Pair Distribution Function for a Two-dimensional Liquid

Abstract

IN some respects, the atoms in simple liquids can be regarded theoretically as behaving like almost rigid bodies. Thus several authors^1,2 have been able to shed light on basic properties of the liquid state simply by analysing the packing statistics of large two and three-dimensional model aggregates of hard spheres. One very important characteristic of such an aggregate is the pair distribution histogram R(ρ); for a model containing N spheres, N R (ρ) δ ρ gives the number of pairs of spheres the centres of which are separated by distances in the interval (ρ,ρ + δ ρ). In the limit of an infinitely large model (N→∞) and infinitesimally small histogram interval (δρ→0), R(ρ) becomes formally equivalent to the familiar pair distribution function, which describes the average distribution of spheres about a typical sphere in the infinite aggregate. In this limit, R(ρ) can be taken to represent the pair distribution function for atoms in an unbounded liquid, and may thus be used in calculating thermodynamic properties of the liquid state. In practice, however, one must deal with finite models and here—quite apart from the more obvious limitations imposed by finiteness—edge effects can seriously restrict the validity of the histogram R(ρ) as an approximation to the pair distribution function of a real liquid.