Solvent transport across anion-exchange membranes under a temperature difference and transported entropy of water

Journal of Membrane Science 92 ( 1994) 85-93

journal of

MsEiEE

Solvent transport across anion-exchange membranes under a temperature difference and transported entropy of water

Takashi Suzuki, Ryotaro Kiyono, Masayasu Tasaka* Department ofMaterials Science and Engineering, Graduate School of Science and Technology, Shinshu University, Wakmato,

Nagano 380, Japan

(Received January 1, 1993; accepted in revised form February 15, 1994)

Abstract

Solvent transport across anion-exchange membranes was measured for aqueous KF, KCl, KN03 (or NaNO,), KIO,, HCOONa, CH,COONa (or K), C6H,COONa, C6H5SOJNa and pCH&,H,SO,Na solutions under a temperature difference and an osmotic pressure difference. Hydrocarbon-type anion-exchange membranes Neosepta@ AM- 1, Aciplex@ A-20 1 and A-22 1, test membranes STA-1 to STA-5, and fluorocarbon-type anion-exchange membrane Tosflex@ IE-DF 17 were used. The water content is represented by the unit: g Hz0 per g dry membrane without the weight of anhydrous counterions. Plots of the volume flux against the temperature difference of both side solutions gave straight lines starting from zero. The direction of thermoosmosis was from the cold to the hot side. The order of water content of membranes is F- > 10, > Cl- >NO, for inorganic ions and CH$OO- > HCOO- > C6H5COO- >p-CH3C6H$O~ (or C6HSS0~ ) for organic ions regardless of the type of membrane. The order of the absolute value of the entropy difference between transported entropy in membranes and partial molar entropy of water in the external solutions is 103 > F- > Cl- > NO, for inorganic ions and C6H5COO- > CH&OO- > HCOO- for organic ions for all membranes.

Keywords: Anion-exchange membrane; Solvent transport; Thennoosmosis; Transported entropy; Volume flux

1. Introduction

In previous papers [ l-3 ] the direction of volume flux under a temperature gradient was dis- cussed for hydrophilic and hydrophobic membranes. For hydrophobic membranes and for cation-exchange membranes in the Li+ form the direction of thermoosmosis was from the hot to the cold side. However, for cation-exchange membranes in the H+ and Na+ forms [ 1,3 ] and for all anion-exchange membranes the direction

*Corresponding author.

of thermoosmosis was from the cold to the hot side [ 2,3]. In this paper, in order to analyze the mechanism of thermoosmosis in further detail, nine anion-exchange membranes and various inorganic and organic 1: 1 electrolytes were used.

In general, some water in ion-exchange membranes is hydrated around the fixed charges and around the counterions and all water and ions are surrounded by the hydrophobic hydrocarbon membrane matrix. Thus, it is expected that the structure of water in the charged membranes is stronger compared with that in the external free solutions [ 41. Therefore, the mean molar trans-

0376-7388/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZO376-7388(94)00048-4

86 T. Suzuki et al. /Journal of Membrane Science 92 (I 994) 85- 93

ported entropy of water in the membrane is smaller than the partial molar entropy of water in the external free solutions. Therefore, the direction of thermoosmosis will be from the cold to the hot side solution [ 5 1. If the ionic form of the membrane changes, the water content and the interaction between counterions and water would vary largely. In this paper the dependence of the thermoosmotic coefficient on the ionic form of the membranes is studied.

2. Experimental

2. I. Membranes

Hydrocarbon-type anion-exchange membranes Neosepta@ AM- 1, Aciplex@ A-201 and A- 221, test membranes STA-1 to STA-5 made by Asahi Chemical Industry, and fluorocarbon-type anion-exchange membrane Tosflex@ IE-DF 17 were used. Ion-exchange capacities were measured by the gravimetric method [ 61. As usual, the ion-exchange capacity is expressed by the

unit: mmol of ion-exchange groups per g of the dry membrane including the weight of counterions. However, the weight of dry membrane including the weight of counterions varies largely with the species of the counterions. Therefore, in this work, the ion-exchange capacity is expressed by the unit: mmol of ion-exchange groups per g of the dry membrane without the weight of anhydrous counterions. The ionic form of the fluorocarbon-type membranes was changed by boil- ing the membranes in the respective salt solutions (1 mol dmm3) for 1 h. With p-toluenesulfonate counterions the exchange was followed by the weight of the dry membrane. The thickness of membranes, ion-exchange capacity and transport number of counterions calculated from the concentration membrane potential are shown in Table 1. The water content is expressed by the unit: g of water per g of the dry membrane without the weight of anhydrous counterions. The water content of ion-exchange membranes varies with the species of counterions as shown in Table 2. The water content was independent of the temperature in the range between 301 and 3 16 K within experimental error.

