Configurational entropy of a hard sphere system using modified density functional approximation (MWDA)

Abstract

A sharp fall in the configurational entropy Sc of the liquid is a typical characteristic of the phenomena of liquid-glass transition that occur in the supercooled state. In the present work we report a calculation of S c for a hard sphere fluid by extending the classical density functional theory (DFT) to describe metastable states. In DFT thermodynamic properties of the undercooled liquid is calculated by identifying a metastable state as one for which a suitable free energy reaches a local minimum with respect to an optimum density distribution. The corresponding minimum value of the free energy is calculated by treating inhomogeneous density as an order parameter for the strongly heterogeneous state. In this work, density distribution of the metastable state is described in terms of Gaussian profiles centered on a lattice of random structure which is determined in terms of a pair distribution function g(R((η/η0)1/3) where η0 is a structure dependent parameter. The extrapolated configurational entropy Sc vanishes at η ≈ ηk and ηk is in agreement with other calculations of configurational entropy. The dependence of ηk on the structural parameter η0 is obtained.