Do theories of the glass transition, in which the structural relaxation time does not define the dispersion of the structural relaxation, need revision?

Upon decreasing temperature or increasing pressure, a noncrystallizing liquid will vitrify; that is, the structural relaxation time, becomes so long that the system cannot attain an equilibrium configuration in the available time. Theories, including the well-known free volume and configurational entropy models, explain the glass transition by invoking a single quantity that governs the structural relaxation time. The dispersion of the structural relaxation (i.e., the structural relaxation function) is either not addressed or is derived as a parallel consequence (or afterthought) and thus is independent of tau(alpha). In these models the time dependence of the relaxation bears no fundamental relationship to the value of tau(alpha) or other dynamic properties. Such approaches appear to be incompatible with a general experimental fact recently discovered in glass-formers: for a given material at a fixed value of T, the dispersion is constant, independent of thermodynamic conditions (T and P); that is, the shape of the a-relaxation function depends only on the relaxation time. If derived independently of tau(alpha), it is an unlikely result that the dispersion of the structural relaxation would be uniquely defined by tau(alpha).