Table 1 The properties of various membranes

Membrane Membrane thickness (mm)

Ion-exchange capacity (mmol/g dry membrane)

Molality of fixed charge” (mmol/g T&O)

Transport numbe?

STA- 1 0.096 0.31 STA-2 0.104 1.13 STA-3 0.118 1.78 STA-4 0.090 1.09 STA-5 0.101 1.05

Neosepta@ AM-l 0.123 1.15

Aciplex” A-201 0.218 1.42 A-221 0.124 2.63

Tosflex@ IE-DF 17 0.230 0.70

YZl- form. “Calculated from the membrane potential in 0.1/0.2 mol/kg KC1 solutions.

5.17 0.98 8.07 0.99 7.74 0.98

10.90 0.98 9.55 0.99

3.29 0.98

3.55 0.98 4.06 0.98

3.50 0.98

Table 2

T. Suzuki et al. /Journal ofMembrane Science 92 (1994) 85-93 87

Water contenta with various counterions for various membranes

Counterion Membrane

STA- 1 STA-2 STA-3 STA4 STA-5 Neoseptam Aciplex@ Aciplex@ Tosflex@’ AM-l A-201 A-22 1 IE-DF 17

F- Cl- I- NO? IO<

HCOO- CH&OO- C6H,COO- Ce,H5SO~ pCH&HdSO<

0.08 0.23 0.46 0.20 0.20 0.49 0.06 0.14 0.23 0.10 0.11 0.35

- -

0.11 0.20 0.36 0.17 0.19 0.31

0.09 0.22 0.40 0.19 0.19 0.45 0.34

-

0.05 0.12 0.16 0.11 0.10 -

0.52 0.40

0.32 0.47 0.42 0.46 0.34

0.25

0.99 0.66 0.35 0.51 0.83 0.79 0.88 0.55

0.35

0.33 0.20

0.15 0.26 0.29 0.31 0.24 0.19

“g H,O/g dry membrane without counterions.

2.2. Electrolyte solutions

The reagents used for the preparation of aqueous KF, KCI, KN03 (or NaNOJ), KIO,, HCOONa, CH,COONa (or K), C6H,COONa, C6HSS03Na and pCH3C,H,S03Na solutions were special grades from Wako Pure Chemical Industries, Ltd., Japan. In order to study the molality dependence of the thermoosmotic coeffr- cients, 0.001 to 4 mol kg- * of LiCl, NaCl and KC1 solutions were used. The dependence on the nature of the membrane was studied with electrolytes of 0.01 mol kg-’ molality.

2.3. Measurements of thermoosmosis

To measure mass transport under a temperature gradient, we used a previously described [ 2 ] thermoosmosis cell consisting of two poly (methyl methacrylate ) chambers separated by a horizontal membrane. The upper, hot chamber ( 1500 cm3) was larger than the lower, cold chamber (96 cm3). The volume flow was calculated from the movement of the meniscus in a glass capillary of 1.05mm radius connected to the lower chamber. The effective area of the membrane was 28 cm2. The temperature in the cold chamber was controlled by a glass tube cooler, through which cold water of a regulated constant temperature was circulated. The solu-

tion in the hot chamber was stirred by a glass propeller while a magnetic stirrer was used in the cold chamber. The magnetic stirrer tip was placed closer to the membrane surface. The two temper- atures in the cold side and the hot side were controlled to fix the mean temperature at 303.2 K.

Although the bulk solutions on the two sides of the membrane were stirred, the effective temperature difference between the two sides of the membrane, d7’, was different from the temperature difference between the bulk solutions, AT,. For this thermoosmosis cell it has already been shown that AT/AT, is 0.70 to 0.73 for various membranes [ 21. Therefore, the effective temperature difference was estimated from assum- ing the relation AT= 0.7AT,.

2.4. Measurements of osmotic volumeflux

The membrane was mounted between two 65 cm3 PVC half cells. The cells were equipped with magnetic stirrers and capillaries for measuring volume flow. The molality of the external salt solution on one side of the membrane was fixed at 0.001 mol kg-‘, and the molality on the other side of the membrane was varied in the range of 0.2 to 0.5 mol kg-‘. The effective area of the membrane was 2.54 cm2. The cell was set in an air thermostat and the temperature was kept at 298.2 2 0.5 K. The rate of volume flow through

88 T. Suzuki et al. /Journal qfhfembrane Science 92 (I 994) 85-93

the membrane was determined from the movement of the liquid meniscus in the capillary.

