Detailed examination of the calculation of the pressure in simulations of systems with discontinuous interactions from the mechanical and thermodynamic perspectives

Abstract

We consider some fundamental aspects of the calculation of the pressure from simulations of systems characterized by discontinuous interactions. The usual approach to the computation of the pressure in such systems is based on the mechanical (or virial) expression, which in turn can be expressed in terms of the value of the radial distribution function at contact or the number of overlaps that would occur under a virtual compression of the system. A less widespread, and formally equivalent, approach invokes the thermodynamic definition of the pressure and involves the estimate of the change in free energy associated with a small volume perturbation. There are, however, important differences in the way the virial and thermodynamic evaluations of the pressure are implemented, and, as a consequence, in the corresponding errors associated with each technique. The bulk pressure is determined with the virial and the thermodynamic routes for the hard-sphere system in the fluid and solid states. Good agreement is found between the two approaches, though the virial route is generally found to provide a greater accuracy. This is also borne out from simulations of hard non-spherical particles characterized by the hard Gaussian overlap potential in isotropic and anisotropic (nematic) fluid states. We show that the tensorial components of the pressure can be determined by a simple extension of the approaches developed for the bulk pressure. The diagonal components evaluated in this way for the hard-sphere solid are found to be equivalent and equal to the bulk pressure within the accuracy of the calculation. The most stringent test of the virial and thermodynamic approaches is the computation of the normal and tangential components (and hence the interfacial tension) of a hard-sphere fluid confined between two structureless hard walls.

Keywords:

• Monte Carlo
• Molecular dynamics
• Isothermal-isobaric ensemble
• Gibbs ensemble
• Pressure tensor
• Surface tension
• Pores
• Hard-core particles

Acknowledgements

Financial support is due to the Spanish Dirección General de Investigación (project number FIS2004-06627-C02-01) and from the Universidad de Huelva and Junta de Andalucía. Additional funding from the Engineering and Physical Sciences Research Council EPSRC of the UK (GR/N03358, GR/N35991, and GR/ R09497), the Joint Research Equipment Initiative (JREI) (GR/M94427), and the Royal Society-Wolfson Foundation refurbishment grant is also acknowledged. Finally, we are both grateful to the Royal Society for the award of an International Short Visit grant which has facilitated our collaborative work.