Charged Plate Beyond Mean-field: One-loop Corrections by Salt-density Fluctuation

TL;DR

This paper develops an exact field-theoretic approach to analyze salt density fluctuations near a charged plate, revealing how electrolyte fluctuations influence free energy and electrostatic interactions.

Contribution

It introduces a systematic method to compute one-loop fluctuation corrections to the Poisson-Boltzmann theory for asymmetric salts near charged surfaces.

Findings

Fluctuation corrections depend on salt concentration and valency.

Electrostatic repulsion between charges is reduced by electrolyte fluctuations.

Closed-form expressions for free-energy corrections are derived.

Abstract

We present an exact field-theoretic formulation for a fluctuating, generally asymmetric, salt density in the presence of a charged plate. The non-linear Poisson-Boltzmann equation is obtained as the saddle-point of our field theory action. Focusing on the case of symmetric salt, we systematically compute first-order corrections arising from electrolytes fluctuation to the free energy density, which can be explicitly obtained in closed form. We find that for systems with low to moderate salt density, fluctuation corrections to the free-energy depends sensitively on the salt concentration as well as their charge valency. Further, we find that electrolyte fluctuation leads to a reduced electrostatic repulsion between two point-charges when they are close to the charged plate.