Semi-Differentiation of Reversible, Soluble-Insoluble Potential Sweep Voltammograms

Semi-differentiation, or convolution as it is sometimes known, is a mathematical technique commonly used to disentangle overlapping peaks in cyclic or linear sweep voltammograms. However, this technique is often misapplied due to misunderstandings of fractional calculus. Additionally, rigorous treatment and validation of the theory of semi-differential analysis of reversible, soluble-insoluble electrochemical reactions is lacking. Peculiarities of semi-differentiation are explored; theoretical relations for semi-differentiated voltammograms are given; the exponential nature of the theoretical curve is explored; theoretical relations are compared to experimental voltammograms for AgNO3 in 1 M nitric acid at 298 K, NiCl2 in LiCl at 974 K, and LaCl3 in LiCl at 971 K; and the diffusion coefficients calculated from theoretical relations developed in this paper are shown to agree with those calculated using the Berzins-Delahay equation.