3. Results and discussion

The phenomenological equations for the fluxes relative to the membrane are given by [ $71:

-Js=L,,AT+CiL,iA,E; (1)

-J, = L,,AT+ CjLijAbj (2)

where J, is the total entropy flux, J, is the absolute mass flux, L,, is the permeability coefficient of the membrane of finite thickness and A shows the difference across the membrane. The difference in electrochemical potential, Ajij, is written as:

APi= (APi)T.p- SiAT+ ViAP+ZiFA~ (3)

where Api is the chemical potential, Si the partial molar entropy, v, the partial molar volume, z, the charge number of component i, P the pressure and # is the electrical potential. At the condition of zero current, I= C,ZiFJi=Oy and using J, = CiV~i for volume flux we have:

-J,=CiviCj(L,i-zj)CkL;kZkF (4)

X [ (q-s,)AT+ (Apj)T,.+viAf’]

where r, is the reduced transport number and Sj is the mean molar transported entropy of component j.

If there is no concentration difference and no pressure difference, for a 1: 1 electrolyte and an anion-exchange membrane, from Eq. (4) we have:

-J,=(D’+D’+D”)AT (5)

and:

DO=&Joo(~o --so)/6 (6)

D’ =zoFqXlv+ (So --so)/6

D”=(c+ +t+q?X)l,,(~-ss,)/6

where:

Lij = i;llij/S

lvi= CkVklki

(7)

(8)

(9)

(10)

l”, =l,+ +I,- (11)

qx=c_ --c+ (12)

s, =s+ +s_ (13)

s;, =s+ +s=_ (14)

The subscripts + , - and 0 refer to cation, anion and water, respectively, Ci, is the concentration in the membrane phase, 6 is the thickness of the membrane, and @Xis the effective concentration of fixed charges. If a membrane has no fixed charge and the solution does not contain electrolyte, D’ and D” disappear and we have D= Do. If the membrane has fixed charges, the additional frictional interaction between fixed charges and the water flow must be considered. The charge effect is predicted by D’ of Eq. (7). At low concentrations D’ is large because r. increases with decreasing concentrations of electrolyte, while at high concentration D’ tends to zero. On the other hand, D” is zero at low electrolyte concentrations. Since the transport number of co-ions increases with increasing concentration of electrolyte, the absolute value of D” would monotonically increase with concentration.

If anion-exchange membranes are ideally permselective for counterions and there is no pressure difference, AP= 0, from Eqs. (5 ) to (8 ) volume flux can be written as [ 5 ] :

-J,=(1/6)(c01,,+z0FqN1~_) (15)

x{(s=,-s,)AT-v,An}

where AK is the osmotic pressure difference across the membrane. Eq. ( 15 ) can be rewritten as:

-Jv=D*{(~o-so)AT-voAn} (16)

where:

D*=(1/6)(Colvo+zoFqSl~_) (17)

If there is no concentration difference, Eq. ( 16 ) becomes:

-J,=DAT (18)

where:

D= (To -s,)D* (19)

T. Suzuki et al. /Journal of Membrane Science 92 (I 994) 8% 93 89

Moreover, if there is no temperature difference, Eq. ( 16 ) becomes:

-Jv=LpAn (20)

where:

Lp=-v,,D* (21)

Therefore, if we have experimentally obtained the values of D and D* we can estimate the value of entropy difference, & -so, and the value of the difference in molar enthalpy of water between the external solution and the membrane at steady stateAho=-T(~o-~o) [l-3].

f. -so = -v,D/L, (22)

= D/D*

Fig. 1 shows the dependence of the thermoosmotic coefficient on molality with Neosepta@ AM- 1. The apparent transport numbers of counterions in membrane AM-l calculated from the concentration membrane potential were 0.98 and 0.80 for 0.1//0.2 and 2.0//4.0 mol kg-’ of KC1 solutions, respectively. At molalities lower than 0.1 mol kg-’ of salt solution, D is nearly constant regardless of the species of counterions within experimental error. Therefore, thermoosmotic experiments were carried out at 0.01 mol kg-’ of salt solutions in order to study the dependence of counterions.

