How `sticky' are short-range square-well fluids?

Abstract

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range $λ$ at a given packing fraction and reduced temperature can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter $τ$. Such an equivalence cannot hold for the radial distribution function since this function has a delta singularity at contact in the SHS case, while it has a jump discontinuity at $r=λ$ in the SW case. Therefore, the equivalence is explored with the cavity function $y(r)$. Optimization of the agreement between $y_{\sw}$ and $y_{\shs}$ to first order in density suggests the choice for $τ$. We have performed Monte Carlo (MC) simulations of the SW fluid for $λ=1.05$, 1.02, and 1.01 at several densities and temperatures $T^*$ such that $τ=0.13$, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)]. Although, at given values of $η$ and $τ$, some local discrepancies between $y_{\sw}$ and $y_{\shs}$ exist (especially for $λ=1.05$), the SW data converge smoothly toward the SHS values as $λ-1$ decreases. The approximate mapping $y_{\sw}\to y_{\shs}$ is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for $y_{\shs}$ the solution of the Percus--Yevick equation as well as the rational-function approximation, the radial distribution function $g(r)$ of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.