In an attempt to study the specific influence of cross-linking on the ␣ relaxation in polymer networks, a series of model heterocyclic polymer networks ͑HPN͒ with well-defined cross-link densities and constant concentration of dipolar units were studied. Model HPN systems were prepared by simultaneous trimerization of 1,6-hexamethylene diisocyanate ͑HMDI͒ and hexyl isocyanate ͑HI͒. These HPN systems were characterized by dielectric relaxation spectroscopy in the 10 Ϫ1 HzϽFϽ10 5 Hz frequency range and in the 123 KϽTϽ493 K temperature interval. The ␣ relaxation in these systems depends on network density and shifts toward higher temperatures as the cross-link density increases for high HMDI/HI ratios. Discussion of the ␣-relaxation shape in light of recent models indicates that segmental motions above the glass transition systematically experience a growing hindrance with increasing degree of cross-linking. Description of the temperature dependence of relaxation times according to the strong-fragile scheme clearly shows that fragility increases as polymer network develops.
Comprehensive analysis of calorimetric data for large number of low molecular weight and polymeric substances has shown that although neither excess entropy at the glass transition temperature ASg nor heat capacity jump ACP (calculated per mole of "beads") nor the ratio of the glass transition temperature to the second-order transition point, Tg/T2, can be regarded as "universal" constants for all glass formers, as implied in the "isoentropic state" concept or Tg, the value of ACP still appears to be an intrinsic constant for a family of substances with a similar structure in the disordered state prior to quenching. The amount of a residual disorder in the glassy state, as measured by the ratio of ASg to the melting entropy, ASm, was found to be predictable by the equation ASg
The potential of the fractional derivative technique is demonstrated on the example of derivation of all three known patterns of anomalous, nonexponential dielectric relaxation of an inhomogeneous medium in the time domain. It is explicitly assumed that the fractional derivative is related to the dimensionality of a temporal fractal ensemble (in a sense that the relaxation times are distributed over a self-similar fractal system). The proposed fractal model of a microstructure of inhomogeneous media exhibiting nonexponential dielectric relaxation is built by singling out groups of hierarchically subordinated ensembles (subclusters, clusters, superclusters, etc.) from the entire statistical set available. Different relaxation functions are derived assuming that the real (physical) ensemble of relaxation times is confined between the upper and lower limits of self-similarity. It is predicted that at times, shorter than the relaxation time at the lowest (primitive) self-similarity level, the relaxation should be of a classical, Debye-like type, whatever the pattern of nonclassical relaxation at longer times.
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