Precise simulation of the freezing transition of supercritical Lennard-Jones

Abstract

The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.

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

“…[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. These differences are expected to be somewhat larger for the triple-point parameters due to the highly compressible nature of the gas phase.…”

“…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).…”