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

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'(sigma(+)) is derived in terms of SPT quantities. This new expression requires the value of the average of a three-particle correlation functionfor which an ideal gas approximation is developed. The resultant predictions for g'(sigma(+)) are compared to those generated from literature equations and to simulation data generated for this work. In addition to simulation data for g'(sigma(+)), simulation values for the three-particle correlation functionare presented for comparison to the approximation. The simple fourth-order integer coefficient polynomial is an accurate predictor of g'(sigma(+)), on the order of or better than what is calculated by existing equations. [GRAPHICS] .