as follows: A film was cast on mercury from a benzene solution of the starting pentablock copolymer of initial concentration 5 wt % by 'Present address: Central Research Laboratory, Sumitomo Bakelite Co. Ltd., 495, Akiba-cho, Totsuka-ku,Yokohama, 245 Japan. 0888-5885/88/2627-0983~01.50/0
evaporating benzene slowly at 25 "C for a period of 4 days. It was then treated successively with methyl iodide vapor, sulfur monochloride, and chlorosulfonic acid in order to introduce anion-exchange and cation-exchange groups into the microseparated A and S domains, respectively, and cross-link I and B domains. The charge-mosaic membrane finally obtained had regularly repeated lamellae in the order, -S--DC-A+-DC-, where S- is the sulfonated S (cation-exchange) layer, A+ the quaternized A (anion-exchange) layer, and DCthe cross-linked I and B (neutral) layer (Takahashi et al., 1986). Each of the lamellae was about 20 nm in thickness. Anion-exchange and cation-exchange capacities of the membrane were 1.04 and 1.06 mequiv/g of dry resin, respectively, the cation transport number for 0.01 and 0.02 mol/L of aqueous solutions of KC1 was 0.55, and the thickness was 100 pm. The anion-transport number of the anion-exchange precursor (only quaternized membrane of the starting pentablock copolymer) was 0.97. On the other hand, a cation-transport number of 0.97 was observed for the cation-exchange membrane prepared by cross-linking and sulfonating the IS1 triblock copolymer, poly(is0prene-bstyrene-b-isoprene) (Miyaki et al., 1984b). These facts suggest that the anion-exchange and cation-exchange domains of the charge-mosaic membrane are highly permselective. Measurement of Water and Solute Flows. Water and salt flows through the charge-mosaic membrane were investigated by use of the cell shown in Figure 1. It consists of two water-jacketed 100-mL compartments (I and 11) separated by the membrane, two horizontal capillaries with inner diameters of 0.884 mm (I side) and 0.889 mm (I1 side) and length of 1 m, two stirring propellers of Teflon in the respective compartments, and platinum black electrodes in compartment 11. Compartments I and I1 were filled with dialysand and dialyzate solutions, respectively, which were vigorously stirred with the propellers by rotating external magnets and were thermostated at 25.0 "C by circulating thermostated water into the water jackets throughout the measurements. The rotating rate of the propellers was set to about 1000 rpm. The effective area of membrane was 3.14 cm2. The volume flow was measured by reading the meniscus positions in the capillaries at appropriate intervals. The conductance of the dialyzate solution was measured at the same time with LCR meter ZM-341 (NF Circuit Design Block Co., Ltd.) connected to the platinum black electrodes. Water flux was determined from the average slope of the plots of volume changes of dialyzate and dialysand solutions against time. The dialysand solution was kept 1988 American Chemical Society
984 Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988
L %/
r
water 25°C
I
I \
1
Figure 1. Schematic diagram of the cell used for the measurements of salt and water flows: (1)membrane; (2, 3) compartments I and 11; (4)capillaries; ( 5 ) three-way stopcocks; (6) stirring propeller; (7) Teflon plate; (8) water jacket; (9) magnet; (10) platinum black electrodes.
within 4% of the initial concentration of KC1 throughout the measurements. The concentration of dialyzate solution, CII, varied more rapidly than that of dialysand solution, CI, after the start of the experiment because the salt concentration of the dialyzate solution was lower than that of the dialysand solution. Therefore, the actual concentration of dialyzate solution at the moment when water flux was measured was determined from conductance of the dialyzate solution. Salt flux was calculated from the increasing rate of conductance. Another cell which has no horizontal capillary was used for more detailed investigation of solute flow through the charge-mosaic membrane. In this case, the dialyzate solution was pumped from a large reservoir to keep the KC1 concentration in the dialyzate unchanged during the experiment, and salt flu was determined from the decreasing rate of the KC1 concentration in the dialysand. The detailed explanation of the measurement method has been given in the preceding paper (Hirahara et al., 1986). Piezodialysis experiments were carried out with a 0.01 mol/L of aqueous solution of KC1, using a batch-type cell in which one membrane surface was in contact with the KC1 solution (inner solution) vigorously stirred and the other surface was in contact with a permeant solution. The inner solution was pressurized at 30-80 atm by nitrogen. The effective area of the membrane was 12.6 cm2,and the volume of the inner solution was about 300 mL. The KC1 concentration of the permeant solution was determined by use of an ion chromatography (Toyo Soda Mfg. Co.) equipped with Toyo Soda's IC-Anion-PW column and CM-8000 conductometer.
