Effect of Membrane Constitution on the Direction of Ionic Transport

Countertransport of ions is defined as the transport of an ion against its own concentration gradient driven by the third driving electrolyte added to...
0 downloads 0 Views 87KB Size
Download PDF
11674

J. Phys. Chem. B 2000, 104, 11674-11679

Effect of Membrane Constitution on the Direction of Ionic Transport Across Bipolar Membranes Mitsuru Higa,* Yuichi Tsukamoto, Naomi Hamanaka, and Koji Matsusaki DiVision of Applied Chemistry and Chemical Engineering, Faculty of Engineering, Yamaguchi UniVersity, Tokiwadai, 2-16-1, Ube City, 755-8611, Japan ReceiVed: May 17, 2000; In Final Form: August 30, 2000

Countertransport of ions is defined as the transport of an ion against its own concentration gradient driven by the third driving electrolyte added to the systems. The simulations and the experiments presented show that in the systems that consist of NaCl, KCl, and CaCl2 solutions divided by a bipolar membrane, there are two types of the countertransport of K+ and Ca2+ ions: forward countertransport (the countertransport in the direction of the concentration gradient of the driving electrolyte, NaCl) and backward countertransport (the countertransport in the direction opposite to the concentration gradient). In the system where the negatively charged layer of the membrane contacts the solution at the high-concentration side of NaCl, the forward countertransport occurs, and the membrane has permselectivity for univalent ions. In the system where the positively charged layer contacts the solution at the high-concentration side, the mode of the countertransport depends on the charge density ratio of the two charged layers.

Introduction A bipolar membrane has a sandwich-like structure of a positively charged layer, P, and a negatively charged layer, N, joined together in series. This membrane has many interesting transport phenomena such as rectification properties,1-3 permselectivity for univalent ion,4-6 water splitting,7-18 and electrical oscillations.19,20 These phenomena are very important clues for developing highly selective membranes as well as for making clear the mechanism of ionic transport in biological systems. Transport properties of a bipolar membrane depend on membrane constitution, which means the charge densities and the thickness of layers in the membrane, and the sequence (PN or NP) of component layers in a system. In an electrodialysis system, the electric current through the membrane depends on the P-N direction to the applied voltage as in semiconductor diodes.1-3 In a diffusion dialysis system, both the membrane potential and the permeability of ions depend on the P-N direction to the ionic concentration gradient in the system.21-25 Let us consider a diffusion dialysis system where a bipolar membrane separates two cells. The two cells contain both the m species Ek electrolytes (1 e k e m) and the n species Ej electrolytes (1 e j e n). Initially, the concentration of Ek in the two cells is identical, and the concentrations of Ej have different values between the cells. Higa et al.26 have simulated that in such a case, the cations or the anions of Ek electrolytes are transported against their concentration gradients due to the diffusion of the driving electrolyte (Ej) under suitable conditions. This transport is referred to as countertransport or antiport. The simulations show that the direction of the countertransport as well as the valence selectivity in the countertransport will be controlled by changing the membrane constitutions. The aim of this study is to analyze the effect of the membrane constitution on the direction of the countertransport and the valence selectivity. Hence, we prepared bipolar membranes and * Corresponding author (E-mail: [email protected], Fax: +81-836-85-9201).

measured the thickness and the charge densities of the two charged layers. The simulations calculated with the measured properties were compared with the experiments of ionic transport in two dialysis systems where the negatively charged layer of the membrane in one case faced the high-concentration side of the driving electrolyte and in another case faced the lowconcentration side. Calculations Ionic transport in the dialysis systems shown in Figure 1 is calculated by using the same method as in ref 27 under the following assumptions: (a) the surfaces of both the charged layers are always in a state of the Donnan equilibrium; (b) the boundary effects on the surfaces are negligible; (c) all the electrolyts dissolve perfectly, and ionic activity coefficients are unity both in the aqueous solutions and in the two charged layers; and (d) the standard chemical potentials in the two layers are equal to those in the solutions, respectively. It is difficult to measure experimentally the ion mobility in two charged layers of a bipolar membrane. Mackie and Meares28 estimated the mobility in a swollen membrane as a function of membrane water content, H, and the mobility in an aqueous solution, ωi. Higa et al.29 reported that the diffusion coefficient of a 1-1 type salt, such as KCl, determined experimentally in swollen poly(vinyl alcohol) (PVA) membranes almost agrees with the prediction of the Mackie and Meares theory, but the diffusion coefficient of a salt with a high valent ion, such as CaCl2, has a smaller value than the prediction. Hence, we estimate the mobility of the ith ion in layer k, ω j i(k), from permeation experiments through PVA membranes30 as:

