Statistical mechanical description of liquid systems in electric field

TL;DR

This paper develops a statistical mechanical framework for liquid systems in electric fields, deriving exact expressions and applying them to analyze how electric fields shift critical temperatures in polar and polarizable liquids.

Contribution

It introduces an exact formulation of the electric field contribution in the statistical mechanics of liquids within the $ ext{E}$-ensemble, including modifications to the Ornstein-Zernike equation.

Findings

Electric field contribution is exactly incorporated into the configurational integral.

The electric field shifts the critical temperature differently for polar and polarizable liquids.

The critical temperature increases for polarizable liquids and decreases for polar liquids under an electric field.

Abstract

We formulate the statistical mechanical description of liquid systems for both polarizable and polar systems in an electric field in the $\mathbf{E}$-ensemble, which is the pendant to the thermodynamic description in terms of the free energy at constant potential. The contribution of the electric field to the configurational integral $\tilde{Q}_{N}(\mathbf{E})$ in the $\mathbf{E}$-ensemble is given in an exact form as a factor in the integrand of $\tilde{Q}_{N}(\mathbf{E})$. We calculate the contribution of the electric field to the Ornstein-Zernike formula for the scattering function in the $\mathbf{E}$-ensemble. As an application we determine the field induced shift of the critical temperature for polarizable and polar liquids, and show that the shift is upward for polarizable liquids and downward for polar liquids.