M. L. WRIUHT
50
Vol. 58
MEMl?R.Ai%EPOTENTIALS FOR KERATIN AND CELLOPHANE AND THE MEYER-TEORELL THEORY BY M. L. WRIGHT Wool Industries Research Association, Headingley, Leeda, England Rsceived A p r i l 33, 1968
I t is emphasieed that membrane potential measurementa are merely ionic transport number determinations for diffusion in the polymer, and that from the membrane potential data alone, no further quantitative information concerning the system can be deduced. The use of the Meyer-Teorell theory for analyzing membrane potential measurements to obtain the ionic mobility ratio is criticized on the grounds that it does not take into account the internal diffusion potential which can arise from a difference in ionic concentration gradients inside the membrane, and this potential difference may exist even when the mobilitiee are equal. Calculation* of the boundary and internal diffusion potential components have been made wing sorption data, whieh a g e e with experiment, and show that the second potential can often account for a large proportion of the total potential. Therefore any data deduced using the ori inal Meyer-Teorell analysis are of doubtful value. It is suggested that, to characterize a membrane, sorption data are required: the ratio of the ionic mobilities can then be calculated; and from this, the individual mobilities can be obtained using membrane conductivity data.
Lo
As a result of the direct measurements of ionic mobilities in polymers which have recently been it is now possible to check the validity of the Meyer-Teorell theory. This theory states that the ionic mobility ratio (not merely the transport number) can be obtained directly from membrane potential measurements. Meyer3 and Teorel14 assumed that 'the concentration of immobile ions present in the membrane, is the same a t all points and this leads to the anomaly that no internal diffusion potential can exist if the positive and negative ionic mobilities are equal; in fact it is possible for the concentration gradients of the two ion species to be unequal in the membrane phase. Clearly for liquid junction potentials in aqueous salt solutions of two components, this cannot arise because of the requirement of electro-neutraIity ; in the membrane this condition is satisfied by means of the immobile charged groups.
Sc o1h .
'i
For a uni-univalent solution, concentration c, then p = RT la c, and therefore FdE/RT = ( L +
- t-)d(ln
c)
(2)
(This derivation is only strictly true for ideal solutions but Meyer and Teorell made a similar assumption. The rigorous treatment for membrane potentials is given in an appendix.) If t* is independent of concentration in the range c1 to c2 this may be integrated a t once to give FAEIRT = (1+
- t-)
In (cl/et)
(3)
When the transport number is expressed in terms of the cationic and anionic concentrations (CK,CA) and mobilities (UK, U A ) of the total internal electrolyte in the membrane, eq. 3 may be rewritten in the familiar Nernst form FAEIRT
[(CKUK
+
- CAUA)/(CBUK
CAuA)]
In
(cI/c2)
(4)
For each concentration range the membrane potential AE gives the transport number for diffusion in the membrane in that range. This simple theory cannot give any information about the actual ratio of mobilities unless the ionic concentrations (or their ratio) in the polymer are known. T o overcome this difficulty Meyer and Teorell introduced two ideas: (i) the concept of immobile sites in the membrane and (ii) the substitution, before integration, of a sorption equation to relate ionic concentrations in the membrane t o those in solution. For the distribution of ions between solution and membrane the general equation6is
a t different concentrations cl, Q. At any point in the membrane consider Soln. an element AB paralCZ lel to the membrane faces (Fig. 1). Let ti* be the transport fl