ω j i(k) )

aH3 ωi (2 - H)2

(1)

where a is correction factor for the Mackie and Meares theory. Assuming that the two charged layers of the membrane have

10.1021/jp001806o CCC: $19.00 © 2000 American Chemical Society Published on Web 11/17/2000

Effect of Bipolar Membrane Constitution on Ion Transport

J. Phys. Chem. B, Vol. 104, No. 49, 2000 11675 j and k. The flux of the ith ion in layer k, Ji(k), is given as33

Ji(k) ) -

RTZiω CRi (k) - CLi (k)βzi j i(k) ln β dk βzi - 1

(5)

where dk is the thickness of layer k. The term β is defined as

β ≡ exp(-F∆φdiff(k)/RT)

(6)

where ∆φdiff(k) is the diffusion potential in layer k. In a dialysis system consisting of univalent ions and bivalent ions, β is the solution of the following equation:34,35

(B1 + 4B2)β2 + (B1 - A1)β - (A1 + 4A2) ) 0

(7)

where R L (k) + ∑ω j i,z-Ci,z(k) ∑ωj i,z+Ci,z+ L R j i,z+Ci,z+ (k) + ∑ω j i,z-Ci,z(k) Bz ) ∑ω

Az )

(8)

The time evolution of the ionic concentrations in the two cells are given from the following equations:

Figure 1. Two dialysis systems used in this study. NaCl is the electrolyte for driving the countertransport of K+ and Ca2+. Initially, the concentrations of KCl and CaCl2 in the two cells are identical (1.0 × 10-3 mol dm-3) and the concentration ratio of the driving electrolyte between the two cells (rc) is equal to 100. In system Pn, layer P contacted with the solution of the high-concentration side; in system Np, the membrane was turned over so that layer P contacted with the low-concentration side.

K+,

(2) Ca2+

Cl-

i

(3)

where zi is the valence of the ith ion and K(j,k) is the Donnan equilibrium constant32 at the interface between layers j and k:

CRi (j)

(10)

(11)

where the sum of Donnan potentials, ∆φdon, is

∑zi(K(j,k))z CRi (j) + zx(k)Cx(k) ) 0

CLi (k)

Ci,tn+1(R) ) Ci,tn(R) + Ji,tnS∆t/V

∆φ ≡ ∆φdon + ∆φdiff

Then, the value of the mobility of and ions in an aqueous solution are 7.9 × 10-13, 3.0 × 10-13, and 8.2 × 10-13 mol m2 J-1 s-1, respectively.31 The membranes used in this study have a higher degree of water content and lower charge density than current bipolar membranes. The assumptions mentioned before are therefore considered to be suitable to these membranes. The Donnan equilibrium and the electroneutrality condition give the following equation:

(K(j,k))zi ≡

(9)

where Ci,tn(L) and Ci,tn(R) are the ionic concentration at time tn at cells L and R, respectively; ∆t ) tn+1 - tn; S is the membrane area (7.07 cm2); and V is the volume of the two cells (100 cm3). The time evolution of the total membrane potential, ∆φ, is also simulated, and is defined as

the same water content, we set a for the ions as

a ) 0.94 for K+, Na+ and Cl- ions; a ) 0.60 for Ca2+ ion

Ci,tn+1(L) ) Ci,tn(L) - Ji,tnS∆t/V

) exp(-ziF∆φdon(j,k)/RT)

(4)

where F, R, and T are the Faraday constant, the gas constant and the absolute temperature, respectively; and CLi (k) and CRi (j) are the ionic concentration at the left-hand side in layer k and the right-hand side in layer j, respectively. The term ∆φdon(j,k) is the Donnan potential at the interface between layers

