Molecular thermodynamics of quantum square-well fluids using a path-integral perturbation theory

ABSTRACT

We present a thermodynamic perturbation theory for fluids composed of N quantum particles of diameter α and mass m contained within a volume V at temperature T, interacting via a pair square-well potential (SW) with energy depth ε and range λ. Our approach is based on the exact analogy between the discretised path- integral formalism of quantum mechanics and the partition function of a classical system composed of necklace molecules, introducing a Zwanzig expansion method, using a quantum hard-spheres fluid (QHS) as reference system in order to calculate the perturbation terms for the Helmholtz free energy A_QSW of the SW system. These terms are obtained with path-integral Monte Carlo simulations in the canonical ensemble, and analytical results are provided as functions of the inverse temperature β = 1/kT, density ρ^* = Nσ³/V, SW range λ and de Broglie thermal wavelength , where h and k are the Planck's and Boltzmann's constants, respectively. Accurate results are obtained for thermodynamic states comprised in the region ρ^* ≤ 0.7, 1.2 ≤ λ ≤ 1.8, and λ*_B ⩽ 0.9. Quantum effects are more noticeable for shorter SW ranges, although the main thermodynamic effects are given by the QHS free energy.

KEYWORDS:

• Perturbation theory
• quantum fluids
• path-integral Monte Carlo
• semiclassical methods

Acknowledgments

We gratefully acknowledge financial support from CONACYT (México) through a PhD scholarship (CS) and a sabbatical grant (AGV), Convocatorias 2015 de Estancias Sabáticas Nacionales, Estancias Sabáticas al Extranjero y Estancias Cortas para la Consolidación de Grupos de Investigación. This work was developed at The School of Chemical Engineering and Analytical Sciences, University of Manchester, United Kingdom, during a sabbatical leave (AGV) and we would like to thank Carlos Avendaño and Andrew Masters for very helpful comments and feedback.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

CONACYT (México) [grant number 259501].