Convolutive modeling of cyclic voltammetry, AC-voltammetry, sine wave voltammetry and impedance spectroscopy with interfacial CPE behaviour and uncompensated ohmic resistances: A Unified Theory

Abstract

The constant phase element (CPE) is a well-established circuit component for the frequency domain simulation of electrochemical reactions at disperse and heterogeneous electrodes. Computing the time-dependent current response of voltammetric experiments with interfacial CPE behaviour is, however, not a straightforward task, owing to the lack of analytical time domain solutions of the convoluted capacitive current. In this paper, a universal framework for the convolutive treatment of cyclic voltammetry (CV), alternating current cyclic voltammetry (ACCV), (large) sine wave voltammetry (LSWV) and electrochemical impedance spectroscopy (EIS) in presence of interfacial CPEs and uncompensated Ohmic resistances is presented. A combination of numerical and analytical inverse Laplace transformation techniques allows the accurate assessment of the non-ideal capacitive behaviour, which can be used in turn for classical convolution algorithms. The convolutive approach bears the advantage that different electrode geometries with any kind of spatial boundary conditions as well as first order homogeneous chemical reactions, coupled to the charge transfer step, can be implemented readily. This offers an exceptionally large degree of flexibility in the simulations for the electrochemical system at hand.