Virial expansion for charged colloids and electrolytes

TL;DR

This paper develops a nonperturbative field-theoretic virial expansion for charged colloids and electrolytes, enabling accurate modeling of dilute solutions and colloidal suspensions with large size and charge disparities.

Contribution

It derives exact low-density coefficients for a binary charged hard-sphere mixture, applicable to both electrolyte solutions and colloids, including a mapping to the one-component plasma model.

Findings

Derived closed-form virial coefficients for charged hard-sphere mixtures.

Mapped the two-component model to a one-component plasma in the colloidal limit.

Identified discrepancies with standard models due to ion exclusion effects.

Abstract

Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (``virial'') expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters $d_+$ and $d_-$ and charge valences $q_+$ and $q_-$ of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically $d_+ \sim d_-$ and $q_+ \sim q_-$, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient.