N. LAKSHMINARAYANAIAH
1588
Membrane Potentials.
Measurement of Electromotive Force of Cells
Containing “Untreated” Collodion Membrane*
by N. Lakshminarayanaiah Department of Pharmacology, Schools of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania (Received November 23, 1966)
Measurements of membrane potentials, counterion transport numbers, and solvent transport numbers for the system KCl(aq) \collodion membrane[KCl(aq) are presented and used to test the Scatchard theory of membrane potential. The agreement between the observed and calculated emf’s of appropriate membrane cells, although initially very poor, proved satisfactory later when proper amends were made for the change in the physical structure of the membrane brought about by the applied electric field.
Of the several theories formulated in recent years to describe the electrical potentials arising across permselective membranes of high fixed charge density, the theory of Scatchard,’ which is based on the application of well-established principles of classical thermodynamics used in the consideration of liquid-liquid junction potentials to the treatment of isothermal diffusion potentials generated across membranes, has been shown2 to be very satisfactory in describing the emf’s of membrane cells of the type Ag,AgCl I NaCl (a1)/membrane]NaCl (a”) IAgC1,Ag (1) containing cross-linked sodium phenolsulfonate membranes of medium fixed charge density. The equation of the Scatchard theory predicting the emf of membrane cell of type 1, although not from first principles, was cast by Hills, et aZ.,a into the form
E
=
“yL1’(t,-
--
10-am,M?w) d In a&
(2)
(where E is the emf of the membrane cell 1, F is the Faraday, mri,is the mean molality of tlheelectrolyte solution of activity a, t+ and 1, are the transference numbers of counterion and solvent, respectively, in the membrane phase, and M is the molecular weight of solvent), a form in which it was derived earlier by Lorimer, et uZ.,* by applying the principles of thermodynamics of irreversible processes to transport phenomena across membranes. Unlike the fixed charge theory of membrane potential The Journal of Physical Chemistry
expounded by TeorelP and Meyer and Sievers,6 the Scatchard theory is very general and stipulates no special property, as, for example, presence of a number of ionogenic groups, in regard to the structure of the membrane. I n view of this, it is no surprise to find the theory to be satisfactory in describing the emf’s of membrane cells even in high salt environment in which there is incomplete ionic selectivity of the membrane. Conversely, it may be presumed that the Scatchard theory would be equally successful in describing the emf’s of cells containing membranes carrying few or nil fixed charge groups. This paper therefore describes the extent of success achieved in integrating eq 2 by using values of I+and 1, measured as functions of activity of the external electrolyte solution of KC1 employing untreated collodion membranes carrying only stray and end carboxylic groups.’
* Presented a t the Tenth Annual Meeting of the Biophysical Society held a t Boston, Mass., Feb. 23-25, 1966. (1) G.Scatchard, J. A m . Chem. SOC.,7 5 , 2883 (1953). (2) N. Lakshminarayanaiah and V. Subrahmanyan, J . Polymer Sci., A2, 4491 (1964). (3) G.J. Hills, P. W. M. Jacobs, and N. Lakshminarayanaiah, Proc. Roy. SOC.(London), A262, 246 (1961). (4) J. W.Lorimer, E. I. Boterenbrood, and J. J. Hermans, Discussions Faraday SOC.,21, 141 (1956). (5) T. Teorell, Proc. Soe. Ezptl. Biol. Med., 33, 282 (1935); Proc. Natl. Acad. Sci. U. S.,21, 152 (1935); Progr. Bwphys. Bwphys. Chem., 3 , 305 (1953). (6) K.H. Meyer and J. F. Sievers, HeEv. C h i n . Acta, 19, 649,665, 987 (1936). (7) K.Sollner, I. Abrams, and C . W. Carr, J . Gen. Physwl., 24, 467 (1940).
EMFOF CELLSCONTAINING "UNTREATED"COLLODION MEMBRANE
1589
Experimental Section The preparation of collodion membranes is described elsewhere.* Rlembranes used in this study had an exchange capacity of 0.2 mequiv/g of wet membrane. Methods already outlined2ss were followed to determine meaningful values for the transport numbers of K f counterion 2(), and water (L). These were measured as functions of external electrolyte (KCl) concentration. AIembrane potentials were measured using half cells and procedures described in our previous publication^.^^^
,
I.
\
4 \
Results and Discussion
B
The emf of the cell Ag, AgClIKCl(m')[membraneIKCl(mI') IAgC1, Ag at 25" for various values of molality of the external solutions are given in Table I. The untreated collodion membranes have low fixed charge concentration and are therefore expected to show lorn selectivity toward counterions. The observed emf of the membrane cell is compared with the E,,, value in E'igure 1. The so-cslled Emax value given by
I -I
-2
-3
0
Log (mean activity)
Figure 1. The variation of EIE,,, with mean external activity: 8, observed values with polymethacrylic acid of high fixed charge density taken from ref 9; 0 , observed values of this study; 0, calculated values from observed transport numbers; X, observed values with membranes used in counterion transport number determinations.
