Modelling Intermediate-Current Transitions in Asymmetric-Valence Binary Electrolytes

TL;DR

This paper develops a theoretical model for asymmetric-valence binary electrolytes, revealing a valence-dependent transition between near-equilibrium and non-equilibrium regimes, with explicit solutions and phase diagrams for predicting steady-state behaviour.

Contribution

It introduces a comprehensive asymptotic analysis of a Poisson-Nernst-Planck model for asymmetric electrolytes, providing explicit solutions and a phase diagram for intermediate-current regimes.

Findings

Identifies a valence-dependent transition point where the boundary layer vanishes.

Derives explicit analytic expressions for specific electrolyte valence ratios.

Provides a phase diagram to predict steady-state behaviour based on ion valences and fluxes.

Abstract

Asymmetric valences in a binary electrolyte can significantly affect the performance of systems such as reverse electrodialysis cells, batteries, and supercapacitors. To generate a theoretical understanding of this effect, we consider a steady one-dimensional Poisson-Nernst-Planck model of an electrolytic cell with imposed constant ionic fluxes, focusing on varying ion valences in a general asymmetric binary electrolyte. Numerical simulations reveal a smooth transition between the qualitatively distinct near-equilibrium and strongly non-equilibrium steady-state regimes. These regimes are distinguished by a valence-dependent transition point at an intermediate current where the classical Debye-scale boundary layer vanishes. We characterise this transition using asymptotic analysis, recovering the Gouy-Chapman and limiting-current results in the appropriate limits, and determining the correct transition results when neither is appropriate. We provide implicit solutions for the potential and ion concentrations of general asymmetric binary electrolytes and, notably, we provide explicit analytic expressions for the asymptotic composite solutions for 2z:z, z:2z, and z:z electrolytes. We show how the results can be presented in a collapsed phase diagram that can be used to predict qualitative intermediate-current steady-state behaviour in terms of ion valences and fluxes.