Phase diagrams of hard spheres with algebraic attractive interactions

The phase diagrams of systems made up of hard spheres interacting with attractive potentials of the form -1/r(3+sigma) are calculated using Monte Carlo simulations, second-order thermodynamic perturbation theory, and an augmented van der Waals theory. In simulations of the systems with sigma=0.1, 1, and 3, fluid-solid coexistence results are obtained using the Gibbs-Duhem integration technique; simulation data for the vapor-liquid coexistence envelopes and critical points are taken from previously published work [P. J. Camp and G. N. Patey, J. Chem. Phys. 114, 399 (2001)]. It is shown that the agreement between the theoretical and simulated phase diagrams improves as the range of the potential is increased, reflecting the decreasing role of short-range correlations in determining the bulk thermodynamics. In the extreme case of sigma=0.1 both theories are in excellent agreement with simulations. Phase diagrams for systems with sigma=4, 5, and 6 are computed using second-order thermodynamic perturbation theory. The results indicate that the vapor-liquid transition becomes metastable with respect to freezing when sigma > or approximately equal to 5, in broad agreement with results for the hard-sphere attractive Yukawa system which is commonly used to model colloidal particles, globular proteins, and nanoparticles.