A NUMERICAL STUDY OF THE EQUILIBRIUM AND NONEQUILIBRIUM DIFFUSE DOUBLE-LAYER IN ELECTROCHEMICAL-CELLS

A numerical solution of the Nernst-Planck and Poisson equations is presented. The equations are discretized in a finite difference scheme using the method of fines on variable spatial and temporal grids. A Gear's stiffly stable predictor-corrector integration procedure which automatically adjusts the order of the predictor and corrector equations (and the step size) to ensure the accuracy of the results is incorporated. Some advantages of our approach over more classical ones are discussed. The numerical solution is applied to the study of the equilibrium and nonequilibrium diffuse electrical double layer (EDL) at the metal electrode/electrolyte solution interface. The prescription of this layer is similar to that used in the classical Gouy-Chapman theory. Electrode kinetics are described by the Butler-Volmer equation. Concentration, faradaic and displacement electric current densities, and electric potential profiles as functions of time across the cell thickness, and particularly in the EDL regions at the metal electrode/solution interfaces, are obtained. Two physical problem are studied: (i) the formation of the equilibrium EDL, and (ii) the transient response of the system to an electrical perturbation. These examples illustrate the potential applications of the numerical method.