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Abstract

A multiordering parameter model for glass-transition phenomena has been developed on the basis of nonequilibrium thermodynamics. In this treatment the state of the glass is determined by the values of N ordering parameters in addition to T and P; the departure from equilibrium is partitioned among the various ordering parameters, each of which is associated with a unique retardation time. These times are assumed to depend on T, P, and on the instantaneous state of the system characterized by its overall departure from equilibrium, giving rise to the well-known nonlinear effects observed in volume and enthalpy recovery. The contribution of each ordering parameter to the departure and the associated retardation times define the fundamental distribution function (the structural retardation spectrum) of the system or, equivalently, its fundamental material response function. These, together with a few experimentally measurable material constants, completely define the recovery behavior of the system when subjected to any thermal treatment. The behavior of the model is explored for various classes of thermal histories of increasing complexity, in order to simulate real experimental situations. The relevant calculations are based on a discrete retardation spectrum, extending over four time decades, and on reasonable values of the relevant material constants in order to imitate the behavior of polymer glasses. The model clearly separates the contribution of the retardation spectrum from the temperature-structure dependence of the retardation times which controls its shifts along the experimental time scale. This is achieved by using the natural time scale of the system which eliminates all the nonlinear effects, thus reducing the response function to the Boltzmann superposition equation, similar to that encountered in the linear viscoelasticity. As a consequence, the system obeys a rate (time) -temperature reduction rule which provides for generalization within each class of thermal treatment. Thus the model establishes a rational basis for comparing theory with experiment, and also various kinds of experiments between themselves. The analysis further predicts interesting features, some of which have often been overlooked. Among these are the impossibility of extraction of the spectrum (or response function) from experiments involving cooling from high temperatures at finite rate; and the appearance of two peaks in the expansion coefficient, or heat capacity, during the heating stage of three-step thermal cycles starting at high temperatures. Finally, the theory also provides a rationale for interpreting the time dependence of mechanical or other structure-sensitive properties of glasses as well as for predicting their long-range behavior.