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ELSEVIER Journal of Membrane Science 92 ( 1994) 75-84

Electrochemical properties of cellulosic ion-exchange membranes I. Equilibrium and permselectivity

M.D. Reboiras

Departamento de Quimica, Facultad de Ciencias, Universidad Autonoma de Madrid, 28049 Madrid, Spain

(Received June 2, 1993; accepted in revised form February 1, 1994)

Abstract

The emf values of the cell Ag,AgCl 1 KC1 (u’ ) 1 membrane 1 KC1 ( II” ) 1 Ag,AgCl have been measured. Two types of cellulosic strong ion-exchange membranes were tested, containing either cationic or anionic fixed groups. The membranes were prepared by grafting acrylic monomers onto paper followed by opening of epoxy groups. The membrane phase was analysed for its electrolyte and water contents, and intramembrane activity coefficients were derived as a function of external electrolyte concentration. The data were used for calculation of the emf of membrane cells using the TMS theory reformulated by Hills et al. The main finding of this investigation is that, for dilute external solutions, the membrane potentials are close to the maximum theoretical value and can be calculated with reasonable accuracy using the fixed charge theory. With a more concentrated solution this is not so; the membrane potentials are progressively smaller than the maximum value and the theory did not give satisfactory agreement between the observed and the calculated emf of the membrane cells. This is readily explained by the decrease in the selectivity of the membranes, the increasing concentrations of co-ions, and the diffusion of electrolyte through the membrane.

Keywords: Membrane potentials; Permselectivity; Activity coefficients; Donnan equilibrium

1. Introduction

Most ion-exchange membranes are cross- linked, three-dimensional polymer networks containing a number of fixed ionogenic groups. They may be classified into two types [ 11: ho- mogeneous, where the whole material is of an ion- exchange character and can be viewed as a polyelectrolyte gel swollen with water or an aqueous solution; and heterogeneous, where the ion-exchange groups are incorporated into the inert matrix by physical mixture or chemical reaction, in which case the polyelectrolyte gel constitutes only a part of the membrane.

There are several factors controlling membrane phenomena, such as ionic concentration within the membrane, composition of the solution outside the membrane solution, ion flux through the membrane and both the amount and the properties of water in the membrane phase, the latter being very different from the properties of free water or even of water in diluted electrolyte solutions [ 2-5 1. Because of its very complex nature, it cannot be said that the behaviour of ions within the membrane has been com- pletely elucidated, and that is why we are under- taking a comprehensive study of electrical trans-

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76 hf. D. Reboiras /Journal of Membrane Science 92 (1994) 75-84

port phenomena in cellulosic ion-exchange membranes.

The membranes under investigation were prepared from parchmentized paper by means of grafting reactions using a mixture of glycidyl acrylate and methyl acrylate followed by opening of epoxy groups; the method gave rise to either positive or negative ionic groups fixed to the cellulosic matrix [ 6,7]. Therefore, the main fea- tures of these membranes are, on the one hand, the hydrophilic properties of their matrix, in contrast with the conventional polymeric mate- rials used in the preparation of most ion-exchange membranes and, on the other hand, the strong character of the ionic fixed groups in comparison with those in the frequently studied cellulose acetate membranes.

Because of the importance of both the func- tional groups of the membrane and the nature of the interactions between the membrane matrix and the ions in relation to the electrochemical behaviour of the membranes, the present studies appear relevant. A detailed characterization of the equilibrium properties and transport coefficients of these membranes might be of interest in order to clarify the behaviour of ions within the membrane in detail, as well as to understand more complex membrane systems.

In this series of papers we shall report on measurements of transport numbers of both ions and water, electrical conductivity and membrane concentration potentials of several electrolytes and concentrations for strong cationic and anionic membranes bearing, respectively, SO, and

-C4H9-l?=(C2H5)2 as fixed groups. The above-mentioned electrochemical parameters are known to be functions of the external solution concentrations in single electrolytes because the absolute mobilities and the relative concentrations in the membrane are functions of the external concentration. We therefore decided to start this investigation by looking at the equilibrium properties of the membranes.

In this paper we report the analysis of both cationic and anionic membrane phases for their electrolyte and water contents and the intramembrane activity coefficients derived as a

function of external electrolyte concentration. Further, the experimentally determined membrane potentials are compared with those calculated by applying the fixed charge Teorell- Meyer-Sievers (TMS) theory. We have chosen KC1 as the electrolyte because of the similar values of the limiting ionic mobilities in aqueous solution of the two ions.

