Phase diagram of the hard-sphere potential model in three and four dimensions using a pseudo-hard-sphere potential

The hard-sphere potential has become a cornerstone in the study of both molecular and complex fluids. Despite its mathematical simplicity, its implementation in fixed time step molecular simulations remains a formidable challenge due to the discontinuity at contact. To avoid the issues associated with the ill-defined force at contact, a continuous potential has recently been proposed-here referred to as the pseudo-hard-sphere potential (pHS) [Báez et al., J. Chem, Phys. 149, 164907 (2018)]. This potential is constructed to match the second virial coefficient of the hard-sphere potential and is expected to mimic its thermodynamic properties. However, this hypothesis has only been partially validated within the fluid region of the phase diagram for hard-sphere dispersions in two and three dimensions. In this contribution, we examine the ability of the continuous pHS potential to reproduce the equation of state of a hard-sphere fluid, not only in the fluid phase but also across the fluid-solid coexistence region. Our focus is primarily on the phase diagram of hard-sphere systems in three and four dimensions; however, we also report on the feasibility of the pHS to reproduce the long time dynamics of a three-dimensional colloidal dispersion. We compare the thermodynamic properties obtained from Brownian dynamics simulations of the pHS potential with those derived from refined event-driven simulations of the corresponding hard-sphere potential. Furthermore, we provide a comparative analysis with theoretical equations of state based on both mean-field and integral equation approximations.