The elusive fluid-and-crystal coexistence state in simulations of monodisperse, hard-sphere colloids

Monodisperse, purely repulsive, hard spheres (MPRHS) are an important model system for mechanistically exploring phase behavior in atomic systems and colloids. Since the 1940s, phase transitions in these systems have been obtained via simulation, theory, and experiments. But there is a gap in this literature: despite decades of reports of phase transition from one pure state to another, no computational studies report spontaneous phase separation into coexisting domains of liquid and crystal regions. This gap owes its origin to the underlying mechanism of entropically-driven phase separation in MPRHS - the competition between short-range entropy and long-range entropy. Frenkel proposed that spontaneous phase separation in simulations of up to 1,000,000 particles would require more than 317,000,000 years to sample enough microstates to converge to phase separated macrostate. Some brute-force simulations do show brief spontaneous coexistence but a metastable crystal or fluid subsequently overtakes the system. To bypass these difficulties, many studies use seeding, gravity, or direct construction of liquid and solid phases to study interfacial energy and nucleation rates of MPRHS systems. WCA potentials have also been used to bypass metastability, where softness provides free volume, lowers osmotic pressure and the energy barrier. It is argued that the transition path taken in bypassing metastability is mechanistically the same as without triggers. But as acknowledged by Alder & Wainwright, explicit observation of spontaneous coexistence is central to computational prediction of first-order transition. Such observation would provide satisfying demonstration of Frenkel's entropy exchange mechanism. We explore literature revealing these interesting behaviors and conclude that computational demonstration of Frenkel's mechanism for MPRHS awaits large systems with careful hardness perturbations.