Random sequential addition of hard spheres

Abstract

We study the random sequential addition (RSA) of hard spheres into three-dimensional space. A virial-like expansion for the fractional available volume, φ, (i.e. that volume which is accessible to the centre of a new sphere) is derived up to third order in packing fraction, η. Comparison with numerical simulations shows that, unlike the two-dimensional case, the third order expansion is a poorer representation of the process than the second-order expansion. We attempt to confirm that the jamming limit is approached in the asymptotic regime according to η(∞) — η(t) ∞ t -1/3. In addition we obtain an improved estimate for the jamming limit packing fraction, η(∞). Simple formulae that interpolate between the low and high density regimes are derived which accurately describe the RSA process over the entire density range. Finally, we compare the structure of the RSA configurations with that of the corresponding equilibrium HS fluid.