We assume an ion-exchange membrane to be a binary polyelectrolyte with complete dissocia- tion, in which the ionizable groups are immobi- lized by being fixed to the matrix and the membrane remains permeable to other ions. The equilibrium condition for the electrolyte ij is

F, = Pr, (1)

where the overbar is used to indicate the membrane phase and the terms without overbars re- fer to the solution.

In order to proceed further, the electrochemical potential p must be broken into its electrical (ZiJ’#) and chemical (RT In ai) contributions, plus one term due to the osmotic pressure, for every species i. We should keep in mind, however, that the concept of the electrochemical potential of one species of ion is something of a mathematical fiction, as the operation of adding only one kind of ion to a system cannot be per- formed if the fundamental electroneutrality con- ditions are to be maintained.

The activity of mobile ions in the two phases, membrane and solution, is governed by the Don- nan relation [ 1,8 ] :

RTln~+=,F(S-p)=(P-P)V, (2) I

where ai is the single-ion molal activity of species i, #-&is called the Donnan potential difference, P-P= n is the difference between the swollen membrane pressure and the hydrostatic pressure in the solution, and Vi is the partial molal vol- ume of i. Whether or not the potential difference may be evaluated depends on whether or not the two solutions inside and outside the membrane are sufficiently dilute for the 7, values (activity coefficients) to be calculated in the usual way. But whether this is so or not, the equilibrium condition for the electrolyte g, /iij = pii, yields

M.D. Reboiras /Journal of Membrane Science 92 (I 994) 75-84 77

If ij dissociates into Vi and VI, Eq. (3) takes the form

(4)

The above relationship may be correlated with the condition of electroneutrality, i.e., Czitii + ox=0 (where x is the concentration of fixed groups attached to the membrane matrix and w is the sign of these groups, equal to - 1 for a neg- atively charged and + 1 for a positively charged membrane), in order to obtain the counter-ion and the co-ion molalities in the membrane phase. For a membrane with w molal concentration of negative fixed groups, in equilibrium with a single ( 1: 1) electrolyte solution, the following equations apply:

fi, =x+m_

and

(5)

m_m+y2, 7cI/ M- rfi+y:

=ew ~~ ( >

(6)

Finding @__ and ti+ from Eq. (6) and substitut- ing into Eq. (5), we find that

ti+=;[l+(l+Q2)112] (7)

-

~_=-$[l-(l+Q~)~/~]

where

These equations cannot be used unless the activity coefficients in the membrane phase are known. These coefficients may be evaluated with

Eq. 16) considering that the term exp(rrV/2RT)=l

2. Experimental

2. I. Membranes

Both cationic and anionic ion-exchange membranes were prepared from sheets of parchment paper with a density of 84 g/m2 by means of a grafting reaction using a mixture of glycidyl acrylate-methyl acrylate (60/40, v/v) according to the procedure described by Riande et al. [ 6,7 1. The grafting reaction was initiated by ceric ions at the optimum pH value. After completion of the reaction, the ionic fixed groups were intro- duced into the sheets by opening the epoxy groups; i.e., negative groups by reaction with a 20% aqueous solution of sodium sulphite-bisul- phite ( 1: 1) at 50°C for 48 h, and positive groups by placing the grafted sheets in a 10% (v/v) solution of diethylamine in dimethylformamide kept at 50°C for 48 h, followed by quatemiza- tion reaction with a 50 (v/v) butyl bromide solution in dimethylformamide at 50°C. The membranes can be prepared in a reproducible form and are easy to handle; the only precaution to be taken is to store them perfectly dry in order to avoid fungal growth on the cellulosic material.

2.2. Electrolyte solutions

Potassium chloride solutions were prepared from reagent grade dried KC1 (Merck, p.a. ) and bidistilled deionized water. The molalities ( 10e3-1 mol of dried salt per kg of water) were adjusted to an accuracy within ? 0.1%.

2.3. Water content of membranes

Pieces of membrane equilibrated in KC1 solutions during 20 min were surface dried between the folds of a filter paper and weighed in a weighing bottle. The amount of water absorbed by the membrane was obtained by difference from the weight of the moist and the dry membrane. The membranes were dried to constant weight in an oven at 110°C.

