Dependence of the configurational entropy on amorphous structures of a hard-sphere fluid

Abstract

The free energy of a hard-sphere fluid for which the average energy is trivial signifies how its entropy changes with packing. The packing η f at which the free energy of the crystalline state becomes lower than that of the disordered fluid state marks the freezing point. For packing fractions η > η f of the hard-sphere fluid, we use the modified weighted density functional approximation to identify metastable free energy minima intermediate between uniform fluid and crystalline states. The distribution of the sharply localized density profiles, i.e., the inhomogeneous density field ρ ( x ) characterizing the metastable state is primarily described by a pair function g s ( η / η 0 ) . η 0 is a structural parameter such that for η = η 0 the pair function is identical to that for the Bernal random structure. The configurational entropy S c of the metastable hard-sphere fluid is calculated by subtracting the corresponding vibrational entropy from the total entropy. The extrapolated S c vanishes as η → η K and η K is in agreement with other works. The dependence of η K on the structural parameter η 0 is obtained.