Glassy zone

Here it has been assumed that the Arrhenius equation is vahd for the glassy zone of this polymer. 

Horizontal shift factors (a ) were determined empirically. No vertical shift factor (To/T) was Incorporated. The empirical shift factors were used with Arrhenlus-type [log = (. AH/2.303R)/ (1/T-l/To)] and HLF-type [log at - Ci (T-To)/(C2 + T-To)] equations. A plot of T-To/log at versus T-To yielded HLF constants and C< 2 resultant values corresponding to the glassy zone... 

The glassy zone is accounted for by Eyring s free-volume model. In this model, liquid is regarded as a mixture of molecular particles and holes, and at the glass-transition point, the fraction of the hole volume available for translation of a molecule that is, the free volume, becomes a constant value of 2.5% [10]. 

At short times, J t) approaches a value of the order of 10 ° cm /dyne (10 Pa ), characteristic of a hard glasslike solid. The corresponding region of the time scale is sometimes called the glassy zone. This small compliance corresponds to the absence of any configurational rearrangements of the chain backbones within the interval of the experiment indeed, curve V shows that below the glass transition... 

The characteristic zones of the viscoelastic time scale are clearly apparent in H the glassy zone to the left of the principal maximum, the trai ition zone where... 

A detailed comparison of theory with experiment is given for polyisobutylene in Fig. 10-18, where the components of the complex compliance are chosen for representation. The general aspects of the onset of the glassy zone are evidently semiquantitatively reproduced. However, the distinct difference in slope between theory and experiment for values of J and J less than 10 cm /dyne is apparent. A similar treatment was made by Shibayama and collaborators, who also introduced varying parameters for the springs and dashpots in the ladder model to modify the shapes of the viscoelastic functions predicted. But a more detailed picture of local molecular motions is needed to explain viscoelastic behavior near the glassy zone. 

Persistence of Relaxation and Retardation Spectra into the Glassy Zone... 

It is in the transition zone between glasslike and rubberlike consistency that the dependence of viscoelastic functions on temperature is most spectacular, just as is the dependence on time or frequency. An example is given in Fig. 11-1 for the real part of the complex compliance of poly(/t-octyl methacrylate). Below —5°C, the experimental frequency range appears to correspond to the glassy zone the compliance is quite low, around 10 - cm dyne Pa ), and does not change... 

Application of Reduced Variables near the Glassy Zone of Time or Frequency... 

In the approach to the glassy zone, the existence of an approximately asymptotic limiting value of the compliance Jg can be taken into account by modifying reduction coordinates 10 and 11 as follows ... 

Anomalies in the application of reduced variables have also been observed in the neighborhood of the glassy zone, especially for several methacrylate polymers, and have been interpreted by assuming that the complex compliance... 

To show the effect of diluent o.n the detailed shapes of viscoelastic functions, it is convenient to employ corresponding-state plots as in Section C of Chapter 12. For the relaxation spectrum, we plot log H - log Tc/Mq against log t - log a o/kT). Of course, for a single polymer and its solutions the only variables are fo and c (which in the pure polymer becomes p). In Fig. 17-9, poly(vinyl acetate) is compared in this manner with its 50% solution in tri-m-cresyl phosphate. The values of log fo at 40°C for these two systems are 1.75 and -5.25, respectively—the diluent reduces the local friction coefficient by a factor of 10. The curves after reduction coincide at the bottom of the transition zone because this is fixed by the corresponding-state conditions, and are rather similar in shape throughout. However, the diluent causes the spectrum to rise somewhat more sharply from the theoretical slope of -5 at short times but at still shorter times it crosses the spectrum of the pure polymer, and its entrance into the glassy zone involves a broader maximum than the latter. 

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