Simulation of the cyclic voltammetric response of an outer-sphere redox species with inclusion of electrical double layer structure and ohmic potential drop

Abstract

A finite-element model has been developed to simulate the cyclic voltammetric (CV) response of a planar electrode for a 1e outer-sphere redox process, which fully accounts for cell electrostatics, including ohmic potential drop, ion migration, and the structure of the potential-dependent electric double layer. Both reversible and quasi-reversible redox reactions are treated. The simulations compute the time-dependent electric potential and ion distributions across the entire cell during a voltammetric scan. In this way, it is possible to obtain the interdependent faradaic and non-faradaic contributions to a CV and rigorously include all effects of the electric potential distribution on the rate of electron transfer and the local concentrations of the redox species O^z and R^z−1. Importantly, we demonstrate that the driving force for electron transfer can be different to the applied potential when electrostatic interactions are included. We also show that the concentrations of O^z and R^z−1 at the plane of electron transfer (PET) significantly depart from those predicted by the Nernst equation, even when the system is characterised by fast electron transfer/diffusion control. A mechanistic rationalisation is also presented as to why the electric double layer has a negligible effect on the CV response of such reversible systems. In contrast, for quasi-reversible electron transfer the concentrations of redox species at the PET are shown to play an important role in determining CV wave shape, an effect also dependant on the charge of the redox species and the formal electrode potential of the redox couple. Failure to consider electrostatic effects could lead to incorrect interpretation of electron-transfer kinetics from the CV response. Simulated CVs at scan rates between 0.1 and 1000 V s⁻¹ are found to be in good agreement with experimental data for the reduction of 1.0 mM Ru(NH₃)₆³⁺ at a 2 mm diameter gold disk electrode in 1.0 M potassium nitrate.