High amplitude periodic signal theory

Summary A theoretical framework is given to evaluate the non-linear response of a halfcell when a periodic potential is superimposed on a base potential. Some interesting features of this approach are: o (i) no restriction is placed on the magnitude of the periodic signal; (ii) formally, all the infinite harmonics in the output current can be evaluated; (iii) the time-averaged part of the current (the so called “rectification” component) is also obtained and its identity in form with its d.c. counter part viz. “the bias response”, is established for the case E * =a constant; (iv) the influence of the bias state on the harmonics ( i.e. the time modulation) and the influence of the harmonics on the time averaged part (Fournier polarogram) become explicit; (v) the formalism deduced here is common to several models like those with parallel electron transfers with or without preceding chemical reactions, numerous mass-transport models, any given non-linear dependence of the rates on the overpotential etc. (vi) the applicability of these results are immediate to different input profiles such as (a) the sinusoidal, (b) the square wave, (c) pulse trains of various forms, (d) the triangular ones etc. (vii) the presentation is not restricted to constant “bias” conditions: it is capable of handling all time deependent bias profiles too, provided the latter are sufficiently slowly varying (as compared to the frequency of the periodic part). The computational procedure is briefly sketched. The limitations on our results arise from the assumptions on (i) the absence of adsorption, (ii) the presence of the supporting electrolyte, and (iii) the linear (in the generalized sense) relationship between the interfacial concentrations and the current (faradaic).