∆φdon ≡ ∆φdon(L,s) + ∆φdon(s,u) + ∆φdon(u,R)

(12)

and the sum of the diffusion potentials, ∆φdiff, is

∆φdiff ≡ ∆φdiff(s) + ∆φdiff(u)

(13)

For system Pn, s and u denote layers P and N, respectively, and for system Np, layers N and P, respectively. In our systems, the electric potentials have a positive value if the potentials are higher at cell R than at cell L. Experiments Sample. Aqueous solutions of a mixture of PVA [poly(vinyl alcohol), Aldrich] and AP-2 [Kuraray Company, Ltd.] were cast for negatively charged membranes, and those of PVA and PAAm [poly(allylamine), Nittobo Industries Inc.] were cast for positively charged membranes. The volume fraction of PVA to AP-2 or to PAAm was changed to control the charge densities. The AP-2 polymer contains sulfonic groups that provide negatively charged sites. The bipolar membranes, BIP-1, BIP2, and BIP-3, were made from the negatively charged PVA membranes and positively charged ones using the same process as described elsewhere.23 Thickness Measurement of the Charged Layers. The bipolar membranes were soaked in an acid dye solution (Suminal

11676 J. Phys. Chem. B, Vol. 104, No. 49, 2000

Higa et al. TABLE 1: Characteristics of the Bipolar Membranes parameter Cx(P) Cx(N) rx H dP dN

(× 102 mol dm-3) (× 102 mol dm-3) (µm) (µm)

BIP-1

BIP-2

BIP-3

5.1 1.5 3.4 0.47 80 80

4.8 4.3 1.1 0.48 85 68

1.3 3.5 0.37 0.40 88 90

Figure 2. Membrane potential versus the KCl concentration, Co. Key: (solid symbols) the data in a dialysis system where layer N contacts the solution at the high-concentration side; (open symbols) the data in a dialysis system where layer P contacts the solution at the high-concentration side; (circles) BP-1; (triangles) BP-2; (squares) BP3. The curves are calculated by fitting the data to the simulation.

Fast Blue R. Sumitomo Chemical Company) for 24 h. Because the dye colors only the positively charged layer dark blue, the thickness of the charged regions can be measured with a microscope. Measurement of Membrane Water Content. The membrane water content, defined as the volume fraction of water in a swollen membrane, was estimated from the following equation:

H≡

(Ws - Wd)/1.0 (Ws - Wd)/1.0 + Wd/1.3

(14)

where Ws and Wd are the weights of a membrane at the equilibrium swollen and dry states, respectively, and 1.0 and 1.3 are the densities of water and PVA, respectively. Measurement of the Membrane Potential. To obtain the charge density of the two charged layers, the total membrane potential was measured in the dialysis systems shown in Figure 1. The concentration of the high-concentration side is 5 times higher than that of the low-concentration side during the measurement. Permeation Experiments. The permeation of K+ and Ca2+ ions in the dialysis systems shown in Figure 1 was measured with the same apparatus as shown elsewhere.34 In the dialysis systems, two cells contain KCl and CaCl2 and a driving electrolyte, NaCl. Initially, the concentrations of KCl and CaCl2 in the two cells were identical, 0.001 mol dm-3, and the concentrations of the driving electrolyte, NaCl, in cells L and R were 0.1 and 0.001 mol dm-3, respectively. The membrane area was 7.07 cm2 and the volume of the two cells was 100 cm3. The concentration change of the two cations in cell L was measured by an ion chromatograph [TOSOH, IC-8010]. The membrane potential change during the permeation experiment was also measured with Ag/AgCl electrodes [TOA, HS-205S] with salt bridges (3N KCl). Results and Discussions Characteristics of the Bipolar Membranes. Figure 2 shows the experimental data of the membrane potential in the two systems as a function of the KCl concentration. The curves are the potentials calculated by fitting the data to the equation of the simulation method. The charge density of both the layers

Figure 3. The experimental data and the calculations of the ionic transport for BIP-2 in system Np. (a) The time-membrane potential curves (the solid circle and solid curve are the data and the calculation). (b) The time-concentration curve at cell L (the solid circle and solid curve are the data and the calculation, respectively, for K+ ion; the open circle and broken curve are for Ca2+ ions).

