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

Abstract

ABSTRACTWe 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 AQSW 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.