Analytic solutions for Baxter's model of sticky hard sphere fluids within closures different from the Percus_Yevick approximation

TL;DR

This paper derives analytical solutions for Baxter's sticky hard sphere model using various closure relations beyond the Percus-Yevick approximation, providing insights into structural and thermodynamic properties with practical implications for colloidal and protein solutions.

Contribution

It introduces a unified analytical approach for solving the Ornstein-Zernike equation with different closures, extending beyond the Percus-Yevick approximation, and compares their accuracy and extensibility.

Findings

Percus-Yevick approximation results are intermediate in accuracy.

Simpler closures are more extendable to multi-component systems.

Perturbative closures yield satisfactory results in colloidal regimes.

Abstract

We discuss structural and thermodynamical properties of Baxter's adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported. Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures, which may yield less accurate predictions but are easily extensible to multi-component fluids, and more sophisticate closures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidal and protein solutions, however, it is found that the perturbative closures, even when limited to first-order, produce satisfactory results.