Mathematical model for evaluating permeability and electrode reversibility in thin-film voltammetry. Part 3: Square-Wave Voltammetric behavior

Abstract

Many electrochemical systems of technological relevance involve a conductive surface coated with a thin layer whose properties determine its permeability to the external solution. The permeability of such a layer can be expressed in terms of the partitioning and confined diffusion of charge-carrying species, which in turn governs their rate and capacity for charge storage and generation. Recently, a general mathematical solution was introduced to describe chronoamperometric and cyclic voltammetry (CV) responses in thin-film (TF) systems. In the present work, this mathematical framework is extended to the analysis of square-wave voltammetry (SWV) responses.Application of the TF model to SWV reveals that the diffusion layer extends much less than in CV, making the corresponding voltammetric responses highly complementary. Although this work is entirely theoretical and emphasizes the importance of analyzing both forward and backward current components, the practical complexity of experimentally resolving these profiles is also acknowledged. For this reason, the analysis is first focused on the relationship between the differential peak current (∆Ip) and the SW frequency ( f ).However, variations in f simultaneously affect two key parameters related to the apparent reversibility and effective thickness of the system. To address this coupling, the model is used to compute the dependence of the dimensionless differential peak current on these parameters, allowing the construction of response surfaces for films with different degrees of permeability. For experimental data analysis, it is proposed to examine the dependence of ∆Ip.f^(-1/2) on log (f^(1/2)) and log (f^(-1/2)) to compare it with the proposed theoretical surfaces in order to estimate the permeability, film thickness, and charge-transfer kinetics of a given TF system. In addition, a set of theoretical surfaces describing the dependence of the peak potential on f is presented to complement the analysis.