How sticky are shortrange squarewell fluids?
Malijevsky, A.; Santos A. ; Yuste S. B.,
The Journal of Chemical Physics, 125 0745071 (2006)
The aim of this work is to investigate to what extent the structural properties of a shortrange squarewell (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 stickyhardsphere (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)(lambda1)](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 lambda1 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 PercusYevick equation as well as the rationalfunction 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 shortrange SW fluid mixtures.
