Hard Core Interactions
Biman Bagchi · 2018
Overview In the statistical mechanical treatment of structure and dynamics of dense gases and liquids, substantial simplification occurs if we can approximate atoms and molecules by some simple shapes (such as spheres or ellipsoids), each interacting with other via a short range repulsive potential. This is because the integrations involved in the evaluation of partition function and pair correlation functions become a lot simpler. A further simplification occurs if we consider a potential that is zero beyond a distance of separation but infinitely large and positive at and below this separation. This is popularly known as a hard sphere potential. In two dimensions, it is also known as a billiard ball model. In the study of liquids, there is additional reason for the importance of the hard sphere potential. Structure of dense liquids is often determined by the harsh short range repulsive potential. Therefore, a liquid made of hard spheres is often used as a reference system in the treatment of real liquids and the attractive part of the potential is treated as a perturbation. The billiard or hard sphere model has been widely used in the kinetic theory of gases also.