Comment on the Asymptotic Form of the Radial Distribution Function in a Quasi - Crystalline Model of Liquids

Abstract

The asymptotic behaviour of the radial distribution function g(R) for a liquid was reexamined recently¹ in a model defining the molecular correlations in terms of a fluctuating local crystalline structure (the quasi-crystalline model). Several different versions of this model have been presented since the earliest one given by Prins.² A more recent version was given by Franchetti³ who derived the following formula for g(R) :

Here the n-summation extends over all the points of a certain chosen lattice, with R_n the distance from a central lattice site and σ² _n a suitably chosen dispersion assigned to the corresponding lattice point. This result was obtained from a minimization procedure applied to a certain functional of the lattice structure. To make (1) more specific, the so-called structural diffusion law given by Prins²

was adopted.³