A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores

TL;DR

This paper develops a variational field-theoretical model to study ionic solutions, accurately capturing hardcore interactions and phase transitions in bulk and nanopores, validated against Monte Carlo simulations.

Contribution

It introduces a novel variational approach incorporating a Fourier cutoff and Carnahan-Starling equation to model ionic phase behavior in confined and bulk systems.

Findings

Accurately predicts ionic chemical potential and energy compared to Monte Carlo data.

Describes ionic liquid-vapor phase transition induced by correlations.

Shows dielectric exclusion and hardcore interactions significantly influence ionic concentrations in nanopores.

Abstract

We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical "ionic liquid-vapor" phase transition induced by ionic correlations at low temperature, before applying it to electrolytes at room temperature confined to nanopores embedded in a low dielectric medium and coupled to an external reservoir of ions. The ionic concentration in the nanopore is then correctly described from very low bulk concentrations, where dielectric exclusion shifts the transition up to room temperature for sufficiently tight nanopores, to high concentrations where hardcore interactions dominate which, as expected, modify only slightly this ionic "capillary evaporation".