The Gilroy-Phillips model of relaxational jumps in asymmetric double-well potentials, developed for the Arrhenius-type secondary relaxations of the glass phase, is extended to a formal description of the breakdown of the shear modulus at the glass transition, the $\alpha$ process. The extension requires the introduction of two separate parts of the barrier distribution function $f\left(V\right),$ with a different temperature behavior of primary and secondary parts, respectively. The time-temperature scaling of the $\alpha$ process, together with a sum rule for the whole barrier distribution function, implies a strong rise of the integrated secondary relaxation with increasing temperature above the glass transition. Thus one gets a quantitative relation between the fragility of the glass former and the fast rise of the picosecond process observed in neutron and Raman scattering. The formalism is applied to literature data of polystyrene, vitreous silica and a sodium silicate glass. In the glass phase of polystyrene, one finds a temperature-independent secondary barrier distribution function, in agreement with an earlier Raman result from the literature. Above the glass transition, the secondary barrier distribution function increases with temperature as predicted. The findings allow for an interpretation of the fragility and the entropy crisis at the glass transition.

• Received 18 August 2000

DOI:https://doi.org/10.1103/PhysRevB.63.104203