Overcoming Pitfalls in Boundary Elements Calculations with Computer Simulations of Ion Selective Membrane Electrodes

Finite difference analysis of ion-selective membranes is a valuable tool for understanding a range of time dependent phenomena such as response times, long and medium term potential drifts, determination of selectivity, and (re)conditioning kinetics. It is here shown that an established approach based on the diffusion layer model applied to an ion-exchange membrane fails to use mass transport to account for concentration changes at the membrane side of the phase boundary. Instead, such concentrations are imposed by the ion-exchange equilibrium condition, without taking into account the source of these ions. The limitation is illustrated with a super-Nernstian potential jump, where a membrane initially void of analyte ion is exposed to incremental concentrations of analyte in the sample. To overcome this limitation, the two boundary elements, one at either side of the sample-membrane interface, are treated here as a combined entity and its total concentration change is dictated by diffusional fluxes into and out of the interface. For each time step, the concentration distribution between the two boundary elements is then computed by ion-exchange theory. The resulting finite difference simulation is much more robust than the earlier model and gives a good correlation to experiments.