Self-consistent electrostatic formalism of bulk electrolytes based on the asymmetric treatment of the short- and long-range ion interactions

TL;DR

This paper introduces a self-consistent electrostatic formalism for bulk electrolytes that asymmetrically treats short- and long-range ion interactions, extending the applicability of previous theories to higher concentrations and capturing complex phenomena like overscreening.

Contribution

It develops a novel asymmetric formalism combining virial and cumulant treatments for ion interactions, improving predictions of electrolyte thermodynamics over existing models.

Findings

Accurately predicts liquid pressure, internal energies, and ion distributions up to molar concentrations.

Reproduces overscreening and underscreening effects in mono- and multivalent electrolytes.

Extends the validity of Debye-Hückel theory to higher concentrations.

Abstract

We predict the thermodynamic behavior of bulk electrolytes from an ionic Hard-Core (HC) size-augmented self-consistent formalism incorporating asymmetrically the short- and long-range ion interactions via their virial and cumulant treatment, respectively. The characteristic splitting length separating these two ranges is obtained from a variational equation solved together with the Schwinger-Dyson (SD) equations. Via comparison with simulation results from the literature, we show that the asymmetric treatment of the distinct interaction ranges significantly extends the validity regime of our previously developed purely cumulant-level Debye-H\"uckel (DH) theory. Namely, for monovalent solutions with typical ion sizes, the present formalism can accurately predict up to molar concentrations the liquid pressure dominated by HC interactions, the internal energies driven by charge correlations, and the local ion distributions governed by the competition between HC and electrostatic interactions. We evaluate as well the screening length of the liquid and investigate the deviations of the macromolecular interaction range from the DH length. In fair agreement with simulations and experiments, our theory is shown to reproduce the overscreening and underscreening effects occurring respectively in submolar mono- and multivalent electrolytes.