Donnan equilibrium in charged slit-pores from a hybrid nonequilibrium Molecular Dynamics / Monte Carlo method with ions and solvent exchange

TL;DR

This paper introduces a hybrid simulation method combining molecular dynamics and Monte Carlo techniques to study ion partitioning in charged slit-pores, extending the applicability of Poisson-Boltzmann theory through charge renormalization.

Contribution

It develops and applies a hybrid nonequilibrium simulation method to analyze Donnan equilibrium in charged slit-pores, demonstrating the extended validity of linearized Poisson-Boltzmann theory with charge renormalization.

Findings

Linearized PB theory can predict Donnan equilibrium in highly charged pores with charge renormalization.

Explicit solvent has limited impact on ion partitioning at low salt concentrations.

Charge renormalization captures surface effects better than mean-field approximations.

Abstract

Ion partitioning between different compartments (\emph{e.g.} a porous material and a bulk solution reservoir), known as Donnan equilibrium, plays a fundamental role in various contexts such as energy, environment, or water treatment. The linearized Poisson-Boltzmann (PB) equation, capturing the thermal motion of the ions with mean-field electrostatic interactions, is practically useful to understand and predict ion partitioning, despite its limited applicability to conditions of low salt concentrations and surface charge densities. Here, we investigate the Donnan equilibrium of coarse-grained dilute electrolytes confined in charged slit-pores in equilibrium with a reservoir of ions and solvent. We introduce and use an extension to confined systems of a recently developed hybrid nonequilibrium molecular dynamics / grand canonical Monte Carlo simulation method ("H4D"), which enhances the efficiency of solvent and ion-pair exchange via a fourth spatial dimension. We show that the validity range of linearized PB theory to predict the Donnan equilibrium of dilute electrolytes can be extended to highly charged pores, by simply considering \textit{renormalized} surface charge densities. We compare with simulations of implicit solvent models of electrolytes and show that in the low salt concentrations and thin electric double layer limit considered here, an explicit solvent has a limited effect on the Donnan equilibrium and that the main limitations of the analytical predictions are not due to the breakdown of the mean-field description, but rather to the charge renormalization approximation, because it only focuses on the behavior far from the surfaces.