was obtained from the fitting. We defined the ratio of the charge densities as

rx ≡

Cx(P) Cx(N)

(15)

The charge density of both the layers, as well as the charge density ratio, the thickness of the layers, and membrane water content are listed in Table 1. Ionic Transport in System Np. First, we discuss the behavior of ionic transport in system Np where layer N contacts with the high-concentration side (cell L) of the driving electrolyte, NaCl. Part a of Figure 3 shows time evolution of the membrane potential using the BIP-2 membrane (rx ) 1). The total membrane potential, ∆φ, has a negative value at the initial conditions (t ) 0), and increases with time to zero. The timepotential curve can be explained as follows. In the system, the

Effect of Bipolar Membrane Constitution on Ion Transport ionic strength of the solution in cell L is much larger than the charge density of layer N, Cx(N), and that in cell R is smaller than Cx(P). Hence, the Donnan-potential sum, ∆φdon is 1. Part a of Figure 4 shows the time-potential curve for the BIP-1 membrane. In the simulations, the initial value of the total membrane potential, ∆φ, is positive. The value of ∆φ decreases with time and has a minimum value at t ≈ 20 h, and then increases to zero. The time-potential curve can be explained as follows. In the case of rx > 1, at the initial conditions (time, t ) 0), the ionic strength of the solution in cell L is much larger than the charge density of layer P, Cx(P), and the ionic strength in cell R is smaller than the charge density of layer N, Cx(N). Hence, the Donnan-potential sum, ∆φdon, is >0. In the driving electrolyte, NaCl, the mobility of the cation is smaller than that of the anion; thus, the sum of the diffusion

J. Phys. Chem. B, Vol. 104, No. 49, 2000 11677

Figure 4. The experimental data and the calculations of the ionic transport for BIP-1 in system Pn. (a) and (b) are the same as in Figure 3.

potentials, ∆φdiff, is |∆φdiff|. Therefore, ∆φ is positive. The intercellular concentration difference of NaCl decreases with permeation time. The value of ∆φdon decreases to zero with the reduction of the concentration difference more steeply than does ∆φdiff. Hence, ∆φ becomes negative when t > 4 h, and increases to zero. The simulation of ∆φ agrees with the experiments, except for the data at the initial stage. The experiments of ∆φ have negative values at all permeation times. We think that the deviation between the experiments and the simulations may occur because the system is not in a steady state at the first stage. Part b of Figure 4 shows time-concentration curves of K+ and Ca2+ ions in cell L. The concentration decrease of the cations shows that both K+ and Ca2+ ions are transported from cell L to cell R against their own concentration gradient between the two cells. In other words, the forward countertransport of the ions occurs. As mentioned before, the experiments of ∆φ have negative values during the permeation experiment. Hence, the countertransport occurs due to the potential. rx ) 1. Part a of Figure 5 shows the time-potential curve for the BIP-2 membrane. In both the simulation and the experiments, ∆φ of the BIP-2 membrane is positive and larger than that of the BIP-1 membrane at t ) 0. The reason for the difference in the time-potential curves between the two membranes is that ∆φdon of the BIP-2 membrane is larger than that of the BIP-1 membrane because Cx(N) of the former is larger than that of the latter. Part b of Figure 5 shows the timeconcentration curve of K+ and Ca2+ ions in cell L. The concentration of the cations increases with time at the first stage

11678 J. Phys. Chem. B, Vol. 104, No. 49, 2000

Higa et al.

Figure 5. The experimental data and the calculations of the ionic transport for BIP-2 in system Pn. (a) and (b) are the same as in Figure 3.