78 M.D. Rehoiras /Journal ofMembrane Scrence 92 (1994) 75-84

2.4. Capacity of membranes

A known weight of dried cationic membrane was immersed in 30 ml of potassium chloride solution and allowed to equilibrate for 1 h, with oc- casional shaking. Then the membrane was washed a number of times with conductivity water until no chloride ions could be detected. The surface dried membrane was treated with exactly 30 mg of 0.05 M HN03 solution and allowed to stand for 1 h. The liquid was carefully decanted and the membrane was washed several times, allowing it to stand for 5-10 min; the washings were transferred to the decanted liquid and the whole was analysed for its acid and chloride contents by titration against carbonate free 0.05 M, NaOH and 0.05 MAgNO,, respectively; a weighing burette was used for measuring the amounts of reagents consumed in the titrations. The acid uptake of the membrane is equivalent to the quantity of fixed charges and the chloride content is equivalent to the concentration of the co-ion. The equilibrium times were chosen on the basis of previous analyses of the chloride uptake and acid exchange made at different times. A re- producibility of +2% was obtained within 30- 40 min.

The analysis of the membrane phase of the anionic membrane was carried out following the same procedure as described for the cationic membrane. The membrane was treated with a 0.03 M CaCl, solution and the Ca*+ and Cl- contents of the decanted liquid were analysed separately by titration against 0.0 1 MEDTA and 0.05 A4 AgN03 in the usual way.

The amounts of counter-ions and co-ions determined for various electrolyte solutions were used in Eq. (6) to derive the corresponding values for the activity coefficient terms in the membrane phase.

2.5. Membranepotentials

Membrane concentration potentials were measured in a cell of the type

Ag,AgCl 1 KC1 (a’ ) 1 membrane 1 KC1 (a” )

I &$1,&s (9)

at room temperature. A membrane previously equilibrated in the more concentrated solution was clamped between two half cells of 5 cm3 vol- ume. Each side of the cell contained an inlet tube with the end adjacent to the membrane surface for pumping previously dried nitrogen into each half cell solution at a rate of loo-120 ml/min. This flow of nitrogen served to disturb or re- move the diffusion layers eventually formed at the two membrane surfaces. The electrodes used were reversible Ag,AgCl electrodes prepared by the method of Brown [ 93, and were connected to a Keithley potentiometer. The e.m.f. values were recorded to an accuracy of + 0.02 mV with a potentiometric recorder (Philips PM 8252A).

The potential was monitored at frequent inter- vals, and reached a steady value after N 30 min. The potential reading was then taken as the steady state emf of the cell. Each potential determined was the mean value of two measurements obtained by exchanging the electrodes in the two chambers in order to compensate for the asym- metry of the electrodes.

By not stirring the solutions adjacent to the membrane lower emf values were recorded, which points to the existence of diffusion layers outwards from the membrane surfaces. It is as- sumed that these diffusion layers will persist even at the rates of stirring used to obtain the maximum emf but should be of negligible thickness compared with that of the membrane itself. The overall accuracy of the method is +- 0.2%.

3. Results and discussion

In Fig. 1 the emf values of the membrane cell (9) for different values of external concentration are shown in dependence on the mean activity. The observed emf of the membrane cell is compared with the maximum possible value of an ideally selective membrane, given by the Nernst equation:

E 2RTln 2 -+e max - - F a’,

(10)

The ai values were calculated from the molali-

M.D. Reboiras /Journal of Membrane Science 92 (1994) 75-84 79

Fig. 1. Variation of E/E,,,,, with the external electrolyte activity: (0 ) cationic membrane; (0 ) anionic membrane.

ties and interpolated values for the activity coefficients in KC1 solutions given in the literature

[ 101. The high values of E/E,,,,, obtained for both

cationic and anionic membranes at low external electrolyte concentrations provide an indication of the good qualities of the membranes as permselective barriers through which negligible transport of solvent or co-ions takes place. With increasing mean molality of the external solution, a gradual decrease of the selectivity is observed owing to the causes already noted.

The membrane potential arises from the contributions of the diffusion potential across the membrane and the interfacial potential difference, often called Donnan potential, and has been the subject of many theoretical and experimental studies [1,&l l-201.

