Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

TL;DR

This paper develops a unified theoretical framework for analyzing ionic fluids under electric fields, revealing how electric fields induce oscillations and stripe states, and comparing these phenomena to equilibrium behaviors.

Contribution

It introduces a unified stochastic density functional theory formulation that justifies modifications to the Poisson-Nernst-Planck model and analyzes correlation functions under electric fields.

Findings

Electric fields induce density and charge oscillations in ionic fluids.

Stripe states form perpendicular to the applied electric field.

Crossover to oscillatory decay occurs before the Kirkwood crossover.

Abstract

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates various frameworks of the equilibrium and dynamic DFTs, the liquid state theory, and the field-theoretic approach, which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We focus on an electric-field-induced synchronization between the emergence of density and charge oscillations, or the crossover from monotonic to oscillatory decay of density-density and charge-charge correlations. The correlation function analysis demonstrates the appearance of stripe states formed by segregation bands perpendicular to the external field. We also predict the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the electric-field-induced crossovers bears a similarity to the underscreening behavior found by simulation and theoretical studies on the oscillatory decay length in equilibrium.