Generic phenomenology of vitrification and relaxation and the Kohlrausch and Maxwell equations

A survey of the development of basic ideas in the phenomenology of relaxation kinetics of glasses is given, beginning with the classical dependences introducing time dependent relaxation times (R. & F. Kohlrausch, Weber, Boltzmann and Williams & Watts) or considering direct structural change (Maxwell, Adams & Williamson, Eyring & Tobolsky). The merits and disadvantages of both approaches are compared and a connection is established between them, allowing the direct switch from one phenomenological model to the other. Using one of the basic principles of the thermodynamics of irreversible processes (sometimes called the Phenomenological Law) in a generic way, new and more general relaxational dependences are derived in two forms: one as a semi-linear approximation and a second one in terms of a generalised first order reaction kinetics formula. It is shown, that from the generic approach, which was used recently also in deriving the kinetics of vitrification both the Kohlrausch and the Maxwell type dependences follow as particular cases. In this way both a derivation and a reappraisal of Kohlrausch’s stretched exponent formula is made in the framework of irreversible thermodynamics. A comparison is given with experimental data and good correspondence is found with the phenomenological models derived and employed.