ESTIMATION OF EFFECTIVE DIAMETERS FOR MOLECULAR FLUIDS

Effective diameters of atoms and molecules can typically be estimated within about 1% from equation-of-state or compressibility data. These estimates correlate well with critical volumes, with molar refractivities, and with tabulated van der Waals volume increments. The correlations hold well even for markedly aspherical or polar molecules. Comparison of a simple perturbed hard-sphere equation of state (the Carnahan-Starling-van der Waals equation, denoted CS-vdW) with molecular dynamics simulations shows that surprisingly good values for both the Lennard-Jones radius and well depth (typically within 1% for σLJ, 10% for εLJ) can be obtained by using pressure-density isotherms or equivalent data. Together with empirical correlations, this permits the LJ potential parameters to be estimated simply from the density (at atmospheric pressure) and the heat of vaporization or boiling point temperature. The temperature dependence of the effective diameter can be estimated from a simple model originally introduced by Boltzmann. More sophisticated perturbative theories of liquids predict a small additional density dependence of the effective diameter. Simple analytical expressions for these theoretical models are presented. In particular, the CS-vdW equation is found to predict reliable absolute densities (within 1%) for liquids at high pressures where direct measurements become difficult. © 1990 American Chemical Society.