Result and Discussion Nonequilibrium Thermodynamic Equation. According to the nonequilibrium thermodynamic analysis by Kedem and Katchalsky (19631, water (volume) and salt flows, J, and J,,respectively, are expresaed by the following equations when the driving forces are hydrostatic pressure Ap, osmotic pressure AT, and chemical potential difference Ap, due to the concentration difference: J, = Lp"(Ap - AT) + C,Lpm(l- a,)Ap, (la) J, = C,L,"(l - a,)(Ap - AT) + C,wm'ApS
(lb)
where Lpmis the filtration coefficient, a, the reflection coefficient, w,' the solute permeability, and C, the logarithmic average concentration defined by the expression, C , = (C, - CII)/ln(Cl/CII). Taking into consideration the
circulating current analysis on a charge-mosaic membrane by Weinstein et al. (1972), C,L "(1 - a,) and Cswm' in eq l a and l b become constant and do not vary with the salt concentration when the membrane consists of sufficiently fine ion-exchange domains, and Cr and CIr are negligibly smaller than the fixed-charge densities of the ion-exchange domains (i.e., the anion- and cation-exchange components are highly permselective) unless concentration polarization occurs on the membrane surfaces. In this case, flows are controlled only by intrinsic properties of the membrane. The phenomenological coefficients a and w,' are very important when we characterize the charge-mosaic membrane. In this work, they were determined as mentioned below, where Ap, of KC1 was approximately given by 2RT In (CdCII). The theoretical analysis on a charge-mosaic membrane (Kedem and Katchalsky, 1963) reveals that the filtration coefficient is approximately written in terms of only the intrinsic properties of each of the anion- and cation-exchange components of the membrane and, therefore, independent of a kind of solute and its concentration: the nonadditive term in Lpmdue to circulating current is negligibly small. Thus, the L," value of the charge-mosaic membrane used can be determined from water flow measurement by using a dialysand solution containing the proper nonelectrolyte which is not (or hardly) permeable through the membrane: the reflection coefficient for such a solute is close to +l. In this work, we chose saccharose as the nonelectrolyte solute. Thus, when Ap is zero, the water flow [J,(mix)] for a mixed solution of saccharose and KC1 can be given as J,(mix) = J,(suc) JJKC1) (24 J,(mix) = -L,"AT(suc) - LPmAT(KC1) C,Lpm(l- a,)Ap, (2b)
+
+
where (suc) and (KC1) represent the values due to saccharose and KC1, respectively. The L," value was determined from J,(suc) data. It then becomes possible to calculate the value of ,u for KC1 from the experimental data of the volume flow for a KC1 solution with eq la, and the value is calculated from the data of salt flow with eq lb. According to the theoretical treatment of a charge-mosaic membrane by Kedem and Katchalsky (1963), the electroosmotic factor F(0, - 8,) (cm3/mol) can be approximately given by (3) when the anion- and cation-exchange components of the charge-mosaic membrane are highly permselective, where JJAp,) and J,(Apd are, respectively, the chemical potential difference terms of J , and J, in eq l a and Ib, paand 8, are, respectively,the electroosmotic permeabilities of the anionand cation-exchange components, and F is the Faraday constant. Water and Salt Flows. In Figure 2a is shown the water flow (J,)for two kinds of dialysand solutions, one containing only 0.05 M KC1 as the solute and the other containing 0.05 M KC1 and 0.2 M saccharose, where J, is plotted against the KCl concentration C, of the dialyzate solution. In these measurements, KC1 solutions not containing saccharose were used as the dialyzate solution. Salt flux (J,)measured in the same course of the above water flux experiment is shown in Figure 2b only by way of suggestion. In this figure, it is seen that the values of J, and J , increased with decreasing CII {i.e.,increasing log (CI/CII)J,
Ind. Eng. Chem. Res., Vol. 27, No. 8, 1988 985 4 ,
3
. - I
'P
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I \
?
