Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range

Abstract

Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.

Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium

“…We evaluate the accuracy of SAFT-VRQ Mie in representing the thermodynamic properties of generic Mie potentials with first and second order Feynman-Hibbs corrections (Mie-FH1 and Mie-FH2), by first comparing to results from molecular simulations. Three choices of attractive and repulsive exponents (λr, λa) will be examined in detail, (10,6), (12,6), and (24,6). These exponents are chosen to span potentials with different degrees of softness.…”

“…A formally exact way to model the full quantum behavior is to use the Path Integral Monte Carlo approach, [20][21][22][23] but in practice the simpler semiclassical approach based on pair potentials is often preferred. Recently, Trejos and Gil-Villegas 24 presented a semiclassical Equation of State (EoS) valid for quantum fluids based on the statistical associating fluid theory for potentials of variable range (SAFT-VR), which they applied to the square well potential with a first-order quantum correction developed specifically for discontinuous potentials. 25,26 Contreras et al 27 mapped the description of the quantum-corrected Lennard-Jones potential onto effective Mie potentials by building on the accurate third order perturbation theory that has been developed for Mie fluids.…”

Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid

“…Besides the SAFT models, alternative approaches to model anisotropic systems have taken into account the non-spherical shape of the molecules combined with a SW interaction [55]- [60]. More recently, it has been possible to generate accurate quantum thermodynamic perturbation theories based on the SW model [61,62].…”

Computer simulation of liquid-vapor coexistence of confined quantum fluids

“…The information presented here is a valuable tool to be used in combination with thermodynamic theoretical approaches developed previously for classical confined fluids, 71-73 that require equations of state for three-and two-dimensional fluids, as well as a semiclassical version of the SAFT-VR approach. 60 …”

“…This new approach, which has given very accurate predictions for a wide range of substances, can be extended to quantum fluids using the method presented in Ref. 60, and specific equations of state could be obtained for the WK-1 potentials studied here.…”