(3)
is the maximum possible value of electrical potential arising across an ideally permselective membrane across which there is negligible transport of co-ions and solvent. The drop in selectivity with the mean external activity i s very marked compared to the smooth decrease in selectivity exhibited by cross-linked polymethacrylic acid membrane of high fixed charge density of nearly 3 m (a:so shown in Figure 1). The collodion
09 -
08..
Table I: Emf's of the Cell Ag,AgCl,KCl(m'),membrane\
t+
KCl(rn~~)~AgCl,Ag itt 25"
Cell no.
1
ml,
mII,
a*I,
a*?
mole
mole
mole
mole
kg-1
kg-1
kg-1
kg -1
E, mv
0.000969 0.001912 0.00464 0.00905 0.01742 0.0410 0.0773 0.145
34.0 43.0 31.0 30.0 33.0 28.1 19.5 21.5
2 3 4 5 6 7
0.002004 0.00501 0.01002 0.0'2005 0.0502 0.1004 0.201
8
0.507
0.001002 0.002004 O.OO501 0.01002 0.02005 0,0502 0.1004 0.201
0.001912 0.00464 0.00905 0.01742 0.0410 0.0773 0.145 0.331
07.
20
06-
- 10
051
-3
-2
Log a*
10 0
-'
Figure 2. Counterion and solvent transport numbers a8 a function of external activity.
membrane, being not very permselective, is not able to keep the co-ions out of the membrane phase even in a very low salt external environment to the same extent as ion-exchange membranes of high fixed charge density. The Scatchard theory has taken the factors causing this
~~
(8) N. Lakshminarayanaiah and
~
~
K. R. Brennen, Electrochim. Acta,
in press. (9) G. J. Hills, P. W. M. Jacobs, and N. Lakshminarayanaiah, Proc. Roy. SOC.(London), A262, 257 (1961).
Volume 70, Number 6 M a y 1966
1590
decrease in selectivity, viz., transport of co-ion and solvent, into account in formulating eq 2. Using the values of t+ and t, determined by electrolysis experiments and given in Figure 2, the cell emf may be evaluated quite realistically, but the difficulty lies in integrating eq 2. From the data of Figure 2, it is possible to derive, by interpolation, the required values of 2+ and t, for each of the membrane interfaces concerned, but the variation of these quantities across the membrane is not known and can only be obtained from B knowledge of the steady-state diffusion profile in the membrane. This profile may be assumed to be linear between the two solution activities with which the two membrane faces are in equilibrium. Thus, the corresponding variation of t + and Zw in the membrane may be inferred from the known variation of these quantities with the external solution molality (see Figure 2). Using the values so derived, eq 2 was integrated numerically by means of Simpson’s rule. The results expressed as a ratio E/Emax are shown in Figure 1. These values are significantly lower than the observed values and are outside the limits of experimental variation which was *2%, In the previous study with high fixed charge membranes,g where the calculated values of emf were also lower than the observed values, several possibilities existing to muse this disagreement have been discussed. However, in the recent paper2 this lack of agreement was shown to be due to use of improper values of Z+ and t,, whereas in this work the effects of both back-diffusion and concentration polarization leading to membrane polarization, which made the transport numbers of the previous studyg improper, have been eliminated.
The Journal of Physical Chemistry
N. LAKSHMINARAYANAIAH
The causes for this unsatisfactory agreement therefore were sought elsewhere. In a number of experiments carried out to determine I+,when high currents especially were employed to eliminate back electrolyte diffusion by shortening the time of electrolysis experiment, sudden changes in current flow were observed. The membranes used in this study have very high impedance (specific conductance k = 10-lo ohm-’ cm-’) and consequently required application of high dc voltages (>loo) to get the required current flow (15-20 ma). The sudden change in current during an experiment was found to be due to a change in the physical structure of the membrane. Determination of the membrane impedance after the electrolysis experiment showed that the membrane had become more conducting than it was before the transport number determination. This pointed to the fact that the membrane had become more porous. As a result, when these membranes were used in the above cell (l), lower cell emf’s were observed. These values, also expressed as E/Emax and shown in Figure 1, agreed reasonably well with the calculated values. Thus, it is found that, provided proper corrections are made where they are due as shown in this study, eq 2 of the Scatchard theory describes satisfactorily the emf’s of cells of type l containing membranes of low fixed charge density.
Acknowledgments. The work was supported in part by U. S. Public Health Service Grant NB-03321 from the National Institute of Neurological Diseases and Blindness and by Grant GB-865 from the National Science Foundation.
