A global finite element Galerkin/B-spline (GBS) numerical model of electrochemical kinetics, transport, and mechanism for multi-geometry working electrodes: Part I. Modeled nernstian voltammetry

Abstract

A Galerkin/B-spline implementation of the finite element numerical method has been devised from first principles to construct a robust, very flexible, computationally fast, and user-friendly algorithmic model (the GBS model) of electrochemical rate-transport processes that accommodates potentially multiple electrode geometries, coupled charge transfer/chemical reaction mechanisms, and reversible to irreversible processes, each interfaced to the core GBS solver via an easily modifiable software driver. This inaugural paper presents in detail the general theoretical path followed to construct the solver whose intrinsic accuracy is limited only by the accuracy of input parameters and that of the chosen computer. GBS results are presented here for reversible (Nernstian) boundary conditions, the Cottrell singularity, and single sweep voltammetry for planar, cylindrical, and spherical geometries. The results are compared numerically and graphically to established analytic/numeric literature values.