A critical Evaluation of higher-order Perturbation Theories for Fluids

The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the... [ view full abstract ]

The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the division of the intermolecular potential into a reference- and perturbation part. The first four perturbation terms are evaluated for various densities and temperatures (in the range ρ* = 0−1.5 and T*=0.5−12) using Monte Carlo simulations in the canonical ensemble. The simulation results are used to test several methods for approximating higher perturbation terms, or for developing an approximate infinite order perturbation series. Additionally, the simulations serve as a basis for developing fully analytical third order BH and WCA perturbation theories. The development of analytical theories allows (1) a systematic examination of the effect of higher order perturbation terms on calculated thermodynamic properties of fluids, and (2) a careful comparison between the BH and WCA formalism. Properties included in the comparison are supercritical thermodynamic properties, vapor-liquid phase equilibria, second virial coefficients, and heat capacities. For all properties studied, we find a systematically improved description upon using a higher order perturbation theory. A result of particular relevance is that a third order perturbation theory is capable of providing a quantitative description of second virial coefficients to temperatures as low as the triple-point of the Lennard-Jones fluid. Heat capacities are described equally well, provided the temperature is not too close to the critical temperature. Specifically, the maximum of the isochoric heat capacity along near-critical isotherms can not be described by a third order theory. Using an approximate fourth order theory, the maximum is captured at least qualitatively. We find no reason to prefer the WCA formalism over the BH formalism.