In KC1 solutions the absolute value of the thermoosmotic coefficient is at first constant and increases with increasing concentration as shown

P x I \I I

_,F L _

10-3 10-z to-’ loo 10'

Molallty of electrolytes. mol/kg

Fig. 1. The relationship between the thermoosmotic coeffl- cient, D, and molality of electrolyte solutions for Neosepta” AM- 1. Electrolytes: LiCl ( 0 ); NaCl ( A ); KC1 ( 0 ).

in Fig. 1. It is because the salt flux toward the hot side increases at high salt molalities and the volume flux due to the interaction between ions and water increases. As expected from Eq. ( 8 ) at high concentrations D” increases with increasing c+ and t+ although (S; -s, ) decreases slightly with increasing concentration. However, in LiCl solutions the absolute value of the thermoosmotic coefficient, D, decreases with increasing concentration. In this case the change of water structure due to Li+ ions in the membrane phase contrib- utes to the decrease of the difference between the transported entropy and the partial molar entropy of water at high concentrations, and reduce volume flux just as thermoosmosis across cation-exchange membranes in the Li+ form oc- curs toward the cold side due to the positive value of the entropy difference. That is, the absolute value of D will decrease because the absolute values of Do and D’ in Eqs. (6) and (7) will decrease due to the decrease of (f. -so ), although the absolute value of D” in Eq. (8) increases at high concentration.

Fig. 2 shows the linear relationship between the volume flux, J,, and the temperature difference of bulk solutions, AT,, for Aciplex@ A-20 1 in 0.0 1 mol kg-’ KF, KCl, KN03, KI03, HCOONa, CH,COONa, C6H,COONa, and p- CH3C6H,S03Na solutions. Similar relationships between J, and AT, were also observed for the other membranes.

The thermoosmotic coefficient calculated from the slopes in Fig. 2 using the method of least squares and the experimental results with the other membranes are plotted in Fig. 3, where the thermoosmotic coefficient per unit thickness of membranes, 6D, were used to compare the dif- ferences among the membranes. The thermoosmotic coefficient depends largely on the mobility of water in the membrane and the water content. The mobility of water is inversely pro- portional to the friction between the membrane matrix containing counterions and water. But we cannot fmd a simple relationship between the thermoosmotic coefficient and the reciprocal of the mobilities of counterions in free solutions. Water in the membrane exists in various states: that is, firmly or weakly bound water to ions and

T. Suzuki et al. /Journal of Membrane Science 92 (I 994) 85-93

0 5 IO 15

Temp.dlff. of bulk solns.. ATO, K

Fig. 2. The dependence of volume flux, J,, on the temperature difference of bulk solutions, AT,, for Aciplex@ A-201 in 0.01 mol kg-’ electrolyte solutions at the mean temperature 308.2 K. Electrolytes: ( 0 ) KF; ( 0 ) KCI; ( 0 ) KN03; (W ) KI09; ( V ) HCOONa; ( V ) CH,COONa; ( A ) C,H,COONa; ( A ) pCH,C,H,S03Na.

D Lo

-801 I I 1 I ?

0 0.2 0.4 0.6 0.8 10 d

l.i

Fig. 3. The relationship between the thermoosmotic coeff- cient, SD, and water content. Membranes: STA-I (0); STA- 2 (0); STA-3 (0); STA-4 (0); STA-5 (0); Aciplex@ A- 201 (0); Aciplexm A-221 (0); Neosepta@ AM-1 (0); Tos- flex” IE-DF 17 (A).

fixed charges, water interacting with the membrane matrix and pure water. All water in the various states will exchange with each other. Then the thermoosmotic coefficient 6D was plotted against the water content in Fig. 3. Fig. 3

shows that the plot gives a smooth curve for each membrane, where many various anions from small halide ions to large organic ions were used as counterions. For the anion-exchange membranes, considering experimental error, the mean molar transported entropy of water is practically all positive. However, for cation-exchange membranes the effect of counterions on the transported entropy of water in the membrane is very strong and the direction of thermoosmotic volume flux varied with the species of counterions [ 3,8]. It is interesting that the effect of the various anions on the structure of water around counterions seems to be small compared with that of cations.

Fig. 4 shows that the osmotic volume flux across Aciplex@ A-22 1 increases linearly with the difference in osmotic pressure of the external salt solutions. Eq. (23 ) was used to estimate the osmotic pressure difference AK.

