N. Kamo, M. Oikawa, and Y. Kobatake
92
TABLE V: ionization Potentials of Some Aromatic Solvents Solveni ~
~
_
_
-
“
_
I”,eV
Ref
9.22 8.77 8.58 8.58 8.48 8.39
a
-
Benzene Toluene o-Xylene’ m-Xylene p-Xyisne Mesitylene
a a
a a 4f
a V J Hammonci, W C Price, J P Teegan, and A D Walsh, Discuss Faraday SOC, 5 3 , 9 (1950)
stronger than. in nz-xylene and mesitylene. If the ionization potentials of these solvents are compared (Table V), it i s seen that 1, of mesitylene is lower (8.39) than those of p - and m-xylene (8.58 and 8.48). Solvation should have been stronger in mesitylene. It seems then that factors of molecular symmetry and stereometry
determine the degree of solvation by the solvent. The solubility of the chloride is much lower than that of the bromide, and the results for the chloride are thus less accurate. However, it appears that the conclusions drawn for the bromide hold also for the chloride. (1) Figure 1 shows two groups of solubility curves, corresponding to inert saturated solvents and donor solvents such as benzene or dioxane. (2) According to the values of the solubility parameter 82 obtained for the various solvents the same difference is found in the behavior of 82 in the two groups of solvents. Its value is a.bout 17-18 in the inert solvents and smaller than 15.6 in donor solvents. In this case, however, the values of (52 remain more scattered even in inert solvents and it is difficult to pinpoint the most probable value. (3) The chloroform solution apparently behaves like a regular solution. (4) The entropy graph also exhibits two groups of solvents. ( 5 ) The same remarks as above for mercuric bromide apply to the solvation in p-xylene.
Effective Fixed Charge Density Governing Membrane Phenomena. Expression of Permselectivity Nacpki Kamo,* Masako Oikawa, and Yonosuke Kobatake Faculty of Pharmaceufical Sciences, Hokkaido University, Sapporo, 060, Japan (Received June 23, 7972)
An equation representing the degree of permselectivity of membrane-electrolyte systems was derived by use of the empirical expressions of the activity coefficients and mobilities of small ions in charged membranes reported in previous parts of this series. The expression obtained for the permselectivity was shown to be applicable for various combinations of membranes and 1:1 type electrolytes. The systems examined here were collodion-based polystyrenesulfonic acid membranes, oxidized collodion membranes, and dextran sulfate and protamine-incorporated collodion membranes with LiC1, KCl, NaCl, KF, and MI03. Based on the permselectivity defined here a simple method for the determination of the effective fixed charge density which governs various transport processes in a charged membrane was proposed, and the implication of the permselectivity of a membrane-electrolyte system was discussed.
This series of papers is concerned with experimental study of the effective fixed charge density governing transport processes in charged membranes. In parts I1 and IV,2 the mobilities and activity coefficients of small ions in polystyrenesulfonic acid incorporated collodion membranes with various 1:1 type electrolytes were determined experimentally. It was shown that both activity coefficients and rnobilities of small ions in charged membranes were represented by the same functional form with the “additivity rule, ” found empirically in the field of polyelectrolyte solutions study,3 and they were expressed by the following equations.
