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

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.

30 pages, 6 Figures, Physical Review E in press

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• Effect of quantum dispersion on the radial distribution function of a one-component sticky-hard-sphere fluid
• Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach
• From the Liouville to the Smoluchowski equation for a colloidal solute particle in a solvent
• Andersen-Weeks-Chandler perturbation theory and one-component sticky-hard-spheres