The Donnan potential is an equilibrium phe- nomenon and, in consequence, it partially ex- cludes the co-ions from the membrane. The stronger the exclusion, the smaller is the electrolyte uptake. As the uptake of the electrolyte by the membrane increases with increasing concentration of the solution, the Donnan potential depends on the ionic concentration. Therefore the results of the chemical analysis of the membrane phase, shown in Tables 1 and 2 as a function of the molality m, and activity a+ of the external solution, allow us to obtain an-insight into the properties of the membrane.

These properties are the water content w of the membrane phase expressed as weight of water per g of wet membrane; the fixed charge din mol per

kg of water in the membrane; total co-ion molality ft_ also expressed as mol per kg of water in the membrane; and counter-ion molality M+, which can be derived from Eq. (5 ) as the electroneutrality condition. The situation with the anionic membrane is analogous. Here, of course, the values for fixed charges, co-ions and counter- ions have the opposite sign. The last column of Tables 1 and 2 gives the values of the mean activity coefficient of the electrolyte in the membrane phase calculated using Eq. ( 6 ) .

The absorption of water by the membranes results from the tendency of the fixed ions to be surrounded by polar molecules and the specific interactions between the polar solvent and the membrane matrix. The decrease in water content with increasing concentration of the external solution is similar to the behaviour found with conventional membranes. The higher values for the amount of water in the anionic membrane can be attributed to the greater affinity of the ammonium groups for the polar water molecules in comparison with the sulphonic groups of the cationic membrane.

Together with sorption of water, strong electrolytes are subject to electrostatic forces arising from the presence of fixed ionic groups and counter-ions in the membrane phase; the result is a Donnan type sorption equilibrium. The Donnan equilibrium has one immediate consequence for electrolyte sorption; it repels co-ions from the ion exchanger, and this prevents the in- ternal co-ion concentration from rising. The ef- ficiency of electrolyte exclusion decreases with increasing solution concentration, and this fea- ture is shown in the values of co-ion molalities of both the cationic and the anionic membrane.

The co-ion and counter-ion values were used to calculate the mean activity coefficients of the electrolyte in the membrane These values have been evaluated by assuming that the swelling pressure term exp (7rV/2RT) is unity, which im- plies a negligible contribution of this term to the values of p+ [ 2 l-241. It is seen that the activity coefficient in the membrane phase, in contrast to that in aqueous solution, increase with concentration. In highly diluted solutions, the mean molal activity coefficients of aqueous electro-

80 M.D. Reboiras /Journal of Membrane Science 92 (1994) 75-84

Table 1 Equilibrium properties of the cationic cellulosic ion-exchange membrane as a function of the external solutions of KC1

a, m, W R m- m+ p* enV/2RT

0.001119 0.001162 0.128 2.369 0.058 2.427 0.0030 0.0022 15 0.002334 0.128 2.393 0.059 2.452 0.0058 0.004925 0.005324 0.128 2.505 0.064 2.569 0.0121 0.009560 0.01063 0.127 2.546 0.069 2.615 0.0225 0.04141 0.05087 0.126 2.707 0.089 2.796 0.0830 0.07869 0.1025 0.125 2.753 0.116 2.869 0.1364 0.1836 0.2619 0.124 2.828 0.145 2.973 0.2796 0.3513 0.5413 0.122 2.875 0.222 3.097 0.4237 0.6485 1.074 0.120 2.921 0.325 3.246 0.6314 1.408 2.466 0.117 2.969 0.639 3.608 0.9273

Table 2 Equilibrium properties of the anionic cellulosic ion-exchange membrane as a function of the external solutions of KC1

a, m+ w X m* M- y* envf2nr

0.001244 0.001294 0.215 1.869 0.048 1.917 0.004 1 0.002460 0.002598 0.214 1.883 0.050 1.933 0.0079 0.005616 0.006098 0.214 1.901 0.052 1.953 0.0176 0.01091 0.01218 0.213 1.917 0.056 1.973 0.0328 0.04258 0.05244 0.211 1.951 0.073 2.023 0.1108 0.08099 0.1056 0.210 1.986 0.084 2.070 0.1942 0.1805 0.2564 0.208 2.033 0.124 2.157 0.3490 0.3434 0.5308 0.205 2.157 0.157 2.314 0.5697 0.6747 1.106 0.202 2.393 0.196 2.588 0.9473

lytes approach unity by virtue of the choice of the reference state. In contrast, in the membrane phase, they drop to quite small values, approach- ing zero, when the external solution is greatly diluted.

