Reversible charge transfer with unknown mass transfer. Characterization and modelling by using a mass-transfer operator determined from experimental data

Abstract

When a charge transfer is reversible and when the two associated mass-transfer steps are of the same nature, the electrical current is formulated very simply as a result of the application of a single mass-transfer operator on a potential-dependent equilibrium constant. The charge-transfer equilibrium constant is then obtained from the current by inversion of this equation. With such a “reverse modelling” approach, the characteristics of this operator can be experimentally measured and the charge-transfer equilibrium constant can be determined for any kind of thermodynamic equilibrium, nernstian or not. Consequently, the response of an electrochemical mechanism to any perturbation function can be modelled without mathematical description of the mass transfer. It is sufficient to measure experimentally, and correct adequately for instrument limitations and double-layer charging, the response of the electrochemical system to a series of steps, and then to use the convolution tool, to obtain “Theoretical” working curves. Conversely, analysis of an experimental response to any kind of perturbation can also be performed by convolution with experimentally determined operator characteristics. The main advantage of this new methodology is the ability to model or to analyse complex mechanisms for which a good mathematical description of the mass transfer is not available, or when the mass transfer mode is unknown. This powerful theory is extremely simple. Apart from the convolution product, the mathematics is easy and reduced to a minimum. The experimental verification of the proposed approach is performed without sophisticated instrumentation on the N-methylphenothiazine redox couple in acetonitrile with a mathematically poorly defined mass transport such as transient convection.