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

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 nonlinear 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 cube of the 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 accurate estimates of the critical parameters of the adhesive hard-sphere model.