Mathematical model of current-polarized ionophore-based ion-selective membranes.

A mathematical model is presented to describe the effects of constant current on ion-selective membranes using theta functions. The model provides exact analytic solutions for calculating the concentration polarization of the ionophore, the ion-ionophore complex, and the charged mobile sites in space and time within the membrane. It also predicts the time course of the membrane potential and the electric field inside the membrane following the application of constant current. This analytic solution is faster to compute than numerical simulations and provides the solution for any given time or position directly. The simulated concentration profiles compare favorably with concentration profiles recorded experimentally using spectro-electrochemical microscopy.