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First derivative of the hard-sphere radial distribution function at contact.

Research paper by David M DM Heyes, Michael M Cass, Arkadiusz C AC Brańka, Hisashi H Okumura

Indexed on: 16 Aug '06Published on: 16 Aug '06Published in: Journal of physics. Condensed matter : an Institute of Physics journal



Abstract

Molecular dynamics simulations have been carried out of the radial distribution function of the hard sphere fluid for a range of densities in the equilibrium fluid and just into the metastable region. The first derivative of the hard-sphere radial distribution function at contact was computed and its density dependence fitted to a simple analytic form. Comparisons were made with semi-empirical formulae from the literature, and of these the formula proposed by Tao et al (1992 Phys. Rev. A 46 8007) was found to be in best agreement with the simulation data, although it slightly underestimates the derivative at the higher packing fractions in excess of about 0.45. Close to contact, within a few per cent of the particle diameter, the radial distribution function can be represented well by a second order polynomial. An exponential function, which has some useful analytic features, can also be applied in this region.