Crossover Scales at the Critical Points of Fluids with Electrostatic Interactions

TL;DR

This paper investigates how electrostatic interactions influence the critical behavior of dielectric fluids, deriving an effective Hamiltonian and estimating the crossover from mean-field to Ising behavior, with results aligning qualitatively with experiments.

Contribution

It introduces a perturbative approach to model electrostatic effects on fluid criticality and estimates the crossover temperature dependence on ionicity.

Findings

Crossover temperature weakly depends on ionicity

Effective Hamiltonian derived at Debye-Hückel level

Trends agree qualitatively with experimental observations

Abstract

Criticality in a fluid of dielectric constant D that exhibits Ising-type behavior is studied as additional electrostatic (i.e., ionic) interactions are turned on. An exploratory perturbative calculation is performed for small ionicity as measured by the ratio of the electrostatic energy to the strength of the short-range nonionic (i.e., van der Waals) interactions in the uncharged fluid. With the aid of distinct transformations for the short-range and for the Coulombic interactions, an effective Hamiltonian with coefficients depending on the ionicity is derived at the Debye-Hueckel limiting-law level for a fully symmetric model. The crossover between classical (mean-field) and Ising behavior is then estimated using a Ginzburg criterion. This indicates that the reduced crossover temperature depends only weakly on the ionicity (and on the range of the nonionic potentials); however, the trends do correlate with the, much stronger, dependence observed experimentally.