\
I
\
I
3x10-' OJ-OL-
lo-'
2 x10-'
10-1
.I
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,n
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Cp I rnol.L-' Figure 3. Reflection coefficient as a function of KC1 concentration of dialyzate solution. Closed circles represent the data measured under weak stirring.
l5
-I
h
I
\
4
6
' '
2~10-'
1 '
"'I
102 / mol, L-'
Cn
Figure 2. Water and KCl flows, J, (a, top) and J, (b, bottom), respectively,for two kinds of dialyeand solutions plotted against KC1 concentration of the dialysate solution: ( 0 , O ) single solution of KC1; (A, A) mixed solution of KC1 and saccharose; (0, m) JJmix) - J,(KC1). Closed data points represent the data measured under weak stirring.
and when the dialysand solution did not contain saccharose, water and salt flows occurred in the same direction, from the dialysand side (I) to the dialyzate side (11) (i.e., negative osmosis occurred). When the dialysand solution contained saccharose, J, assumed a negative value at CII = 0.05 mol/L (=CI) (Le., normal osmotic flow occurred), increased with decreasing Cn, and finally turned positive, while the J, value was in fair agreement with the data which were measured for the dialysand solution not containing saccharose. These facts indicate that, in our charge-mosaic membrane, the AT term (pressure-dependent term) of J, in eq 1 is comparable to the Ab, term, whereas the AT term of J, is negligibly smaller than the Aps term. In Figure 2a is plotted also the value of J,(mix) - J,(KC1) calculated from the measured values of J,(mix) and JJKC1). It is almost independent of KC1 concentration in dialyzate, and this fact suggests the validity of eq 2. The Lpmvalue calculated from the average of J,(mix) - J,(KCl) was 3.5 X cm3 dyn-' s-l. The reflection coefficient (a,) for KC1 was then estimated from J,(KCl) data by using eq l a with the LPmvalue. It is shown in Figure 3 together with C,(1 - u,). u, was a large negative value, and C,(l - r~,) was almost independent of Cn as expected for a well-performed charge-mosaic membrane. Figures 2 and 3 contain the data measured with dialysand and dialyzate solutions weakly stirred by use of the cell containing magnetic chips [refer to Figure 2 of the previous paper (Miyaki et al., 1984b)l only for comparison. The J, value was considerably lower than that for strong stirring, and therefore, the calculated um value was low, while the J,(mix) - JJKC1) value was close to that for strong stirring. This fact reflects the much greater sensitivity of u, to the circulating current effect caused by concentration difference of KC1 than Lpm: this effect is
c p I mo1.L-1
Figure 4. Salt flow as a function of KCl concentration of dialyzate solution for various KCl concentrations of dialysand solution: (0) 0.2 mol/L; (A) 0.05 mol/L; (0) 0.02 mol/L; (0) 0.01 mol/L.
apt to be influenced by concentration polarization on the membrane surface because of the very fine mosaic pattern of our membrane as discussed in the preceding paper (Hirahara et al., 1986). In Figure 4 is shown salt flow (J,)as a function of CII for various CI values. Each curve represents a monotonical increase in J, with decreasing CII; the curves for CI, 0.05 and 0.2 mol/L, were linear above 0.02 mol/L of CII, while below 0.02 mol/L of CI J, did not show such a linear increase against log CII and approached constant values differing by CIS The linear increase of J, is theoretically expected for a charge-mosaic membrane having a sufficiently fine geometric arrangement that consists of highly permselective anion- and cation-exchange regions. In this case, the AT term of eq l b becomes negligibly smaller than the Ap, term. The deviation from linearity is attributable to concentration polarization on the membrane surfaces caused by incomplete stirring of the solutions (Hirahara et al., 1986). Figure 5 shows J, and J, for KC1 solutions plotted against log CI, together with calculated phenomenological coefficients. They were measured with CI/Cn fixed to 2.0. In this figure, J, increases with increasing CIand J, follows a curve convex upward. If the flows are completely membrane-controlled, J, and C,(1 - cm) should be constant. The deviation of data points from the theoretical expectation is attributable to concentration polarization in the low CI range and a lowering of permselectivity in the high CI range. The J, values calculated from the tangents to the J, vs log CII curves in Figure 4 show a tendency to
986 Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988
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IA
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5
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7
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7
0
0.2
0.4
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c1 (sac) / m01.1-l Figure 7. Water and salt flows measured for mixed solutions of saccharose and KC1: they are plotted against saccharose concentration, CI(sac),of the dialysand solution.
