Computer simulation of ion-selective membrane electrodes and related systems by finite-difference procedures

A simple but powerful numerical simulation for analyzing the electrochemical behavior of ion-selective membranes and liquid junctions is presented. The computer modeling makes use of a finite-difference procedure in the space and time domains, which can be easily processed (e.g., with MS Excel software) without the need for complex mathematical evaluations. It leads to convincing results on the dynamic evolution of concentration profiles, potentials, and fluxes in the studied systems. The treatment accounts for influences of convection, flow, or stirring in the sample solution that act on the boundary diffusion layer and it is even capable of including the effects of an electrolyte flow through the whole system. To minimize the number of arbitrary parameters, interfacial reactions are assumed to be near local equilibrium, and space-charge influences are considered via phase-boundary potential differences. The applicability of the computer simulation is demonstrated for different ion-selective membranes as well as for liquid junctions. The numerical results are in excellent agreement with experimental data.