How "sticky" are short-range square-well fluids?

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 η and reduced temperature T * = k B T ∕ ϵ can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter τ ( T * , λ ) . Such an equivalence cannot hold for the radial distribution function g ( r ) since this function has a delta singularity at contact ( r = σ ) in the SHS case, while it has a jump discontinuity at r = λ σ in the SW case. Therefore, the equivalence is explored with the cavity function y ( r ) , i.e., we assume that y SW ( r ∣ η , T * ; λ ) ≈ y SHS ( r ∣ η , τ ( T * , λ ) ) . Optimization of the agreement between y SW and y SHS to first order in density suggests the choice τ ( T * , λ ) = [ 12 ( e 1 ∕ T * − 1 ) ( λ − 1 ) ] − 1 . 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 ( T * , λ ) = 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 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. 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.