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

Abstract

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.

Keywords:

• small systems
• confined fluid
• equation of state
• analytic theory
• statistical mechanics

Acknowledgements

MK thanks the Islamic Azad University, Ayatollah Amoli Branch, for its generous financial support during the research project. The authors thank Prof. Donald L. Thompson for useful discussions.

Additional information

Funding

This research was supported by the US Army Research Office [grant number W911NF 12-1-0146].