Frequency dependence glass transition temperature

After the pioneering work of Owen et al. (1956, 1957) on diluted localized moments in metals (Cu Mn), twenty years later a large amount of experimental ESR work has been devoted to classical spin-glass systems. The experiments can be divided in two groups one in the SG state at T -c Tg and one at T > Tg, where Tg is the glass transition temperature which depends on the measuring frequency. 

When dipoles are directly attached to the chain their movement will obviously depend on the ability of chain segments to move. Thus the dipole polarisation effect will be much less below the glass transition temperature, than above it Figure 6.4). For this reason unplasticised PVC, poly(ethylene terephthalate) and the bis-phenol A polycarbonates are better high-frequency insulators at room temperature, which is below the glass temperature of each of these polymers, than would be expected in polymers of similar polarity but with the polar groups in the side chains. 

Figure B8.2.1 shows the fluorescence spectra of DIPHANT in a polybutadiene matrix. The h/lu ratios turned out to be significantly lower than in solution, which means that the internal rotation of the probe is restricted in such a relatively rigid polymer matrix. The fluorescence intensity of the monomer is approximately constant at temperatures ranging from —100 to —20 °C, which indicates that the probe motions are hindered, and then decreases with a concomitant increase in the excimer fluorescence. The onset of probe mobility, detected by the start of the decrease in the monomer intensity and lifetime occurs at about —20 °C, i.e. well above the low-frequency static reference temperature Tg (glass transition temperature) of the polybutadiene sample, which is —91 °C (measured at 1 Hz). This temperature shift shows the strong dependence of the apparent polymer flexibility on the characteristic frequency of the experimental technique. This frequency is the reciprocal of the monomer excited-state...

The glass transition temperature of PE by DSC measurements is -110°C. The glass transition temperatures by DMTA measurements can be higher, depending on the frequency. These results relate to some grades only and cannot be generalized. 

The glass transition temperatures by DTMA measurements can be higher, depending on the frequency. 

For the reactive system cured at a temperature, T higher than its maximum glass transition temperature Tgoo (= — 12°C), s Soto decreases to reach plateau values that are frequency dependent (Fig. 6.9a). As there is no vitrification, the plateau observed corresponds to the behavior of a network in a rubbery state. 

Molecular weight affects mainly the a relaxation. Although the temperature of the a peak is often taken as a value for the glass transition temperature, Tg, the two temperatures are not equivalent because the first is strongly dependent on frequency. 

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. 

Here cci is the liquid expansion factor fg is the fractional void or free voltune at the glass temperature Tg, B is related to the fractional void voliune required to be in the vicinity of a segment for that segment to make a jump and is an inherent jump frequency factor, which may depend slightly on temperature, but much less so than does f itself. These interpretations are based principally on recent theoretical investigations of mass transport in liquids near their glass transition temperature. Unfortunately, the values for B, fg and cannot usually... 

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. 

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