Fluids of spherical molecules with dipolar-like nonuniform adhesion. An analytically solvable anisotropic model

TL;DR

This paper introduces an analytically solvable anisotropic model of sticky hard spheres with nonuniform, dipolar-like adhesion, providing explicit correlation functions and insights into structural ordering in complex fluids.

Contribution

It extends Baxter's model by incorporating anisotropic, dipolar-like adhesion and solves it analytically using a Percus-Yevick closure with orientational linearization.

Findings

Derived explicit orientation-dependent pair correlation functions

Provided accurate expressions for model parameters with less than 1% error

Revealed how anisotropic adhesion influences molecular correlations

Abstract

We consider an anisotropic version of Baxter's model of `sticky hard spheres', where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate `dipolar sticky' correction (positive or negative, depending on the mutual orientation of the molecules). The resulting nonuniform adhesion varies continuously, in such a way that in each molecule one hemisphere is `stickier' than the other. We derive a complete analytic solution by extending a formalism [M.S. Wertheim, J. Chem. Phys. \textbf{55}, 4281 (1971) ] devised for dipolar hard spheres. Unlike Wertheim's solution which refers to the `mean spherical approximation', we employ a \textit{Percus-Yevick closure with orientational linearization}, which is expected to be more reliable. We obtain analytic expressions for the orientation-dependent pair correlation function $g(1,2) $. Only one equation for a parameter $K$ has to be solved numerically. We also provide very accurate expressions which reproduce $K$ as well as some parameters, $\Lambda_{1}$ and $\Lambda_{2}$, of the required Baxter factor correlation functions with a relative error smaller than 1%. We give a physical interpretation of the effects of the anisotropic adhesion on the $g(1,2) $. The model could be useful for understanding structural ordering in complex fluids within a unified picture.