A class of mathematical models for alternated-current electrochemical measurements accounting for non-linear effects

The traditional approach to the modelling of alternated-current electrochemical measurements is daunted by three major drawbacks: (i) only linear behaviour of the interface investigated is accounted for; (ii) the physical meaning of many model parameters is not straightforward; and (iii) entangled inverse parameter identification problems are generated. In this paper we address these problems by defining additional mathematical models related to the Fourier expansion of a more general, physically meaningful nonlinear electrochemical kinetic reaction system. The traditional linear model is regained as the truncation at the first harmonic of the series. Analytical expressions are derived for experimental observables relating to the nonlinear electrochemical behaviour that can be measured independently during the same experiment. Eventually, we show that the higher-harmonic models can be used as a general regularization tool to reduce the number of the multiple globally optimum solutions in the nonlinear leastsquares fitting of alternated-current data, highlighted in Bozzini and Sgura [Numerical issues related to the modelling of electrochemical impedance data by nonlinear least squares, Int. J. Nonlinear Mech. 40(4) (2005) 557–570].