Partial nearest neighbor PDF for multi-component material systems

Abstract

We develop general expressions for partial nearest neighbor probability density functions (PNNPDF’s) for equilibrium multi-component systems, valid for arbitrary partial densities, temperatures, and interaction potentials; thus providing an alternative means of describing structure at the microscopic (atomic scale) level for multi-component material systems. This paper thus complements an earlier paper (U.F. Edgal and D.L. Huber, J. Phys. Chem. B 108, 13777–13788 2004) in the analytical investigation of the classical statistical thermodynamics of multi-component systems. The connection between PNNPDF’s and the commonly employed partial m-body distribution functions is detailed. Results for PNNPDF’s and partial m-body distribution functions applicable for the poisson-distributed multi-component system and the low density binary mixture of hard spheres are provided. The statistical geometry of the systems is further studied through a brief investigation of particle clustering. A major hallmark of the above investigation involves the several multiple integrals and multiple sums encountered, that were quite formidable to perform, even in the absence of particle interactions.