Radial Distribution Function of Hard Spheres at Different Densities

Abstract

The model of hard sphere system has important part in modern theories of liquids. Hard sphere fluid is considered as the most intensively studied system among all model fluids. The thermodynamic and structural properties of real fluids can be studied with the help of hard spheres fluid. The exact solution of Ornstein-Zernike (OZ) equation with Percus-Yevick (PY) along with the equation of state provides an approximate analytical expression for radial distribution function (RDF). This work intends to study the radial distribution function of Hard sphere (HS) using the PY approximation for different densities ranging from low to high to find out their structural properties, packing behavior, phase transitions, and thermodynamics. We use FORTRAN program for this purpose. At low densities, the RDF has a single peak at a distance corresponding to the hard sphere diameter, indicating that the particles are well-  separated and not interacting with each other like gaseous. As density increases, the peak becomes broader and shifts to smaller distances, indicating that the particles are coming into closer contact and interacting more strongly with each other. The height of the peak also increases, indicating that there is a greater probability of finding a particle at a certain distance from another particle.