A corresponding states approach to Small-Angle-Scattering for polydisperse ionic colloidal fluids

TL;DR

This paper introduces a simplified scaling approach to approximate scattering functions in polydisperse ionic colloidal fluids, extending previous nonionic models and validated through analytical and numerical solutions.

Contribution

It develops a conformal scaling method for polydisperse ionic fluids based on a monodisperse reference system, improving upon existing approximations.

Findings

Good agreement with exact MSA predictions up to relevant polydispersity

SA outperforms the decoupling approximation in ionic cases

Applicable to both analytical and numerical solutions of OZ equations

Abstract

Approximate scattering functions for polydisperse ionic colloidal fluids are obtained by a corresponding states approach. This assumes that all pair correlation functions $g_{\alpha \beta}(r)$ of a polydisperse fluid are conformal to those of an appropriate monodisperse binary fluid (reference system) and can be generated from them by scaling transformations. The correspondence law extends to ionic fluids a {\it scaling approximation} (SA) successfully proposed for nonionic colloids in a recent paper. For the primitive model of charged hard spheres in a continuum solvent, the partial structure factors of the monodisperse binary reference system are evaluated by solving the Orstein-Zernike (OZ) integral equations coupled with an approximate closure. The SA is first tested within the mean spherical approximation (MSA) closure, which allows analytical solutions. The results are found in good overall agreement with exact MSA predictions up to relevant polidispersity. The SA is shown to be an improvement over the ``decoupling approximation'' extended to the ionic case. The simplicity of the SA scheme allows its application also when the OZ equations can be solved only numerically. An example is then given by using the hypernetted chain (HNC) closure. Shortcomings of the SA approach, its possible use in the analysis of experimental scattering data and other related points are also briefly addressed.