THE POTENTIAL DISTRIBUTION-BASED CLOSURES TO THE INTEGRAL-EQUATIONS FOR LIQUID STRUCTURE - THE LENNARD-JONES FLUID

The potential distribution theorems for the test particles provide a c onnection to the chemical potentials and the cavity distribution funct ions y(r) much used in molecular theory. These relations can be capita lized for establishing the closure relations for the Ornstein-Zernike equation. In this study, we formulate a class of closures with built-i n flexibilities in order to satisfy the potential distribution theorem s (or the related zero separation theorems) and thermodynamic consiste ncy. The theory is self-contained within the Integral equation framewo rk. We test it on the Lennard-Jones fluid over ranges of temperatures (down to T=0.81) and densities (up to rho*=0.9). To achieve self-suff iciency, we exploit the connections offered by writing down n members of the mixture Ornstein-Zernike equations for the coincident oligomers up to n-mers. Then the potential distribution theorems generate new c onditions for use in determining the bridge function parameters. Five consistency conditions have been identified (three thermodynamic and t wo based on zero-separation values). This self-consistency allows for bootstrapping and generation of highly accurate structural and thermod ynamic information. The same procedure can potentially be extended to soft-sphere potentials other than the Lennard-Jones type. (C) 1997 Ame rican Institute of Physics.