Modified Poisson–Boltzmann analysis of ion concentration and capacitance in confined electrolytic microchannels

Understanding ion electrosorption under strong electric fields is essential for advancing electrochemical desalination technologies and high-performance energy storage devices. In this work, we apply a symmetric modified Stern–Poisson–Boltzmann framework that incorporates steric constraints arising from the finite size of ions in aqueous electrolytes confined within an electrified channel. Unlike classical Gouy–Chapman theory, the proposed model accounts for excluded-volume effects, enabling the analysis of concentrated solutions and high surface potentials. We employ analytical expressions for the electric potential distribution, surface charge density, differential capacitance, and diffuse layer thickness for monovalent and divalent electrolytes at the equilibrium state that are solved numerically at the equilibrium state. Increasing electrode potential enhances surface charge density by orders of magnitude, while higher ionic valence significantly compresses the diffuse layer at low potentials but introduces repulsive crowding at strong polarization. The model further predicts that ion-removal efficiency in the channel center depends critically on electrode spacing, bulk concentration, and applied potential, with removal rates exceeding 90% under optimized conditions. These findings provide theoretical insight into steric-limited electrokinetic processes and offer design guidelines for electrochemical water purification and electrostatic energy-storage systems.