Combining intermolecular potentials for the prediction of fluid properties: Two-body and three-body interactions

Equation of state for the Mie (λr,6) fluid with a repulsive exponent from 11 to 13

An empirical multi-parameter equation of state in terms of the reduced Helmholtz energy is presented for the Mie (λ_r-6) fluid with a repulsive exponent λ_r from 11 to 13. The equation is fitted to an extensive dataset from molecular dynamics simulation as well as the second and third thermal virial coefficients. It is comprehensively compared with the SAFT-VR model and is a more accurate description of the considered fluid class. The equation is valid for reduced temperatures T/T_c from 0.55 to 4.5 and for reduced pressures of up to p/p_c = 265. A good extrapolation behavior and the occurrence of a single Maxwell loop down to the vicinity of the triple point temperature are realized.

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

Analytical formulas are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc, and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard-Jones and Ingham in 1924, Corner in 1939, and Wallace in 1965. The formulas are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulas give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.