On statistical mechanics of small systems: accurate analytical equation of state for confined fluids

M Khanpour and LA Rivera-Rivera and TD Sewell, PHYSICS AND CHEMISTRY OF LIQUIDS, 53, 467-480 (2015).

DOI: 10.1080/00319104.2015.1006631

Some relations are derived using statistical mechanics to describe the effects of surroundings on the properties of systems for sizes below the thermodynamic limit. A general expression for the free energy of closed, small systems is derived and then used to obtain the dependence of the thermal properties on density and temperature, including general expressions for equations of state and internal energies. Comparisons between predictions of the current theory and the results of molecular dynamics (MD) simulations are made for 3D hard-sphere and Lennard-Jones fluids for which the surroundings are modelled as reflecting hard walls that confine the system along one direction. The analytical predictions are in excellent agreement with the MD results.

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