Application of Nernst-Planck and Poisson equations for interpretation of liquid-junction and membrane potentials in real-time and space domains

In this paper, we show a numerical model designed for analysing the propaga tion of ionic concentrations and electrical potential in space and time in the liquid-junction and in the solution I ion-exchanging membrane system. I n this model, diffusion and migration according to the Nernst-Planck flux e quation govern the transport of ions. The electrical interaction of the spe cies is described by the Poisson equation. These two equations and the cont inuity equation make a system of partial differential equations that is num erically resolved by the finite difference method. Consequently, the contac t and/or boundary potential and diffusion potential are presented as a resu lt of the physicochemical properties of the system rather than assumed a pr iori in order to find an analytical solution in the form of an equation. We show that the paradigmatic equations in potentiometry, such as Henderson a nd Nikolskii-Eisenman (N-E), are special cases in our model. Although we di scuss the examples relevant to electroanalytical potentiometry and, in part icular, to the field of ion-selective membrane electrodes (ISE), it is evid ent that the method presented here is a good tool for solving broader probl ems in membrane biology and electrochemistry with membranes. (C) 2001 Elsev ier Science B.V. All rights reserved.