Viscous liquids and the glass transition. VII. Molecular mechanisms for a thermodynamic second order transition

It has been previously shown that the ’’configurational’’ specific heat ΔCp of a liquid above Tg contains significant contributions from nonconfigurational sources such as changes with structural state (fictive temperature) of (1) lattice vibrational frequencies, (2) anharmonicity, and (3) numbers of molecular groups participating in secondary relaxations. Using the potential energy U of the structural state as an order parameter, we calculate the behavior of the liquid specific heat for simple models based on the first two mechanisms, and show that either gives a second order transition of the type generally conjectured as necessary to account for the entropy–temperature relation of the equilibrium supercooled liquid. We give qualitative arguments for believing that the third mechanism acts similarly. We show also that all three mechanisms if acting simultaneously give a single transition. Direct experimental evidence that anharmonicity, the most plausible mechanism on the basis of present scanty evidence, depends on structural state is lacking, but an order-of-magnitude calculation shows that only a small dependence on structural state is necessary to account quantitatively for observed ΔCp’s at the glass transition.