The vanishing limit of the square-well fluid: the adhesive hard sphere model as a reference system

TL;DR

This study investigates the critical behavior of square-well fluids with very narrow wells, revealing linear relationships in virial coefficients and providing improved estimates for the adhesive hard-sphere model's critical parameters.

Contribution

It offers new simulation data for narrow well widths, clarifies the relation between virial coefficients and critical temperature, and refines the critical parameter estimates for the AHS model.

Findings

B_2*c depends linearly on delta for small delta

Critical density remains constant in scaled units

Improved estimates for the AHS model parameters

Abstract

We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B_2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature T_c is estimated via a constant B_2*c assumption, due to the highly non linear transformation between B_2*c and T_c. This explains the previously observed validity of the law of corresponding states. The critical density rho_c is also found to be constant when measured in units of the cubed average distance between two bonded particles (1+0.5 delta)/sigma. The possibility of describing the delta -> 0 dependence with precise functional forms provides improved acccurate estimates of the critical parameters of the adhesive hard-sphere AHS model.