Mesoscopic theory for size- and charge- asymmetric ionic systems. I. Case of extreme asymmetry

TL;DR

This paper develops a mesoscopic mean-field theory for highly asymmetric ionic systems, predicting phase coexistence and structure, especially in extreme size and charge asymmetry regimes relevant to colloidal solutions.

Contribution

It extends previous primitive model theories to include arbitrary size and charge asymmetries, focusing on the extreme asymmetry limit with new phase diagram predictions.

Findings

Predicted coexistence of dilute gas and crystalline phases.

Identified bcc structure with lattice constant ~3.6σ+ for macroions.

Theoretical results align with experimental observations in colloidal systems.

Abstract

A mesoscopic theory for the primitive model of ionic systems is developed for arbitrary size, $\lambda=\sigma_+/\sigma_-$, and charge, $Z=e_+/|e_-|$, asymmetry. Our theory is an extension of the theory we developed earlier for the restricted primitive model. The case of extreme asymmetries $\lambda\to\infty$ and $Z \to\infty$ is studied in some detail in a mean-field approximation. The phase diagram and correlation functions are obtained in the asymptotic regime $\lambda\to\infty$ and $Z \to\infty$, and for infinite dilution of the larger ions (volume fraction $n_p\sim 1/Z$ or less). We find a coexistence between a very dilute 'gas' phase and a crystalline phase in which the macroions form a bcc structure with the lattice constant $\approx 3.6\sigma_+$. Such coexistence was observed experimentally in deionized aqueous solutions of highly charged colloidal particles.