Communication: Direct determination of triple-point coexistence through cell model simulation.

In simulations of fluid-solid coexistence, the solid phase is modeled as a constrained system of Wigner-Seitz cells with one particle per cell. This model, commonly referred to as the constrained cell model, is a limiting case of a more general cell model, which is formed by considering a homogeneous external field that controls the number of particles per cell and, hence, the relative stability of the solid against the fluid phase. The generalized cell model provides a link that connects the disordered, fluid phase with the ordered, solid phase. In the present work, the phase diagram of this model is investigated through multicanonical simulations at constant pressure and histogram reweighting techniques for a system of 256 Lennard-Jones particles. The simulation data are used to obtain an estimate of the triple point of the Lennard-Jones system. The triple-point pressure is found to be higher compared to previous work. The likely explanation for this discrepancy is the highly compressible nature of the gas phase.

Simulation of phase boundaries using constrained cell models.

Despite impressive advances, precise simulation of fluid-fluid and fluid-solid phase transitions still remains a challenging task. The present work focuses on the determination of the phase diagram of a system of particles that interact through a pair potential, φ(r), which is of the form φ(r) = 4ε[(σ/r)(2n) - (σ/r)(n)] with n = 12. The vapor-liquid phase diagram of this model is established from constant-pressure simulations and flat-histogram techniques. The properties of the solid phase are obtained from constant-pressure simulations using constrained cell models. In the constrained cell model, the simulation volume is divided into Wigner-Seitz cells and each particle is confined to moving in a single cell. The constrained cell model is a limiting case of a more general cell model which is constructed by adding a homogeneous external field that controls the relative stability of the fluid and the solid phase. Fluid-solid coexistence at a reduced temperature of 2 is established from constant-pressure simulations of the generalized cell model. The previous fluid-solid coexistence point is used as a reference point in the determination of the fluid-solid phase boundary through a thermodynamic integration type of technique based on histogram reweighting. Since the attractive interaction is of short range, the vapor-liquid transition is metastable against crystallization. In the present work, the phase diagram of the corresponding constrained cell model is also determined. The latter is found to contain a stable vapor-liquid critical point and a triple point.

Simulation of fluid-solid coexistence via thermodynamic integration using a modified cell model.

Despite recent advances, precise simulation of fluid-solid transitions still remains a challenging task. Thermodynamic integration techniques are the simplest methods to study fluid-solid coexistence. These methods are based on the calculation of the free energies of the fluid and the solid phases, starting from a state of known free energy which is usually an ideal-gas state. Despite their simplicity, the main drawback of thermodynamic integration techniques is the large number of states that must be simulated. In the present work, a thermodynamic integration technique, which reduces the number of simulated states, is proposed and tested on a system of particles interacting via an inverse twelfth-power potential energy function. The simulations are implemented at constant pressure and the solid phase is modeled according to the constrained cell model of Hoover and Ree. The fluid and the solid phases are linked together by performing constant-pressure simulations of a modified cell model. The modified cell model, which was originally proposed by Hoover and Ree, facilitates transitions between the fluid and the solid phase by tuning a homogeneous external field. This model is simulated on a constant-pressure path for a series of progressively increasing values of the field, thus allowing for direct determination of the free energy difference between the fluid and the solid phase via histogram reweighting. The size-dependent results are analyzed using histogram reweighting and finite-size scaling techniques. The scaling analysis is based on studying the size-dependent behavior of the second- and higher-order derivatives of the free energy as well as the dimensionless moment ratios of the order parameter. The results clearly demonstrate the importance of accounting for size effects in simulation studies of fluid-solid transitions.