Figure 6. The experimental data and the calculations of the ionic transport for BIP-3 in system Pn. (a) and (b) are the same as in Figure 3.

because ∆φ > 0. This result means that the backward countertransport occurs. That is, the direction of the countertransport at rx ) 1 is in the opposite direction of that at rx > 1. When t ≈ 20 h, ∆φ becomes negative; hence, both the cations diffuse from cell L to cell R, so that the concentration in cell L decreases with time. rx < 1. Parts a and b of Figure 6 show time evolution of the membrane potential and the concentration of K+ and Ca2+ ions in cell L for the BIP-3 membrane. Because Cx(N) in the membrane is larger than Cx(P), ∆φ has positive values during all the permeation time. The electrochemical potential of both the cations in cell R is larger than that in cell L. Hence, both the cations are transported against their concentration gradient from cell R to cell L (the backward countertransport). Thus, the concentration of the ions in cell L increases with time. The value of ∆φ decreases with time, and the concentration difference of the ions between the two cells increases with time. Hence, the electrochemical potential of the cations in cell R is smaller than that in cell L at t > 50 h. Therefore, after reaching a maximum concentration at t ) 50 h, both the cations diffuses from cell L to cell R. The maximum concentrations of the two ions in the case of rx < 1 are larger than those in the case of rx ) 1 because ∆φ in the former is larger than that in the latter at all the time intervals. In system Pn, the mode of the countertransport through a bipolar membrane depends on rx: when rx > 1, the forward countertransport occurs; when rx ) 1 or rx < 1, the backward countertransport occurs. This result means that the direction of

the countertransport will be controlled by changing the charge densities. To compare the countertransport through a bipolar membrane with that through a single (not bipolar) charged membrane, we simulated the countertransport through a negatively charged membrane. Our simulations (results not shown) revealed that only a few kinds of driving electrolyte can control the direction of the countertransport through a negatively charged membrane, whereas any kind of driving electrolyte can control the direction of the countertransport through a bipolar membrane. The simulations also revealed that a bipolar membrane has permeselectivity for bivalent ions in system Pn and for univalent ion in system Np.27 In our experiments, system Pn did not show the permeselectivity for bivalent ions because the mobility of Ca2+ ions in the membranes is much smaller than that of K+ ions. A bipolar membrane will have permeselectivity for bivalent ions in system Pn in the case where the mobility of the bivalent ions in the system is almost the same as that of univalent ions. The prediction of the simulation for the countertransport across the bipolar membranes agrees quantitatively with the experimental data except for the time-concentration curve of K+ ion in the BIP-3 membrane. The deviation probably comes from the assumptions in the simulation (the water content in the two layers has the same value, and the ionic mobility in the two layers is a function of the water content in terms of the Mackie and Meayer theory). In addition to this, Ramı´rez et al.24 reported the effect of a diffusion double layer on the transport properties of a bipolar membrane. The other effects that should

Effect of Bipolar Membrane Constitution on Ion Transport be taken into account are the possible existence of a neutral layer between the two charged layers, and the difference of the dielectric constant between salt solutions and the membrane.36 Higa and Kira37 reported that the ionic mobility in a waterswollen membrane depends on the membrane potential. It has been reported that the less water content a swollen PVA membrane has, the more deviation between the experiments of the ion mobility in a swollen membrane and the estimated value in terms of the Mackie and Meayer theory. The BIP-3 membrane has much a lower water content than the other membranes. Hence, we think that one of the reasons the deviation occurs is that the estimated values of the ion mobility in the two charged layers of the BIP-3 membrane differ from the real values. Although these factors were not taken into account, the calculation demonstrates qualitatively the relationship between the ionic transport across the bipolar membranes and the membrane constitution. Conclusions The simulations and the experiments reported here show that countertransport in a dialysis system consisting of a bipolar membrane and mixed NaCl, KCl, and CaCl2 electrolyte solutions has two modes: forward countertransport and backward countertransport. The mode of the countertransport depends on the charge density ratio, rx, of two charged layers of the membrane and the sequence of the layer in the two dialysis systems. In system Np, the forward countertransport occurs in all the bipolar membrane. In this system, the membrane has permselectivity for univalent ions. In system Pn, the mode of the countertransport depends on rx: when rx > 1, the forward countertransport occurs; when rx ) 1 or rx < 1, the backward countertransport occurs. The maximum concentration in the countertransport at rx < 1 is larger than that at rx ) 1. The present simulations are calculated under the assumption that the membrane matrix is hydrophilic. Hence, the simulations will be applicable to some extent to the ionic transport across bipolar membranes whose matrix is hydrophobic, except for those with very low water content. Acknowledgment. This work was supported by the Grantin-Aid for Scientific Research on Priority Areas (A), No. 11167257, and Grant-in-Aid for Scientific Research (C), No. 11640583, of the Ministry of Education, Science, Sports and Culture.

