A Novel Dimensionless Parameter for Predicting Peak Currents in Square-Wave Voltammetry

Square-wave voltammetry (SWV) is most advanced electroanalytical technique widely employed for probing redox processes owing to its superior resolution and signal-to-noise characteristics. Despite its advantages, a fundamental theoretical limitation persists, i.e., the absence of a unified formalism capable of accurately describing peak current behavior under a broad spectrum of kinetic and experimental conditions. In contrast to linear scan voltammetry, where the Randles–Ševčík equation provides a direct and well-established relationship between peak current and system parameters, SWV introduces inherently complex, time-dependent perturbations of interfacial concentration gradients due to its pulsed excitation protocol. These perturbations, compounded by the interplay of square-wave amplitude, potential step, temperature, diffusion coefficient, and electron-transfer kinetics, have hindered the derivation of a general analytical expression governing peak current magnitudes in SWV.
In the present study, we conducted comprehensive theoretical simulations of a simple one-electron redox system: Red  ⇌  Ox + e- modeled under the Butler-Volmer formalism, accounting for diffusion-controlled mass transport. Through this analysis, we introduce a novel dimensionless parameter X defined as:
X = const. x [(dE⋅F)/(RT)] [(Esw/dE)0.5] K/(1+K)
which consolidates the contributions of the most critical physical and experimental variables, i.e. temperature (T), potential step (dE), square-wave amplitude (Esw), electron-transfer rate constant (ks), frequency (f), and diffusion coefficient (D) via the dimensionless kinetic parameter K. Our preliminary results demonstrate that, when the ratio of square-wave amplitude to potential step is held constant, the peak currents in SW voltammograms remain invariant across wide ranges of temperatures and kinetic regimes, provided that this unified parameter X is fixed.
This study therefore reports, for the first time, the identification of a dimensionless descriptor that integrates the multifactorial influences on peak current behavior in SWV. The findings establish a conceptual basis for the development of a generalized theoretical framework for SWV and contribute to a deeper understanding of kinetic redox processes under square-wave perturbation.