SALT FLUX AND ELECTROMOTIVE-FORCE IN CONCENTRATION CELLS WITH ASYMMETRIC ION-EXCHANGE MEMBRANES AND IDEAL 2 1 ELECTROLYTES/

The previously proposed Nernst-Planck-Donnan description (J. Phys. Che m. 1996, 100, 7623) of the salt flux and the emf in concentration cell s with asymmetric ion exchange membranes is generalized to encompass i deal 2:1 electrolytes (doubly charged cation and singly charged anion) . Any point in the membrane may be considered to be in Donnan equilibr ium with a given external salt concentration. The profile of this salt concentration through the membrane determines the ion concentrations, the local salt flux, the profile of electric field strength, and the immediate value of the emf. The Donnan potential and ion distribution are found as the unique, positive and real root of a third-degree poly nomial. In this paper we focus on the stationary state rather than the initial state. For this purpose, the stationary state nonlinear diffe rential equation for the salt concentration profile is solved numerica lly by the ''shooting method''. We consider salt concentration profile s, ion concentration profiles, and field strength profiles in three di fferent cases: (1) a very weak cation exchange membrane (VWC), (2) a w eak anion exchange membrane (WA), and (3) a strong anion exchange memb rane (SA). The membranes are asymmetric with spatial dependence of the Nernst distribution coefficient for the salt, of the fixed charge den sity, and of the ion diffusion coefficients. We study both directions of stationary flow through the membranes. The emf is a functional of t he salt concentration profile and is found by numerical integration. T he overall behavior of the VWC is almost Fickian with respect to diffu sion of salt in both direction, and there is practically no diffusion asymmetry. However, there may be considerable differences in the stati onary state emf values for the two directions of diffusion. The WA is close to Fickian for the diffusion in one direction, but strongly non- Fickian with reversed diffusion flux. There is a large diffusion and e mf asymmetry for stationary state diffusion in the two directions for large differences of concentration. The order of magnitude found for t he calculated stationary state emf asymmetry corresponds to observed v alues for various membranes. The SA is strongly non-Fickian, but there is practically no diffusion asymmetry. The SA is almost an ideal anio n exchange membrane because of the Donnan exclusion from the membrane of the doubly charged cation. Thus, the emf measured with electrodes r eversible to the anion should be zero, and so it is found within numer ical uncertainty.