Isotherms volume recovery/relaxation

Importantly for the structural recovery of glasses, the model predicts an equilibrium decay function which is of KWW form (jS= 1 —n), see equation (81), for even a single primitive species. Thus the requirement of a non-exponential decay function is fulfilled by the model. Although the other models use a broad relaxation function to describe behavior, they neither make the prediction of equation (91), nor can the general equation (89) result from them. In general, n and t can be functions of Tand d however, we treat only the case where t is a function of 8, i.e. t = T (r, 5(t )). Then, rewriting equation (86) in terms of t and identifying the macroscopic variable 0 with the departure from equilibrium 5, we find that, for isothermal volume recovery, equation (89) becomes... 

As pointed out earlier, most aging studies of blends have employed enthalpy relaxation and very few measurements have been made using volume relaxation. Notably, the volume changes during isothermal volume recovery are small, typically of the order of 1% or less and require high-precision measurements. 

The decrease in volume that accompanies physical aging is known as volume recovery or volume relaxation. Dilatometry (Dil) can be used to follow the volume relaxation in glasses by monitoring the time-dependence of the volume change on aging. The material is either cooled from above Tg to the aging temperature 7], (down-jump) and the isothermal volume contraction is measured or the sample is heated in the glassy state (up-jump), in which case an expansion follows. 

A similar equation can be derived for the enthalpy. It turned out that this modification to give the retardation time a free volume dependence, was successful in describing one-step isothermal recovery but unsuccessful in describing memory effects. Kovacs, Aklonis, Hutchinson and Ramos (1979) attributed the latter to the contributions of at least two independent relaxation mechanisms involving two or more retardation times. These authors proposed a multiparameter approach, the so-called KAHR (Kovacs-Aklonis-Hutchinson-Ramos) model. The recovery process is divided into N subprocesses, which in the case of volumetric recovery may be expressed as ... 

Work by Kovacs [75] on the volume relaxation of poly(vinyl acetate) highlighted the nonlinearity in the kinetics of isothermal recovery processes, and that the distribution of relaxation times, t, was necessary if the memory effects in glasses were to be explained. These ideas are incorporated in some of the phenomenological models developed to describe the aging of a glass and met in earlier sections. 

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