(e-+ # X ) / ( C - 4- X ) , y- = 7-0 u+ = Sc+O(C- + # X ) / ( C - + X ) , u- =
y + = y+o
u-0
The Journal of iPhysicni Chemistry, Voi. 77, No. 1, 1973
(1)
(2)
Here yi, ui, 710, and u10 (i = +,-) stand for: the activity coefficient and mobility of ion species i in the membrane and in the bulk solution, respectively, C- and X are the concentration of anion adsorbed in the membrane (in moles per liter of the water in the membrane), and the stoichiometric concentration of charges fixed in the membrane. According to the convention suggested by Guggenheim,4 y+O can be equated with 7 - 0 for a 1 :I type electrolyte, and they are replaced by the mean activity coeffiN. Kamo, Y. Toyoshima, H. Nozaki, and Y. Kobatake, Koiioid-Z. Z. Polym., 248, 914 (1971). T. Ueda, N. Kamo. N. Ishida, and Y. Kobatake, J. Phvs. Chem., 76. 2447 (1972). A. Katchalsky, Z. Alexadrowicz, and 0. Kedem, “Chemical Physics of Ionic Solution,” Wily, New York, N. Y., 1966, p 296. E. A. Guggenheim, Phi/. Mag., 19, 588 (1935)
Reduced Expression of Permselectivity
93
+
cient ylt* of the electrolyte component. In eq 1 and 2, represents the fraction of counterions in the unbounded form, i.e., exclJding those tightly bound to the polymer skeletons constituting the membrane. +X may be referred to as the thermodynamically effective fixed charge density of the membrane. It must be noted that the concentration dependences of ' y t arid of u+ have the same functional form with 4X.es a sole parameter, and that y- and u- in the membrane are niot affected appreciably by the presence of negative charges fixed in the membrane. As was shown in a different series of papers,5 various membrane phenornena are represented quantitatively in terms of the effective charge density 4 X of the membrane as a characterlstir parameter for a given combination of membrane and electrolyte in question. However, each ion species has its own mobility in the bulk solution, and this leads to different values of observed membrane potential and of the other transport processes across the membrane depending on the species of electrolyte component used. Therefore, it may be worthy of developing a general method of charactel ization of membrane-electrolyte systems, which is applicable to any system irrespective of the ion species involved. This will be done by introducing a parameter representing the permselectivity ot the membrane as will be discussed in this article. Consider a system in which a negatively charged membrane is immer.sed in an electrolyte solution of concentration C Under this condition the Donnan equilibrium for small ions holdt, between the membrane phase and the solution. Then we have
c
c
(3)
{ 7 1")2C2 = y + +y - -
The maw fixed tyansference number of anion in the membrane, 7-,is defined by ', -
= u-C-/(u+C+
+ u-c-)
(4)
Introducing eq I, 2, atid 3 into eq 4 together with the electrical neutrality condition, z.e., C+ = C - X , we obtain
+
--- 1
-/-
"-
+
(4p 4- 1)X _-1 (4t;Z c 1 ) X c (2a.- 1)
a---
(5)
where E and a stand for the relative concentration defined + ~ respectively. On the by C/+X, and L ~ + ~ / ~+U LO), other hand, the apparent transference number of anion in the membrane, T ~ is~defined ~ from the observed membrane potential i p by the following Nernst equation. Acp
s
-(RT/F)(I
- 27app-)
In (C2/Ci)
(6)
Here C1 and C:! are the concentrations of the external solutions on thie t w o sides of the membrane, and R, T, and F have their usrial thermodynamic meanings. In part I1 of this serjes,6 thc difference between T- and T ~ was ~ shown to be less, than 2% in wide range of salt concentration when the averaged concentration (CI + C2)/2 was replaced by C. Therefore, if we replace T - by 7app-, and C by ( C l C2)/2 eq 5 is applicable even when the concentrations on the two sides of the membrane are different. Rearrangement of eq 5 leads to
+
1 1 ._(4p 4- 1)YJ a .- (2a
Tapp
.- -a
= P, ( 7 )
_ I -
-
1)(1
-
TaPp-)
Here P8 is a me9surp of permselectivity of the membraneelectrolyte system as will be discussed in the subsequent paragraph.
When the external salt concentration C is high enough in comparison with +X,i e . , f = C/+X >> 1, .the equation of membrane potential is reduced to A q = -(BT/F)(2a
- 1)In (Cz/Cl)
(8)
This equation Is nothing but a diffusion potential of an electrolyte in the bulk solution, and/or equal to the membrane potential for a system with a membrane having no ~ ~ (1 - - a ) , which fixed charges. In this case, T ~ becomes in turn, Ps defined by eq 7 reduces to zero. On the other hand, when C
