Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics

This paper is the fifth in a series exploring the physical consequences of the solidity of highly viscous liquids. Paper IV proposed a model where the density field is described by a time-dependent Ginzburg-Landau equation of the nonconserved type with rates in k space of the form Gamma0+Dk2. If a is the average intermolecular distance, the model assumes that DGamma0a2. This inequality expresses a long-wavelength dominance of the dynamics, which implies that the Hamiltonian (free energy) to a good approximation may be taken to be ultralocal, i.e., with the property that equal-time field fluctuations are uncorrelated in space. Paper IV also briefly discussed how to generalize the model by including the molecular orientational fields, the stress tensor fields, and the potential energy density field. In the present paper it is argued that this is the simplest model consistent with the following three experimental facts: (1) Viscous liquids approaching the glass transition do not develop long-range order; (2) the glass has lower compressibility than the liquid; (3) the alpha process involves several decades of relaxation times shorter than the mean relaxation time. The paper proceeds to list six further experimental facts of viscous liquid dynamics and shows that these follow naturally from the model.