Article

# Simulation of phase boundaries using constrained cell models

Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095, USA.
(Impact Factor: 2.35). 08/2012; 24(37):375105. DOI: 10.1088/0953-8984/24/37/375105
Source: PubMed

ABSTRACT

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.

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##### Article: Communication: Direct determination of triple-point coexistence through cell model simulation
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ABSTRACT: 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.
The Journal of Chemical Physics 10/2012; 137(14):141101. DOI:10.1063/1.4758698 · 2.95 Impact Factor
• ##### Article: Freezing Transition Studies Through Constrained Cell Model Simulation
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ABSTRACT: In the present work, a simulation method based on cell models is used to deduce the fluid–solid transition of a system of particles that interact via a pair potential, $\phi \left( r\right)$ ϕ ( r ) , which is of the form $\phi \left( r\right) = 4\epsilon \left[ \left( \sigma /r\right) ^{2n}- \left( \sigma /r\right) ^{n}\right]$ ϕ ( r ) = 4 ϵ [ ( σ / r ) 2 n − ( σ / r ) n ] with $n=10$ n = 10 . The simulations are implemented under constant-pressure conditions on a generalized version of the constrained cell model. The constrained cell model is constructed by dividing the volume into Wigner–Seitz cells and confining each particle in a single cell. This model is a special case of a more general cell model which is formed by introducing an additional field variable that controls the number of particles per cell and, thus, the relative stability of the solid against the fluid phase. High field values force configurations with one particle per cell and thus favor the solid phase. Fluid–solid coexistence on the isotherm that corresponds to a reduced temperature of 2 is determined from constant-pressure simulations of the generalized cell model using tempering and histogram reweighting techniques. The entire fluid–solid phase boundary is determined through a thermodynamic integration technique based on histogram reweighting, using the previous coexistence point as a reference point. The vapor–liquid phase diagram is obtained from constant-pressure simulations of the unconstrained system using tempering and histogram reweighting. The phase diagram of the system is found to contain a stable critical point and a triple point. The phase diagram of the corresponding constrained cell model is also found to contain both a stable critical point and a triple point.
International Journal of Thermophysics 04/2013; 35(9-10). DOI:10.1007/s10765-013-1430-2 · 0.96 Impact Factor