Electrochemical digital simulation with highly expanding grid four point discretization: Can Crank–Nicolson uncouple diffusion and homogeneous chemical reactions?

Abstract

The digital simulation of electrochemical experiments where homogeneous chemical reactions are coupled to the heterogeneous charge transfer is considered by means of the sequential treatment of chemical and diffusional effects on concentrations. For the first time, this strategy is employed in combination with implicit time-integration schemes, in particular with a modification of the Crank–Nicolson method (CN), and with highly expanding grid four-point discretization (HEGFPD). CN leads to significant improvements with respect to explicit integration schemes previously considered in the literature whereas HEGFPD gives rise to very fast computations. The errors committed by this method are evaluated for different reaction mechanisms (with first- and second-order coupled homogeneous chemical reactions) at planar and spherical electrodes. It is demonstrated that, after selecting the appropriate conditions, this is a very efficient procedure, giving rise to very accurate results. Thus, simple criteria are established for the selection of the adequate simulation parameters.