Nonlinear Frequency Response of Electrochemical Methanol Oxidation Kinetics: A Theoretical Analysis

Abstract

In this theoretical contribution, nonlinear frequency response analysis was applied for the investigation of electrochemical methanol oxidation. This technique expresses the input–output behavior of any weakly nonlinear system with the help of the Volterra series expansion and generalized Fourier transform into so-called higher order frequency response functions. These functions contain the system’s nonlinear fingerprint. They can be derived analytically from a nonlinear model. These functions can be obtained experimentally from the measurement of higher harmonics induced by a high amplitude sinusoidal perturbation of the system of interest. Frequency response functions up to the second order have been derived analytically for four different model varieties describing the kinetics of the electrochemical methanol oxidation. The first-order frequency response function corresponds to the reciprocal value of the well-known electrochemical impedance, which represents the linear part of the frequency response. This function does not contain sufficient information for discrimination between the different kinetic models. In contrast, the symmetrical second-order frequency response functions H2(ω,ω)H2(ω,ω) show differences in shape, which substantiate the availability of the theoretical prerequisites for model discrimination. A detailed parametric study for all four model variants has been performed. The results show that the basic features of the shapes of the H2(ω,ω)H2(ω,ω) amplitude spectra corresponding to the four models remain unique. The ubiquitousness of the qualitative differences between the competing models, for the whole set of parameters chosen for our analysis, suggests that the aforementioned amplitude spectra contain sufficient information for an unequivocal model discrimination.