A scaling approximation for structure factors in the integral equation theory of polydisperse nonionic colloidal fluids

TL;DR

This paper introduces a new scaling approximation within integral equation theory to efficiently estimate structure factors in polydisperse colloidal fluids, showing improved accuracy over existing methods for both hard sphere and Lennard-Jones interactions.

Contribution

The paper develops and tests a novel scaling approximation for structure factors in polydisperse colloidal fluids, applicable to various potentials and compared against multiple existing theories.

Findings

Scaling approximation performs well for both hard sphere and Lennard-Jones fluids.

Compared favorably with experimental and simulation data, outperforming some traditional theories.

Offers a simple yet effective method for analyzing scattering data in polydisperse systems.

Abstract

Integral equation of pure liquids, combined with a new "scaling approximation" based on a corresponding states treatment of pair correlation functions, is used to evaluate approximate structure factors for colloidal fluids constituted of uncharged particles with polydispersity in size and energy parameters. Both hard spheres and Lennard-Jones interactions are considered. For polydisperse hard spheres, the scaling approximation is compared to theories utilized by small angle scattering experimentalists (decoupling approximation, local monodisperse approximation)and to the van der Waals one-fluid theory. The results are tested against predictions from analytical expressions, exact within the Percus-Yevick approximation. For polydisperse Lennard-Jones particles, the scaling approximation combined with a "modified hypernetted chain" integral equation, is tested against molecular dynamics data generated for the present work. Despite ist simplicity, the scaling approximation exhibits a satisfactory performance for both potentials and represents a considerable improvement over the above mentioned theories. Shortcomings of the proposed theory, its applicability to the analysis of experimental scattering data, and its possible extensions to different potentials are finally discussed.