J. Phys. Chem. B, Vol. 104, No. 49, 2000 11679 References and Notes (1) Mauro, A. Biophys. J. 1962, 2, 179. (2) Coster, H. G. L. Biophys. J. 1965, 5, 669. (3) Sokirko, A. V.; Ramı´rez, P.; Manzanares, J. A.; Mafe´, S. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 1040. (4) Glueckauf, E.; Kitt, G. P. J. Appl. Chem. 1956, 6, 511. (5) Tanaka, Y.; Seno, M. J. Membr. Sci. 1981, 8, 115. (6) Mizutani, Y. J. Membr. Sci. 1990, 54, 233. (7) Grossman, G. J. J. Phys. Chem. 1976, 80, 1616. (8) Nagasubramanian, K.; Chlanda, F. P.; Liu, K.-J. J. Membr. Sci. 1977, 2, 109. (9) Bassignana, I. C.; Reiss, H. J. Phys. Chem. 1983, 87, 136. (10) Mani, K. N. J. Membr. Sci. 1991, 58, 117. (11) Simons, R. J. Membr. Sci. 1993, 82, 65. (12) Alvarez, F.; Alvarez, R.; Coca, J.; Sandeaux, J.; Sandeaux, R.; Gavach, C. J. Membr. Sci. 1997, 123, 61. (13) Grib, H.; Bonnal, L.; Sandeaux, J.; Sandeaux, R.; Gavach, C.; Mameri, N. J. Chem. Technol. Biotechnol. 1998, 73, 64. (14) Strathmann, H.; Krol, J. J.; Rapp, H.-J.; Eigenberger, G. J. Membr. Sci. 1997, 125, 123. (15) Krol, J. J.; Jansink, M.; Wessling, M.; Strathmann, H. Sep. Purif. Technol. 1998, 14, 41. (16) Mafe´, S.; Ramı´rez, P.; Alcaraz, A. Chem. Phys. Lett. 1998, 294, 406. (17) Holdik, H.; Alcaraz, A.; Ramı´rez, P.; Mafe´, S. J. Electroanal. Chem. 1998, 442, 13. (18) Chou, T.-J.; Tanioka, A. J. Phys. Chem. B. 1998, 102, 7866. (19) Shashoua, V. E. Nature 1967, 215, 846. (20) Shashoua, V. E. Faraday Symp. Chem. Soc. 1974, No. 9. 174. (21) Higuchi, A.; Nakagawa, T. J. Membr. Sci. 1987, 32, 267. (22) Higuchi, A.; Nakagawa, T. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3609. (23) Higa, M.; Kira, A. J. Phys. Chem. 1995, 99, 5089. (24) Ramı´rez, P.; Mafe´, S.; Manzanares, J. A.; Pellicer, J. J. Electroanal. Chem. 1996, 404, 187. (25) Higa, M.; Tanioka, A.; Kira, A. J. Phys. Chem. B. 1997, 101, 2321. (26) Higa, M.; Kira, A. J. Phys. Chem. 1992, 96, 9518. (27) Higa, M.; Tanioka, A.; Kira, A. J. Chem. Soc., Faraday Trans. 1998, 94, 2429. (28) Mackie, J. S.; Meares, P. Proc. R. Soc. London 1955, 232, 498A. (29) Higa, M.; Kira, A. J. Phys. Chem. 1994, 98, 6339. (30) Higa, M.; Koga, M.; Tanioka, A. Seni-gakkaishi 2000, 56, 290. (31) International Critical Tables; McGraw-Hill: New York, 1949. (32) Donnan, F. G. Z. Phys. Chem. 1934, A168, 369. (33) Goldman, D. E. J. Gen. Physiol. 1943, 27, 37. (34) Higa, M.; Tanioka, A.; Miyasaka, K. J. Membr. Sci. 1990, 49, 145. (35) Higa, M.; Tanioka, A.; Miyasaka, K. J. Membr. Sci. 1991, 64, 255. (36) Coster, H. G. L. Biophys. J. 1973, 13, 113. (37) Higa, M.; Kira, A. J. Phys. Chem. 1994, 98, 6339.