Simulation of fluid-solid coexistence via thermodynamic integration using a modified cell model

• Published in: Journal of physics. Condensed matter 2012-04, Vol.24 (15), p.155101-9
• Main Authors: Nayhouse, Michael, Amlani, Ankur M, Heng, Vincent R, Orkoulas, G
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computer simulation; Condensed matter; Fluid flow; Fluids; Free energy; Solid phases; Thermodynamics
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/24/15/155101

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.