0.01
1 .o
0.1
CI
I mo1.C'
Figure 5. Water and salt flows and calculated phenomenological coefficients measured for KCl solutions with CI/Cn fixed to 2 . 0 (0) water flow, (e) salt flow;(A)c,(1 - um); (a)F(& - &); (A)JBvalue calculated from the tangent to the J , vs log CrI curve in Figure 4;a, top; b, bottom. \
8r
AP latm
321
Figure 8. Results of piezodialysis experiment with a KCl solution salt enrichment E,; (0)volume flux J,. The of 0.01 mol/L: (0) dashed and dash-dot lines represent the calculated values of E, and J,., respectively.
3
1
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'
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1
1
1
1
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'
c,
i
'
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10-4
10-5
10-6
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Figure 6. Plot of salt permeability w,' vs C,: the symbols represent the same meanings as shown in Figure 4.
approach a constant value in the low CI range. The electroosmotic fador F(&,- &) (cm3/mol)calculated from these J , and J,data by the use of eq 3 is also shown in Figure 5b. F(& - &) is almost constant and ranges from 600 to 720 in the CI range studied, indicating that 1 mol of KC1 takes 30-40 mol of water along when it passes through the membrane irrespective of salt concentration. Figure 6 shows the plot of salt permeability wm' vs C,, which was calculated from the data shown in Figure 4. The data points show a tendency to follow a curve that monotonically decreases with increasing C,. The dash-dot line represents the theoretical prediction when salt flow is membrane-controlled, where Cswm' was arbitrarily allowed to assume 1.1 X 10-ls (mo12/(cm3dyn 9)). The data points
are close to the curve in the range of high C,, but they are far below the curve in the range of low C,. This is also attributable to concentration polarization. All data points could not be fitted by the theoretical curve by adjusting the C,w,' value. Water and salt flows were investigated for mixed solutions of saccharose and KCl. Here compartments I and I1 were filled with the mixed solution and a single solution of KC1, respectively, and J, and J, were measured by changing the saccharose concentration at side I (CI(sac)J with KC1 concentrations at I and I1 sides fixed to 0.2 and 0.04 mol/L, respectively. The experimental results are shown in Figure 7. J, showed negative osmosis (i.e., positive value) in the range of low CI(sac), rapidly decreased with increasing CI(sac),and turned negative in the range of high CI(sac). On the other hand, J , showed only a slight decrease. These data indicate that our chargemosaic membrane enables an effective desalination of solutions containing nonelectrolytes even if the concentration is very high. Piezodialysis. The results of the piezodialysis experiment are shown in Figure 8, where salt enrichment E, (%)
Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 987
I
0.2
0.4
In ( CIICx 1
0.6
0.8
Figure 9. Salt flow for KCl solutions which were measured with CII fixed to 0.01 mol/L and Ap = 0. The value of Csw,‘ calculated from mo12/(cm3 the slope of the best-fitted line for the data was 4.9 X dyn s).
and volume flux (J,)are plotted against the hydrostatic pressure difference, Ap. E, is defined by E , = lOO(CII/CI - 1) (4) where C, is the concentration of the high-pressure solution and C, is the concentration of the permeant solution. The curves in these figures represent the values of E, and J, calculated by the use of eq 1with Lpm,3.5 X cm3/(dyn mol/cm3, and Csw,’, 4.9 X s), C,(1 - c,), 7 X mo12/(cm3dyn s). This C,w,’ value was determined from the KC1 flow data shown in Figure 9, which were measured with Cn fixed to 0.01 mol/L and A p = 0. The Csw,’ value was calculated from the slope of the straight line in this figure. The values of Lpmand C,(1- a,) me equal or nearly equal to ones estimated from the experimental data of water flow shown in the preceding section. The data points of E, and J, increase with increasing A p and approximately coincide with the respective calculated curves. Although some complicated factors may contribute to the slight deviation of the data from the calibrated curves, such a piezodialysis effect is undoubtedly what had been expected for a typical charge-mosaic membrane (Leitz, 1976). Here it should be noted that salt enrichment (E,) is also dependent on CI. We observed that E, decreased with increasing CI for charge-mosaic membranes prepared from the other starting pentablock copolymer (Miyaki et al., 1984b). Our membrane exhibits significant piezodialysis effect only in the very low CI region, which almost disappears in the CI region of higher than 0.1 mol/L. Such a feature of the membrane will inevitably restrict its application field. Further improvement of a fabricating method of a charge-mosaic membrane as well as the detailed fundamental analysis of piezodialysis is desired in order to apply the membrane to a useful piezodialysis process.
