Related Experiment Video
Updated: May 31, 2026

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
Published on: October 16, 2017
First derivative of the hard-sphere radial distribution function at contact
David M Heyes1, Michael Cass, Arkadiusz C Brańka
1Division of Chemistry, School of Biomedical and Molecular Sciences, University of Surrey, Guildford GU2 7XH, UK.
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.
Related Concept Videos
Central-Force Motion
Curvilinear Motion: Polar Coordinates
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...
Gravitational Potential Energy for Extended Objects
Atomic Orbitals
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Thin-Walled Hollow Shafts

