Communication: A simple method for simulation of freezing transitions

Abstract

Despite recent advances, precise simulation of freezing transitions continues to be a challenging task. In this work, a simulation method for fluid-solid transitions is developed. The method is based on a modification of the constrained cell model which was proposed by Hoover and Ree [J. Chem. Phys. 47, 4873 (1967)]10.1063/1.1701730. In the constrained cell model, each particle is confined in a single Wigner-Seitz cell. Hoover and Ree pointed out that the fluid and solid phases can be linked together by adding an external field of variable strength. High values of the external field favor single occupancy configurations and thus stabilize the solid phase. In the present work, the modified cell model is simulated in the constant-pressure ensemble using tempering and histogram reweighting techniques. Simulation results on a system of hard spheres indicate that as the strength of the external field is reduced, the transition from solid to fluid is continuous at low and intermediate pressures and discontinuous at high pressures. Fluid-solid coexistence for the hard-sphere model is established by analyzing the phase transition of the modified model in the limit in which the external field vanishes. The coexistence pressure and densities are in excellent agreement with current state-of-the-art techniques.

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

“…The details of these simulations have been discussed in previous work. [5][6][7][8][9] As is evident in Fig. 1, at very low densities and pressures, the system behaves as an ideal gas, i.e., p* ∼ = ρ.…”

“…Similar mechanical stability points have also been seen in constant-volume simulations of soft-sphere and Lennard-Jones systems. 3,4 Recently, Nayhouse et al [5][6][7][8][9] proposed a simulation method for liquid-solid transitions which is based on constant-pressure simulations of generalized cell models. They found that the mechanical stability point of the solid phase, as modeled through the constrained cell model, appears in the form of an inflection point at about the same density and pressure as in previous work.…”

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

“…As already commented, sizedependence issues can formally be resolved through finitesize scaling analysis for first-order phase transitions. [1][2][3] This task is, however, computationally demanding due to the substantial density range (from the low-ρ ideal-gas to the high-ρ incompressible regime) that must be sampled in a single simulation. Regarding system-size effects, previous work [3][4][5] associated with finite-size scaling analysis of liquid-solid coexistence at fixed T * using cell models indicates that the estimate of the pressure for N = 256 differs by 4%-6% from the N = ∞ value.…”

“…The likely explanation for this discrepancy is the highly compressible nature of the gas phase. Recently, Nayhouse et al [1][2][3][4][5][6][7] proposed a series of simple and efficient direct and indirect simulation techniques for accurate simulation of fluid-solid coexistence. These approaches are based on extensions or generalizations of the constrained cell model 8,9 description of the solid phase.…”

“…In previous work, these simulation techniques were used to calculate fluid-solid coexistence points at a fixed temperature [1][2][3] and the fluid-solid phase boundary was determined through a thermodynamic integration technique 4,7 based on histogram reweighting. 10,11 For the cases for which the phase diagram of the system of interest contained a triple point, the corresponding triple-point temperature and pressure was estimated from the common intersection of the various saturation curves (i.e., evaporation and melting).…”