Scattering functions for multicomponent mixtures of charged hard spheres, including the polydisperse limit. Analytic expressions in the Mean Spherical Approximation

TL;DR

This paper derives a comprehensive analytical formula for scattering intensity in multicomponent charged hard sphere fluids, including polydisperse systems, using the Mean Spherical Approximation, aiding interpretation of scattering experiments.

Contribution

It extends Vrij's uncharged mixture formula to charged systems within MSA and introduces a framework for matrices with dyadic structure in these solutions.

Findings

Provides a closed-form expression for scattering intensity in charged mixtures.

Includes the polydisperse limit with continuous size and charge distributions.

Discusses properties of special matrices in MSA solutions.

Abstract

We present a closed analytical formula for the scattering intensity from charged hard sphere fluids with any arbitrary number of components. Our result is an extension to ionic systems of Vrij's analogous expression for uncharged hard sphere mixtures. Use is made of Baxter's factor correlation functions within the Mean Spherical Approximation (MSA). The polydisperse case of an infinite number of species with a continuous distribution of hard sphere diameters and charges is also considered. As an important by-product of our investigation, we present some properties of a particular kind of matrices (sum of the identity matrix with a dyadic matrix) appearing in the solution of the MSA integral equations for both uncharged and charged hard sphere mixtures. This analysis provides a general framework to deal with a wide class of MSA solutions having dyadic structure and allows an easy extension of our formula for the scattering intensity to different potential models. Finally, the relevance of our results for the interpretation of small angle neutron scattering experimental data is briefly discussed.