Freezing Transition Studies Through Constrained Cell Model Simulation

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, $$\phi \left( r\right) $$ , which is of the form $$\phi \left( r\right) = 4\epsilon \left[ \left( \sigma /r\right) ^{2n}- \left( \sigma /r\right) ^{n}\right] $$ with $$n=10$$ . 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.