Structure–entropy relationship in repulsive glassy systems

The entropy of glass can be evaluated from the experimental structure data and given laws of intermolecular forces. The method is based on the functional relation ∂2S/∂E2=−〈(ΔE)2〉−1, which connects the entropy function S=S(E) to structure via the energy E and the spatial energy fluctuations 〈(ΔE)2〉. This method, previously applied to a model cohesive system, is extended to strong repulsive systems. In cohesive systems at low thermal temperature, E is mainly potential energy which can be determined from pair potentials and molecular pair distributions. In contrast, in strong repulsive systems, characteristic of systems subject to high external pressure, E is mainly kinetic and its dependence on structure can be derived only by quantum mechanics which relates the strong repulsive forces to an effective volume available for molecular motion. This dependence has a form peculiar to the wave nature of the particles, and is illustrated by a cell model treatment of a disordered dense packed hard spheres system. In the low thermal temperature limit, it leads to an entropy independent of Planck's constant and of the particle mass.