Frequency dependence of glass transition

Figure 41 Film thickness dependence of glass-transition temperature at a constant frequency for polymer films of 4 to 400 nm thickness. Reproduced with permission from Zhou, D. Huth, H. Gao, Y. etal. MacroinoleculesZm, 41, 7662-7666...

Discussion of the dipolar relaxation involves two issues first, the average dipolar mobility at a given temperature and degree of conversion, as measured by the frequency of the maximum in the loss factor fmax (or by its reciprocal, the typical dipolar relaxation time xd), and, second, the detailed distribution of relaxation times as measured by the frequency dependence of the permittivity and loss factor. In spite of the clear evidence that the dipolar relaxation is associated with the glass transition... 

The curves showing the frequency dependence of loss functions [tan 5, G"(g)), or / (to)] permit the detection in the frequency domain, at temperatures just slightly above the glass transition temperature, of a prominent absorption or a process. The unavailability of experimental devices to measure mechanical viscoelastic functions at high frequencies impedes the detection of a fast process or P relaxation in the high frequency region. This latter process is usually detected in the glassy state at low frequencies. 

Accordingly, since the dispersion and xa are obtained independently as separate and unrelated predictions, in such models the dispersion (or the time/frequency dependence) of the structural relaxation bears no relation to the structural relaxation time. This means it cannot govern the dynamic properties. As have been shown before [2], and will be further discussed in this chapter, several general properties of the dynamics are well known to be governed by or correlated with the dispersion. Therefore, neglect of the dispersion means a model of the glass transition cannot be consistent with the important and general properties of the phenomenon. The present situation makes clear the need to develop a theory that connects in a fundamental way the dispersion of relaxation times to xa and the various experimental properties. 

Wo is the maximum value ofW- the barrier height - and is related to glass transition temperature. There has been much discussion in the literature about the functional dependence of exponent s on temperature and frequency. The various frequency dependencies of s values is shown schematically in Figure 8.12. 

The principles of time-temperature superposition can be used with equal success for dielectric measurements as well as dynamic mechanical tests. Analysis of the frequency dependence of the glass transition of the adhesive in the system described above shows that it follows a WLF type dependence whereas the transition of PET obeys Arrhenius behaviour. This type of study can be used to distinguish between different types of relaxation phenomena in materials. 

Temperature-Modulated Calorimetry of the Frequency Dependence of the Glass Transition of Poly(ethylene terephthalate) and Polystyrene... 

For polymers with a glass transition temperature well above room temperature, the dipole contribution to the dielectric constant will be weak. However, low Tg polymers exhibit a strong contribution as shown in Figure 4 for the composite DMNPAA PVK ECZ TTSIF with Tg = 16°. The frequency-dependence of the dielectric constant has been deduced for this material from frequency-dependent impedance measurements and the sample was approximated to a capacitor and a resistor in parallel. In the range of frequencies / = cy / 2 r = 0 to 1000 Hz, a good fit to the experimental data is found with the superposition of just two Debye functions with the following parameters = 3.55, Cdc = 6.4, Aj = 0.8, A2 = 0.2, r = 0.004 s and... 

Figure 3.2 Temperature-dependent conversion degree of glass transition and volume fraction of glassy state (derived from glass transition of an E-glass fiber polyester composite during a dynamic mechanical analysis (DMA) test at a heating rate of5°Cmin and a dynamic oscillation frequency of 1 Hz) [3]. (With permission from SAGE.)...

The slow, irreversible cold crystallization is followed in Fig. 6.53 for more than 10 days with quasi-isothermal TMDSC to a fixed value of RAF. At the end of the crystallization there is no frequency dependence of the heat-capacity. The crystallization and the glass transition to the RAF occur simultaneously (see also Fig. 6.18). 

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