Global space correlations of polarization, charge density, and electric field in electrolytes under the fixed-potential condition

TL;DR

This paper investigates how polarization, charge density, and electric field fluctuations behave in electrolytes between metallic electrodes under fixed potential, revealing size-dependent global correlations and their relation to dielectric properties.

Contribution

It provides a theoretical analysis of global space correlations of key electrostatic quantities in electrolytes under fixed-potential conditions, highlighting size effects and fluctuation-based dielectric constants.

Findings

Global correlations of polarization and electric field are volume-inversely proportional when film thickness is less than the Debye length.

Surface charge density fluctuations contribute to global electric fluctuations on electrode surfaces.

The effective dielectric constant depends on film thickness, Debye length, and fluctuation variances.

Abstract

We examine the thermal fluctuations of the polarization $p$, the charge density $\rho$, and the electric field $E$ in dilute electrolytes inserted between pararell metallic electrodes, where we fix the applied potential difference $\Phi_a$ between the two electrodes. If the film thickness $H$ is shorter than the Debye screening length $\kappa^{-1}$, the space correlation of the polarization $p_z$ and the electric field $E_z$ along the surface normal (in the $z$ direction) acuire global components inversely proportional to the film volume $V$, which vary slowly along the $z$ axis and are homogeneous in the $xy$ plane. The areal charge density on each electrode surface also has a component homogeneous on the surface, which produces the global electric fluctuations. On the other hand, if $H$ much exceeds $\kappa^{-1}$, the global correlations of $p_z$ and $\rho$ become small in the bulk region outside the electric double layers, but that of $E_z$ remains almost unchanged by ions in the whole cell at fixed $\Phi_a$. The dielectric constant $\epsilon_{\rm eff}$ depends on $H$ and $\kappa$ and is expressed in terms of the fluctuation variances of $p_z$ and $\rho$ and that of the noblocal surface charge density at fixed $\Phi_a$.