Precise simulation of the freezing transition of supercritical Lennard-Jones

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.

A comparison of methods for melting point calculation using molecular dynamics simulations

Accurate and efficient prediction of melting points for complex molecules is still a challenging task for molecular simulation, although many methods have been developed. Four melting point computational methods, including one free energy-based method (the pseudo-supercritical path (PSCP) method) and three direct methods (two interface-based methods and the voids method) were applied to argon and a widely studied ionic liquid 1-n-butyl-3-methylimidazolium chloride ([BMIM][Cl]). The performance of each method was compared systematically. All the methods under study reproduce the argon experimental melting point with reasonable accuracy. For [BMIM][Cl], the melting point was computed to be 320 K using a revised PSCP procedure, which agrees with the experimental value 337-339 K very well. However, large errors were observed in the computed results using the direct methods, suggesting that these methods are inappropriate for large molecules with sluggish dynamics. The strengths and weaknesses of each method are discussed.

Communication: phase transitions, criticality, and three-phase coexistence in constrained cell models

In simulation studies of fluid-solid transitions, the solid phase is usually modeled as a constrained system in which each particle is confined to move in a single Wigner-Seitz cell. The constrained cell model has been used in the determination of fluid-solid coexistence via thermodynamic integration and other techniques. In the present work, the phase diagram of such a constrained system of Lennard-Jones particles is determined from constant-pressure simulations. The pressure-density isotherms exhibit inflection points which are interpreted as the mechanical stability limit of the solid phase. The phase diagram of the constrained system contains a critical and a triple point. The temperature and pressure at the critical and the triple point are both higher than those of the unconstrained system due to the reduction in the entropy caused by the single occupancy constraint.

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.