Elsewhere [ 12,16,22,23,25], similar results have been reported, stirring up many controver- sies. Some workers [ 12,25 ] have attributed this anomaly to the occlusion of electrolyte in the membrane surface and co-ion sorption by the membrane impurities. Even after correction for the contribution of these two factors, the limiting value of the activity coefficient extrapolated to infinite dilution of the external solution may well be somewhat smaller than unity [ 25 1. All these facts have resulted in criticism of quanti- tative studies based on the Donnan theory, and other theories have been suggested as alterna- tives [ 121. Nevertheless, meticulous work [ 18- 20,221 supports Donnan’s theory and the causes

of the peculiar decrease in activity coefficients remain to be fully understood, mainly because of the unusual environment of the ions inside the membrane.

After obtaining values of the ion concentration, as well as the fixed ion concentration, which characterize the membranes, it is possible to pre- dict theoretically the contribution of the interfacial potential difference to the membrane potential by using a suitable model for the membrane. That used here is based on the reformulation by Hills et al. of the TMS theory [ 13 1.

Let us consider that the electromotive force of a cell such as (9 ) arise from the contributions of the electrode potentials and the membrane potential. The total membrane potential is consid- ered to be composed of two Donnan potentials at the two solution-membrane interfaces ( ’ ) and ( n ) and a diffusion potential arising from un-

M.D. Reboiras /Journal ofMembrane Science 92 (1994) 75-84 81

reference electrode

electrode potential

Donnan potential

Donnan potential

electrode potential

potential

Scheme 1.

equal concentrations at the two membrane faces (Scheme 1).

The concentration potential is given by

d”-~‘=(~“-9”)_(9’-d’)+(~“_~‘) (11)

The difference between the Donnan potentials may be obtained from Eq. (2) :

($y-p)_(q$ L&)

RT a’l. RT a’ 1 =Flnd”-~lnd,+p(~‘I/)-~K”~)

(12) where d +=HI+Y; and d_= M-Y_ and Hi+, y+ and y._ are respectively the molal concentrations and the activity coefficients inside the membrane. The diffusion potential &” -6 ’ may be equated to that of the liquid junction. Assuming that the total ion concentration changes linearly through the diffusion zone for a 1: 1 electrolyte the following expression may be used

(13)

where ZI+ and a_ are cation and anion mobilities and M’+, mt’;, HK and HI ‘L are the ion molalities at points ( ’ ) and ( n ).

The diffusion potential is obtained by substi- tuting Eq. (7) into Eq. ( 13 )

p_-,=“I+-“_ El, ~[CJ+(l+Q”)“*] u++z-_ F X”[U+(l+Q”*)“*]

(14)

in which o= (a+-zi_)/(zI++a_) and dis the concentration of fixed ions.

Using reversible anion electrodes, the contribution of the two electrodes to the total emf is given by

&RTln a’_ F a? (15)

From Eqs. (12), (14) and (15), the following expression for the membrane cell emf is obtained:

E=gln y’_x’[-l+(l+Q’*)“*] + F )CY”[-l+(l+Q”*)“*]

URT 7 In

X, [U+ (i+QQ) */*I Xn[U+(1+Q”2)1’2] (16)

The values of dand Q given by Eq. (8 ) have been obtained experimentally, whereas jr_ and exp(aV/2RT) cannot be determined without making some assumptions. By replacing the ra- tio y’_/jC by unity and equating (rr I? ) ’ to (nVJ/ , which are reasonable approximations as discussed in ref. 13, the emf values of membrane cells were calculated, and they are shown in Ta- bles 3 and 4 for the cationic and the anionic membrane, respectively. The accepted simplifi- cations amount to equating the electrochemical environment of each interface and to neglecting

82 M.D. Reboiras /Journal of Membrane Science 92 (1994) 75-84

Table 3 The emf of the cell Ag,AgCl (KC1 (m’ ) 1 cationic membrane ( KC1 (m” ) ( Ag,AgCl

Q Donnan potential Diffusion potential Reference electrode Ecell &e,, - Eobs (mv) (mv) (RT/F)ln 7, (mv) (mv)

(mv)

