How sticky are short-range square-well fluids?
Malijevsky, A.; Santos A. ; Yuste S. B.,
The Journal of Chemical Physics, 125 074507-1 (2006)
The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range lambda at a given packing fraction eta and reduced temperature T*=k(B)T/epsilon can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter tau(T*,lambda). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r=sigma) in the SHS case, while it has a jump discontinuity at r=lambda sigma in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that y(SW)(r parallel to eta,T*;lambda)approximate to y(SHS)(r parallel to eta,tau(T*,lambda)). Optimization of the agreement between y(SW) and y(SHS) to first order in density suggests the choice tau(T*,lambda)=[12(e(1/T*)-1)(lambda-1)](-1). We have performed Monte Carlo (MC) simulations of the SW fluid for lambda=1.05, 1.02, and 1.01 at several densities and temperatures T* such thattau(T*,lambda)=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.: Condens. Matter 16, S4901 (2004)]. Although, at given values of eta and tau, some local discrepancies between y(SW) and y(SHS) exist (especially for lambda=1.05), the SW data converge smoothly toward the SHS values as lambda-1 decreases. In fact, precursors of the singularities of y(SHS) at certain distances due to geometrical arrangements are clearly observed in y(SW). The approximate mapping y(SW)-> 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.