Despite recent advances, precise simulation of freezing transitions continues to be a challenging task. The main difficulties in simulations of fluid-solid coexistence are the very dense, nearly-incompressible nature and the different symmetry of the two coexisting phases. Precise simulation of freezing is a topic of considerable theoretical and practical importance. In protein solutions and colloidal suspensions for instance, it is typically observed that fluid-fluid demixing is metastable against crystallization.
In this work, a simulation method, based on a modification of the constrained cell model of Hoover and Ree, is proposed and tested on hard-sphere and Lennard-Jones systems. In the fully occupied constrained cell model of Hoover and Ree, each particle is confined within its own Wigner-Seitz cell. Constant pressure simulations of the constrained cell model indicate, as Hoover and Ree first pointed out, that it exhibits a point of mechanical instability at about 60% expansion from close packing. Below that point, the solid is mechanically unstable since without the confinement imposed by the cell walls it will rapidly disintegrate to a disordered fluid-like phase.
In their original work associated with freezing of hard-sphere systems, Hoover and Ree considered a modified cell model by introducing an external field of variable strength. High values of the external field variable favor configurations with one particle per cell and thus stabilize the solid phase. Normal system behavior is restored in the limit of vanishing external field. Hoover and Ree argued that as the strength of the field varies, one might be able to go continuously from the fluid to the solid phase and vise versa. They did not, however, exclude the possibility of critical/Curie type of terminal point that separates continuous from discontinuous behavior.
In the present work, the modified cell model is simulated under constant-pressure conditions using tempering and histogram reweighting techniques. Simulation results on hard-sphere and Lennard-Jones systems indicate that the transition from the fluid to the solid is continuous below the mechanical stability point. Beyond the point of mechanical stability, however, the passage from the fluid to the solid occurs via a first-order phase transition at a finite value of the external field. As the pressure increases, the magnitude of the field that sustains coexistence decreases. The previous observations suggest that the fluid-solid transition of the system under consideration can be studied by analyzing the field-induced transition of the modified cell model in the limit of vanishing external field. The coexistence pressure and densities for hard-spheres and Lennard-Jones systems are determined via finite-size scaling techniques for first-order phase transitions. The results so obtained are in close accord with available data from other techniques.
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