An = vgR TAc, (23)

Where v is the number of moles of ions formed from 1 mole of electrolyte, g the osmotic coefficient and AC, the concentration difference of the external salt solutions. For KIO, solutions the values of g at 273.2 K [ 91 were used instead of that at 298.2 K because of the lack of data. More- over, for C,H,COONa, C6H,S03Na and p- CH,C,H,S03Na solutions the values of g were assumed to be 0.9. For the other electrolytes the

Osmotic pressure’ dlff An. MF)~I

Fig. 4. The dependence of volume flux, J,, on the osmotic pressure difference, Ax, across Aciplex@ A-221 at 298.2 K. Electrolytes: (0 ) KF; ( l ) KCI; (0) KI; (0 ) NaNOJ; ( n ) K103; ( V ) HCOONa; ( V ) CH,COONa; ( A ) C,H,COONa; ( A ) p-CHXC,H4S03Na.

T. Suzuki et al. /Journal of Membrane Science 92 (I 994) 85-93

Table 3 The values of entropy difference of water with various counterions

91

Counterion -(&-so) (J K-i mol-‘)

STA-3 Neosepta@ AM-l

Aciplex@’ Aciplex@ Tosflex@ A-201 A-22 1 IE-DF 17

F- 1.21 2.15 1.60 1.38 0.35 Cl- (-0.1) 0.88 1.05 0.43 0.2 I- (2.8) NO, 0.70 1.0 0.47 (0.2) IO, 1.3 2.6 2.4 2.95 1.04 HCOO- 1.26 0.57 0.30 CH&OO- 1.01 2.7 1.94 1.32 0.59 C6HSCOO- (2.4) 2.2 2.22 1.56 CsHSSOr (0.4) pCH3C6H$0y (-0.4) (i.1) (i.6)

80

60

40

20

0

I ,I 1 I , ,-

A I’ i i’ -

A /’ A /’

/’ - l ’

/’ ,’

9’ ,’

l

I

0 0.2 0.4 0.6 08 1.0 1.2

Water content. q/qqdry membr wlthout counterIons

Fig. 5. The relationship between the coefficient dD* and water content. Membranes: STA-3 (0); Aciplex@ A-201 (0); Aciplex@ A-221 (0); Neoseptaa AM-l (Cl ); Tosflex@’ IE- DF 17 (A).

values of g given in ref. 10 were used to estimate the difference in osmotic pressure. The values of D* were calculated from the slopes in Fig. 4 using Eqs. (20) and (2 1). Fig. 5 shows the values of the coefticient SD* against the water content for various membranes. The plot of 6D* against the water content is scattered compared with Fig. 3 (for the coefficient SD). Using the data of D and D*, the values of - (& -so ) are estimated and shown in Table 3. For Aciplex @ A-22 1 in the

10, form the entropy difference 3.89 J K-l mol-’ corresponds to the enthalpy difference dh0= 1.1 kJ mol-’ at 283 K.

As shown in Table 2 and ref. 2 the order of the water content of membranes is F- > 10, > Cl- >NO, for inorganic ions and CH&OO- > HCOO- > C6H5COO- > p- CH3C6H4S0~ (or C6H5SO~ ) for organic ions regardless of the type of membrane. On the other hand,the order of absolute value of the entropy difference between transported entropy and partial molar entropy of water is 10, >F- >Cl- >NO, for inorganic ions and C6H5COO- > CH&OO- > HCOO- for organic ions for all membranes. For inorganic anions the order of the entropy difference is similar to the order of water content. On the other hand for organic anions the order of the entropy difference is opposite to the order of water content. The ratios of the residence time for organic anions were reported: r*_ /r; = 1.28 for CH,COO-,r?/r;S = 2.0 for C6H5COO- and r*_/tz =0.6 for C6HSS0~, where r? and 7: are the residence times of water hydrated around anions and free water, respectively [ 11,12 1. The order of the ratios of the residence time is coin- cident with that of the entropy difference for organic anions. The hydrophobic part of organic ions may contribute to the water structure in the membrane and to reduce the entropy of water

[131.

92 T. Suzuki et al. / Journal of Membrane Science 92 (1994) 85-93

4. List of symbols

Subscripts - and 0 refer to anion and water species, respectively.

