Breaking boundaries in Electrochemistry: Unveiling a new dimensionless number to tackle convective transfer effect on the voltamperometric answer

Abstract

This study introduces the Theokane number ($T_k$) as a groundbreaking dimensionless number in Electrochemistry. $T_k$ enables the determination of the operating state of an electrochemical (EC) system—indicating whether it is in a transient state (characteristic of cyclic voltammetry) or a steady state (typical of linear sweep voltammetry)—based on a given combination of potential scan rate and residence time. It aims to bridge the gap between various voltamperometric methods. $T_k$ uniquely compares the duration of the potential scan applied to an EC system to the residence time of the reaction mixture at the electrode. This comparison is pertinent in environments ranging from microfluidic setups to macroscale reactors, including stirred vessels.

$T_k$ is particularly crucial for understanding the ‘continuous answer’ of an EC system subjected to voltamperometric polarization across a spectrum of potential scan and stirring rates. Voltammograms recorded in a micro-reactor under varying conditions highlight the influence of operating parameters on EC responses. The approach introduced in this study accomplish three key objectives: i) it validates the $T_k$ number through the comparison of experimental and simulation data, ii) it proposes a range for its applicability; and iii) it opens a new mode for analyzing EC responses. It is important to note that $T_k$ is applicable to both quasi-reversible and irreversible systems.