0.001162 0.3149 - 55.68 -0.44 - 149.50

0.002334 0.3192 - 54.75 -0.44 - 132.30

0.005324 0.3211 - 52.24 -0.46 -113.50

0.01063 0.3338 - 50.90 -0.41 -97.54

0.05087 0.3686 -44.37 -0.51 -63.99

0.1025 0.4191 - 37.56 -0.53 -51.22

0.2619 0.4644 -31.82 -0.55 - 32.76

0.5413 0.5768 - 20.88 -0.58 - 22.08

I .074 0.7032 - 11.08 -0.61 -11.82

2.466 1.023 -6.31 -0.70 - 1.94

35.33 0.47

40.09 -0.61

33.25 -0.45

73.59 -0.73

32.33 0.18

42.64 1.18

32.27 1.64

30.29 4.29

23.14 - 5.44

Table 4 The emf of the cell Ag,AgCl 1 KC1 (m’ ) 1 anionic membrane 1 KCl( m” ) 1 Ag,AgCl

m, Q Donnan potential Diffusion potential Reference electrode E,,,, &,I, - Ls (mv) (mv) (RT/F)ln Fk (mv) (mv)

(mv)

0.001294 0.3247 60.23 0.32 141.32

0.002598 0.3307 59.13 0.33 134.46

0.006098 0.3357 58.13 0.33 103.87

0.01218 0.3470 56.26 0.34 87.86

0.05244 0.3939 49.49 0.35 56.67

0.1056 0.4200 45.85 0.37 42.14

0.2564 0.5088 35.85 0.41 27.06

0.5308 0.5589 29.78 0.43 14.46

1.106 0.5955 24.08 0.57 1.39

34.81 0.17

42.18 0.37

33.89 0.53

69.34 0.96

32.48 0.48

40.12 2.66

31.25 3.14

31.74 4.53

M.D. Reboiras /Journal of Membrane Science 92 (1994) 75-84 83

the effect of differential swelling of the membrane, but without thermodynamic support. Further, the diffusion potential was calculated on the bases of the limiting mobilities of K+ and Cl- observed in aqueous solution using the relation

,_&+ -ng- -ng+ +ng- (17)

Columns 3-5 in the tables are the values of the calculated parameters relating to individual half- cells, and the last column shows the difference between the membrane cell emf experimentally observed and calculated using Eq. ( 16) for specific combinations of m’ and m”. For both the cationic and the anionic membrane, the results obtained theoretically and experimentally agree reasonably well (within 1% error) up to an external electrolyte concentration of 0.1 m; above that concentration the agreement is very poor. Above this concentration range the discrepan- cies between the observed membrane cell emf values and those calculated are much higher, co- inciding with the decreasing in permselectivity reflected in the electrical potential difference already shown in Fig. 1.

This behaviour, together with the values of the equilibrium parameters, suggests the character- istics of the membranes and the nature of the phenomena observed. When in contact with electrolyte solutions of low or moderate concentration, the membranes contain a large number of counter-ions but relatively few co-ions, as reflected in the high values of the Donnan potential. Counter-ions are admitted to the membrane, but co-ions, on the other hand, are efficiently excluded from the membrane and thus find it difficult to pass through (low diffusion potential values). The membranes are permselective for counter-ions and their behaviour closely approaches that of an ideally semiperme- able membrane. However, as the concentrations of the external electrolyte solutions are in- creased, the Donnan exclusion becomes less ef- fective, co-ion uptake becomes higher and thus the permselectivity is reduced.

The decrease in selectivity as the result of the Donnan uptake of electrolyte is the basis of the initial TMS theory as expressed in Eq. ( 16)) but

this theory is inadequate to explain the experimental results when the membranes are in contact with electrolytes of high concentration. This result suggests that the membranes under study behave in the same fashion as conventional membranes, since results similar to those found here have already been reported for other membrane systems [ 14,2 11.

The principal reason for the lack of accuracy of Eq. ( 16) in justifying the concentration potential values of the membranes at high electrolyte concentrations is that it fails to take into account the steady flow of solvent associated with the establishment of the membrane potential. The electroosmotic transport of solvent is well established and involves an additional contribution of the membrane potential. However, no means exist for calculating the solvent transport number from equilibrium principles; it can be found only from separate experiments extended over the whole range of external electrolyte concentrations. It may be expected that water trans- fer through the membranes should be a function of the water content of the membranes. Thus the measured potential would be a function of the water content of the membrane. We expect to give an account in due course of accurate results con- cerning the influence of water transport on the membrane potentials, once the experiments cur- rently in progress have been concluded.

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