ISOBARIC VOLUME AND ENTHALPY RECOVERY OF GLASSES .2. A TRANSPARENT MULTIPARAMETER THEORY

A multiordering parameter model for glass-transition phenomena has bee n developed on the basis of nonequilibrium thermodynamics. In this tre atment the state of the glass is determined by the values of N orderin g parameters in addition to T and P; the departure from equilibrium is partitioned among the various ordering parameters, each of which is a ssociated with a unique retardation time. These times are assumed to d epend on T, P, and on the instantaneous state of the system characteri zed 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 asso ciated 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 r ecovery 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 experim ental situations. The relevant calculations are based on a discrete re tardation spectrum, extending over four time decades, and on reasonabl e values of the relevant material constants in order to imitate the be havior of polymer glasses. The model clearly separates the contributio n of the retardation spectrum from the temperature-structure dependenc e of the retardation times which controls its shifts along the experim ental time-scale. This is achieved by using-the natural time scale of the system which eliminates all the nonlinear effects, thus reducing t he response function to the Boltzmann superposition equation, similar to that encountered in the linear viscoelasticity. As a consequence, t he system obeys a rate (time) -temperature reduction rule which provid es for generalization within each class of thermal treatment. Thus the model establishes a rational basis for comparing theory with experime nt, and also various kinds of experiments between themselves. The anal ysis further predicts interesting features, some of which have often b een overlooked. Among these are the impossibility of extraction of the spectrum (or response function) from experiments involving cooling fr om high temperatures at finite rate; and the appearance of two peaks i n the expansion coefficient, or heat capacity, during the heating stag e of three-step thermal cycles starting at high temperatures. Finally, the theory also provides a rationale for interpreting the time depend ence of mechanical or other structure-sensitive properties of glasses as well as for predicting their long-range behavior.