Semioperations and Convolutions in Voltammetry

Abstract

AbstractIt is often useful to transform a measured signal into a form that is more easily interpreted. Thus, in voltammetry, where the measurement is of a current responding to a perturbation of the electrode potential, the complications arising from diffusional transport may be readily alleviated through the use of semioperators or convolutions. The use of semiintegration enables the voltammetric current to be transformed into an alternative signal that, in the case of a planar electrode, is linearly related to the concentrations of reactant and product at the electrode surface. Numerous advantages of semiintegration have been widely demonstrated. However, semiintegration is but a special case of the more general procedure of convolution. Convolving the voltammetric current with specifically designed functions of time allows the benefits of semiintegration to be applied to other electrode geometries and other experimental circumstances. The prime motive for semiintegration or convolution is to gain access to information about concentrations at the electrode surface. This information opens the door to the measurement of such quantities as bulk concentrations, rate constants, standard potentials, and diffusivities, as well as suggesting mechanisms and enabling the calibration of electrodes.