Thermodynamic properties of model molecules with hexagonal symmetry from statistical mechanical theory

Abstract

The thermodynamic behavior of planar hexagonal model molecules interacting through a 6- and 7-center Lennard-Jones potential is considered. The influence of molecular size on various thermodynamic properties is elucidated. It is shown that the second virial coefficients obey a microscopic scaling, which causes serious ambiguities for devising effective potential models for real substances. By use of a perturbation theory the vapor–liquid coexistence curves and the critical points are established. Some regularities of distinct properties on the pVT surface are found. The reduced coexisting curves can be used to obtain unambiguous potential parameters for real substances with hexagonal molecular scaffold by using only two experimental points. Thus, all results are rationalized by empirical correlations for easy use. For benzene as an example this procedure results in a model that reproduces vapor pressures and dew densities over two orders of magnitude. Bubble densities are given within a few percent and second virial coefficients are predicted within the experimental scatter throughout the measured temperature range.

Dynamic Global Potentials and Second Virial Coefficients from Trajectory Calculations

“…Another approach is to use perturbation theory with reduced parameters. 5 This is a pragmatic approach which yields potentials for neat gases and gas mixtures. The potentials that are obtained by this approach are basically static potentials.…”

“…Many physical properties of gases depend on details of the intermolecular potential that are largely unknown. Therefore, parameters in empirical or calculated potentials are adjusted until agreement is obtained with experimental data such as viscosity, thermal conductivity, or the second virial coefficient ( B ( T )). − (There is extensive literature on the subject and additional references can be found in refs and −9.) The pragmatic way by which empirical potential parameters can be obtained from B ( T ), defined by the equation is by systematic iterations until a reasonable agreement between calculated and experimental B ( T ) is obtained.…”

“…Early work used simple empirical potentials such as Lennard-Jones (LJ), Kihara, exp-6, Sutherland, square well, and others 1,2 to calculate B ( T ). More recently, advanced computational methods were used to obtain intermolecular potentials. − Atomic force field calculations were used to calculate B ( T ) as well as thermodynamic properties of gas phase and liquid benzene . It turns out that, in spite of the good agreement between experiment and calculations of the values of B ( T ) in the gas phase, only specific force fields gave a good agreement with liquid-phase results as well .…”

“…Here again, a variety of different PES gave a good agreement with experimental values of B ( T ). Another approach is to use perturbation theory with reduced parameters . This is a pragmatic approach which yields potentials for neat gases and gas mixtures.…”

“…However, inversions are impractical and in the rarest of cases, when the procedure applies, the results are not unique . More than one potential can be obtained. − Therefore, reliable pairwise potentials remain one of the pressing problems of molecular dynamics. In the following, we show how starting from pairwise potentials it is possible to obtain B ( T ) and thus verify experimentally the validity of an intermolecular potential.…”