EChem++ – An object-oriented problem solving environment for electrochemistry. Part 7: Simulation of equilibrium electron transfer processes with implicit Dirichlet boundary conditions

We present a direct approach to include equilibrium electron transfers into electrochemical simulation models based on the finite element method. This reaction step is described by the Nernst equation combined with a mass flux balance equation. Mathematically, the Nernst equation is an implicit Dirichlet boundary condition with two coupled concentrations. These boundary conditions are imposed within a numerical solver consisting of Rosenbrock schemes and an adaptive finite element method by means of Lagrange multipliers. The algorithm described in this study is integrated into the object-oriented, open source code for the problem solving environment EChem++. Simulations of an equilibrium electron transfer under cyclic voltammetric and chronoamperometric conditions in a one-dimensional cell geometry under semi-infinite linear diffusion show the validity and applicability of this method in the context of molecular electrochemistry.