When Two Interfaces Meet: A Unified Theory for Thin-Membrane Voltammetric Ion Selective Electrodes

Voltammetric solid-contact ion-selective electrodes (SC-ISEs) exhibit electrochemical responses that arise from the coupling of heterogeneous electron transfer at the electrode-membrane interface with ion transfer at the membrane-sample boundary. In this work, a novel theoretical framework is developed for voltammetric SC-ISEs based on thin membranes, capturing the intrinsic consequences of coupling two polarized interfaces in series under markedly different mass-transport conditions in the membrane and solution phases. The theory describes the current/charge-potential-time responses and the corresponding interfacial potentials and dynamic ion and redox-species concentrations, accounting for the effects of membrane and solution composition, membrane thickness, and experimental timescale. Besides, the theory enables quantitative analysis of experimental voltammetric outcomes. A systematic classification of cyclic voltammetry (CV) responses is obtained in terms of three dimensionless parameters that quantify ion availability in the sample solution relative to the confined membrane. Simple relationships for peak positions and practical diagnostic criteria based on CV shape and scan-rate dependence are derived to verify thin-membrane conditions and the absence of kinetic or ohmic limitations, identifying indeed whether charge compensation proceeds via ion release or uptake.