Solution of the Ornstein-Zernike Equation for a Mixture of Sticky Hard Spheres and Yukawa Closure

Abstract

We consider the solution of the Ornstein-Zernike equation for the most general closure consisting of a sum of M Yukawa type exponentials.

$$ {{c}_{{ij}}}(r) = \sum\limits_{{n = 1}}^{M} {\hat{K}_{{ij}}^{{(n)}}{{e}^{{ - {{z}_{n}}(r - {{\sigma }_{{ij}}})}}}/r} $$

A formal solution was found for an arbitrary mixture of hard spheres in previous work. We study here the limiting case when one of the exponentials, labelled s becomes infinitely attractive with zero range: $\hat{K}_{{ij}}^{{(s)}} \to \infty$ and z _s → ∞, but

$$ \hat{K}_{{ij}}^{{(s)}}/{{z}_{s}} = \theta _{{ij}}^{{(s)}} $$

In this limit the s potential is equal to Baxter’s sticky potential, as was shown Mier y Terán and co-workers.¹ We obtain formal equations for the sticky plus Yukawa potential.