Ion asymmetry and electric double layer formation in electrolytic ducts: a combined equilibrium and dynamic study

This study investigates the structure and dynamics of the Electric Double Layer (EDL) formed in electrolytic solutions and Room-Temperature Ionic Liquids (RTILs) under the influence of an external electric field. The analysis accounts for steric effects in their most general form, specifically considering ions of finite size that differ in both size and valence. The purpose of the study is twofold: First, we focus on the system's final equilibrium state, drawing conclusions about the electric field, electric potential, surface charge density, capacitance, and the relative reduction in ion concentration in the bulk of the solution. Second, we develop a method to calculate the time evolution of ion drift using the Modified Poisson-Nernst-Planck (MPNP) equations, which enables the estimation of the relative reduction in ion concentration across the duct as a function of time. By comparing the outcomes of the two methods, we demonstrate their consistency and identify their respective applicability ranges. Our results show that the time-dependent model provides more reliable predictions for ducts narrower than 10 −4 m, while for larger ducts, both methods converge to equivalent results. These findings highlight the advantages and limitations of each approach and provide guidance for the appropriate modeling of EDLs in electrochemical systems. • Ionic valence & size asymmetry effects on EDL formation. • Closed-form equilibrium expressions for potential, charge density, and capacitance. • Dynamic MPNP model vs. analytical equilibrium comparison. • Establishes applicability limits of equilibrium approximations. • Effects of applied voltage & ionic concentration on EDL behavior.