Conclusion The following may be concluded. (1)We measured volume flow (J,)and salt flow (J,) through a charge-mosaic membrane prepared from a pentablock copolymer of the ISBA1 type and observed a very high permeability for KCI, pronounced negative osmosis, and piezodialysis effect. (2) The reflection coefficient (a,) and solute permeability (w,‘ ) were calculated from the experimental data of J, and J,. Behaviors of these phenomenological coef-
ficients were almost consistent with those expected from the theoretical analysis by Kedem and Katchalsky in the concentration range where concentration polarization on the membrane surfaces could be suppressed. (3) The electroosmotic factor F(P, - 0,)was also calculated from the J, and J,data. It was almost constant and ranged from 600 to 720 cm3/mol in the CI range studied. (4)J , was considerably lowered by the presence of saccharose in a dialysand solution, while J, showed only a slight decrease even if the saccharose concentration was very high. (5) The salt enrichment (E3 increased with an increasing applied hydrostatic pressure difference and approximately coincided with the curve calculated from the phenomenological equations.
Acknowledgment We acknowledge Dr. A. Akimoto, S. Ohno, and M. Akazawa, TOSOH Corporation, Tokyo, Toyama and Ayase, Japan, for their encouragement and useful suggestions during this work and Prof. M. Tasaka, Faculty of Engineering, Shinshu University, Nagano, Japan, for his helpful suggestion. This work was partly supported by a Grantin-Aid for Scientific Research from the Ministry of Education, Japan. Registry No. H,O, 7732-18-5; KCl, 7447-40-7; (butadiene)(isoprene) (styrene) (4-vinylbenzyl) (dimethylamine)(blocker copolymer), 106849-11-0.
Literature Cited Carr, C. W.; Sollner, K. Biophys. J . 1964, 4, 189-201. Fujimoto, T.; Ohkoshi, K.; Miyaki, Y.; Nagasawa, M. Science (Washington,D.C.) 1984a, 224, 76-76. Fujimoto, T.; Ohkoshi, K.; Miyaki, Y.; Nagasawa, M. J. Membr. Sci. 1984b, 20, 313-324. Funabashi, H.; Miyamoto, Y.; Isono, Y.; Fujimoto, T.; Matsushita, Y.; Nagasawa, M. Macromolecules 1983, 16, 1-5. Hirahara, K.; Takahashi, S.; Iwata, M.; Fujimoto, T.; Miyaki, Y. Ind. Eng. Chem. Prod. Res. Dev. 1986,25, 305-313. Igawa, M.; Tachibana, T.; Ueki, I.; Tanaka, M.; Seno, M. Ind. Eng. Chem. Fundam. 1985,24, 485-488. Kedem, 0.;Katchalsky, A. Trans, Faraday SOC.1963,59,1918-1930, 1931-1940. Leitz, F. B. In Membrane Separation Processes; Meares, P., Ed.; Elsevier: Amsterdam, 1976; p 261. Matsushita, Y.; Choshi, H.; Fujimoto, T.; Nagasawa, M. Macromolecules 1980, 13, 1053-1058. Miyaki, Y.; Fujimoto, T. Membrane (Jpn.) 1983, 8, 212-224. Miyaki, Y.; Iwata, M.; Fujita, Y.; Tanisugi, H.; Isono, Y.; Fujimoto, T. Macromolecules 1984a, 17, 1907-1912. Miyaki, Y.; Nagamatsu, H.; Iwata, M.; Ohkoshi, K.; Se, K.; Fujimoto, T.; Nagasawa, M. Macromolecules 198413, 17, 2231-2236. Neihof, R.; Sollner, K. J . Phys. Colloid Chem. 1950, 54, 157-177. Neihof, R.; Sollner, K. J . Gen. Physiol. 1955, 38, 613-622. Sollner, K. Biochem. 2. 1932, 244, 370-381. Takahashi, S.; Matsumura, K.; Toda, M.; Fujimoto, T.; Hasegawa, H.; Miyaki, Y. Polym. J . 1986, 18, 41-49. Weinstein, J. N.; Caplan, S. R. Science (Washington,D.C.) 1968,161, 70-72. Weinstein. J. N.:.~CaDlan. S. R. Science (Washington,D.C.) 1970,169, 296-298. Weinstein, J. N.; Misra, B. M.; Kalif, D.; Caplan, S. R. Desalination 1973,12, 1-17. Weinstein, J. N.; Bunow, B. J.; Caplan, S. R. Desalination 1972,11, 341-377.
Received for review August 21, 1987 Revised manuscript received January 26, 1988 Accepted February 11, 1988