¢s

D D* F g h0 J,

Js Jv Lij

Lis, Lsi

Zss

Lp lv,

P R St

T ti vi

zi A A T

aTb

Iti

concentration of water in the membrane ( m o l m -3) salt concentration of the external solution (mol m - 3 ) thermoosmotic coefficient (m K- ~ s- ~ ) coefficient defined by Eq. (3) Faraday constant (96485 C mol -~ ) osmotic coefficient molar enthalpy of water (J mol- l ) absolute mass flux of component i (mol m - 2 s - j )

total entropy flux (J K -~ m - : s - l ) volume flux (m s- l ) phenomenological coefficient (mol 2 J - m - 2 s - t )

phenomenological coefficient (tool K- t m - 2 s -~ )

p h e n o m e n o l o g i c a l c o e f f i c i e n t (J K - 2 m - 2 s - t )

hydraulic permeability (m s- ~ Pa- t ) phenomenological coefficient ( J - t m 4 S -1 ) pressure (Pa) gas constant (8.314 J K - l tool -~ ) partial molar entropy of component i (J K- l mo1-1 ) mean molar transported entropy of component i (J K- ~ mol- ~ ) absolute temperature (K) transport number of component i partial molar volume of component i ( m 3

mol- ~ ) charge number of component i difference across the membrane effective temperature difference across the membrane (K) temperature difference of bulk solutions (K) thickness of the membrane (m) chemical potential of component i (J tool- 1 ) total chemical potential of component i (J mol-i )

p

7C Ti

T*

Ox

O

number of moles of ions formed from 1 mole of electrolyte osmotic pressure (Pa) reduced transport number of component i (molC -1 ) residence time (s) effective concentration of fixed charges (mol m -3) electrical potential (V)

Acknowledgements

We thank Tokuyama Soda Co., Ltd. for supplying Neosepta ® AM-1, Asahi Chemical Indus- try Co., Ltd. for supplying Aciplex ® A-201, A- 221 and test membranes STA-I to STA-5, and Tosoh Co., Ltd. for supplying Tosflex ® IE-DF 17.

References

[ 1 ] M. Tasaka, T. Mizuta and O. Sekiguchi, Mass transfer through polymer membranes due to a temperature gradient, J. Membrane Sci., 54 (1990) 191.

[2]M. Tasaka, T. Urata, R. Kiyono and Y. Aki, Solvent transport across anion-exchange membranes under a temperature difference and an osmotic pressure difference, J. Membrane Sci., 67 (1992) 83.

[3]M. Tasaka, T. Hirai, R. Kiyono and Y. Aki, Solvent transport across cation-exchange membranes under a temperature difference and under an osmotic pressure difference, J. Membrane Sci., 71 (1992) 151.

[ 4 ] J.-Y. Huot and C. Jolicoeur, Hydrophobic effects in ionic hydration and interactions, in R.R. Dogonadze, E. Kal- man, A.A. Kornyshev and J. Ulstrup (Eds.), The Chemical Physics of Solvation, Part A, Elsevier, Am- sterdam, 1985, Chap. 11.

[ 5 ] M. Tasaka and M. Nagasawa, Thermoosmosis through charged membranes. Theoretical analysis of concentration dependence, Biophys. Chem., 8 (1978) 111.

[6]K. Bunzl and B. Sansoni, Determination of the ion ex- changers by difference weighing, Anal. Chem., 48 ( 1976 ) 2279.

[7]M. Tasaka, Thermal membrane potential and thermoosmosis across charged membranes, Pure Appl. Chem., 58 (1986) 1637.

[ 8]J.W. Lorimer, Non-isothermal transport phenomena in charged membranes, in E. Selegny (Ed.), Charged Gels and Membranes, Part 2, Reidel, Dordrecht, 1976, p. 65.

[ 9 ] V.M.M. Lobo, Handbook of Electrolyte Solutions, Part A, Elsevier, Amsterdam, 1989.

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[ lo] R.A. Robinson and H. Stokes, Electrolyte Solutions, 2nd ed., Butterworths, London, 1959.

[ 111 H. Uedaira and H. Uedaira, Hydration of organic ions in aqueous solutions, Zh. Phiz. Khim., 42 ( 1968) 3024.

[ 12]H. Uedaira and A. Ohsaka, Seitai-kei no mizu (Water in biological systems) Kodan-sha, Tokyo, Japan, 1989, p. 54.

[ 13lE.R. Nightingale, Jr., On the specificity of electrolyte solvation. Viscosity and infrared characterization of ionic hydration, in B.E. Conway and R.G. Barrdas (Eds.), Chemical Physics of Ionic Solutions, Wiley, New York, 1966, Chap. 7.

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Solvent transport across anion-exchange membranes under a temperature difference and transported entropy of water