Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations. Part 15: patch-adaptive simulation of example transient experiments described by Nernst–Planck–electroneutrality equations in one-dimensional space geometry

Abstract

The patch-adaptive strategy for electrochemical kinetic simulations, introduced in Part 5 of the present series of papers, with extensions described in Part 14, is applied to five typical examples of time-dependent models of transient experiments represented by Nernst–Planck–electroneutrality equation systems in one-dimensional space geometry. The models describe: potential step chronoamperometry for a charge neutralisation reaction at a planar electrode in the absence of the supporting electrolyte; potential step chronoamperometry for a planar electrode coated with a polymer film under conditions of migration–diffusion of redox ions; potential step chronoamperometry of uncharged species at a hemispherical electrode in the presence of a low concentration of supporting electrolyte; cyclic voltammetry for an electrode reaction (initially at equilibrium) involving uncharged species, at a planar electrode in the absence of the supporting electrolyte; and current step chronopotentiometry for a liquid|liquid junction between two binary electrolytes. The calculations lead to analogous conclusions, with regard to the performance of the strategy, as in the case of the models represented by the Nernst–Planck–Poisson equations solved in Part 14. New observations reveal that highly non-linear boundary conditions present an additional challenge for the Newton iterative method utilised by the strategy. The ability of the strategy to solve non-local boundary conditions expressing current equality at distant boundaries is also demonstrated. However, formulating such boundary conditions correctly is not straightforward, so that their use is not recommended. Adaptive solutions suggest inaccuracies in the literature solutions for two example models.