Predicting the slope of the radial distribution function of a hard disk fluid

Abstract

The slope of the radial distribution function at contact is investigated for a pure component two-dimensional hard disk fluid. Using the framework of scaled particle theory (SPT), an exact equation for g'(σ +) is derived in terms of SPT quantities. This new expression requires the value of the average of a three-particle correlation function for which an ideal gas approximation is developed. The resultant predictions for g'(σ +) are compared to those generated from literature equations and to simulation data generated for this work. In addition to simulation data for g'(σ +), simulation values for the three-particle correlation function are presented for comparison to the approximation. The simple fourth-order integer coefficient polynomial is an accurate predictor of g'(σ +), on the order of or better than what is calculated by existing equations.