Correlation functions in ionic liquid at coexistence with ionic crystal. Results of the Brazovskii-type field theory

TL;DR

This paper uses a field-theoretic approach to calculate correlation functions in an ionic liquid near phase coexistence, revealing how fluctuations modify mean-field predictions and lead to specific oscillatory behaviors.

Contribution

It introduces a renormalized field-theoretic method to analyze correlation functions in ionic liquids, highlighting differences from mean-field results and providing detailed behavior near phase transition.

Findings

Correlation functions show damped oscillations similar to Gaussian approximation.

Fluctuations renormalize amplitude and decay length, preventing divergence.

Decay length and oscillation period are density-independent at phase transition.

Abstract

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in the Gaussian approximation [Ciach at. al., J. Chem. Phys. {\bf 118}, 3702 (2003)]. The fluctuation contribution leads to a renormalization of both the amplitude and the decay length of the correlation functions. The renormalized quantities show qualitatively different behavior than their mean-field (MF) counterparts. While the amplitude and the decay length both diverge in MF when the $\lambda$-line is approached, the renormalized quantities remain of order of unity in the same dimensionless units down to the coexistence with the ionic crystal. Along the line of the phase transition the decay length and the period of oscillations are independent of density, and their values in units of the diameter of the ions are $\alpha_0^{-1}\approx 1$ and $2\pi/\alpha_1\approx 2.8$ respectively.