Shift factor, glass transition

As previously described, the resin shifts the glass transition temperature of the isoprene part. It is possible to explain/predict the shift from the master curves of the pure [SIS-SI] by calculating the modified elementary times Tq and ToHF through Eqs. (16, 17), taking into account the change in the mobility factor (friction coefficient) [5, 25] and considering an increase in the Vogel temperature (Too) of the WLF (Williams, Landel and Ferry [16]) equation. 

Note that subtracting an amount log a from the coordinate values along the abscissa is equivalent to dividing each of the t s by the appropriate a-p value. This means that times are represented by the reduced variable t/a in which t is expressed as a multiple or fraction of a-p which is called the shift factor. The temperature at which the master curve is constructed is an arbitrary choice, although the glass transition temperature is widely used. When some value other than Tg is used as a reference temperature, we shall designate it by the symbol To. 

The glass transition involves additional phenomena which strongly affect the rheology (1) Short-time and long-time relaxation modes were found to shift with different temperature shift factors [93]. (2) The thermally introduced glass transition leads to a non-equilibrium state of the polymer [10]. Because of these, the gelation framework might be too simple to describe the transition behavior. 

This behavior is in between that of a liquid and a solid. As an example, PDMS properties obey an Arrhenius-type temperature dependence because PDMS is far above its glass transition temperature (about — 125°C). The temperature shift factors are... 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

The purpose of this paper is to establish the fundamental links between the glass transition, viscoelastic relaxation, and yield stress by investigating the relaxation processes in polymers. The relationship between temperature and relaxation time scale is represented by a shift factor (a). At temperature T... 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

With Nishi and Wang results as reference points, the glass transition temperatures of blends shown in Figure 7.1 can be reorganized by the shifting factor AFg, which is defined by... 

Figure 7.2. Glass transition temperatures of quenched PVDF/PMMA blends after adjustment with a shifting factor (+) Martinez-Salazar et al. (A) Nishi and Wang (o) Noland et (+) Morales et al. (A) Roerdink and Challa. ...

Mijovic et al. analyzed the annealed blends from melts using dynamic mechanical thermal analysis and achieved similar results after an adjustment for shifting factors, AT s, as shown in Figure 7.3. The results were extended to include blends having a PVDF concentration greater than 80 wt %. It can be observed that the glass transition temperatures of the annealed blends reduce rapidly when the PVDF concentrations are above 80 wt %. 

Stress relaxation master curve. For the poly-a-methylstyrene stress relaxation data in Fig. 1.33 [8], create a master creep curve at Tg (204°C). Identify the glassy, rubbery, viscous and viscoelastic regions of the master curve. Identify each region with a spring-dashpot diagram. Develop a plot of the shift factor, log (ax) versus T, used to create your master curve log (ot) is the horizontal distance that the curve at temperature T was slid to coincide with the master curve. What is the relaxation time of the polymer at the glass transition temperature ... 

For semi-crystalline polymers with melting points of more than 100 °C above the glass transition temperature and for amorphous polymers far above the glass transition temperature Tg (at around T = Tg + 190°C), the shift factors obtained from time-temperature superposition can be plotted in the form of an Arrhenius plot for thermally activated processes ... 

For amorphous polymers which melt above their glass transition temperature Tg, the WLF equation (according to Williams, Landel, Ferry, Eq. 3.15) with two material-specific parameters q and c2 gives a better description for the shift factors aT than the Arrhenius function according to Eq. 3.14. 

Fig. 7. Calculated shift factor as a function of temperature and cooling rate as PVAc is cooled through the glass transition region [28]...

Over certain temperature ranges, the shift factor may exhibit a behavior which agrees better with an Arrhenius temperature dependence (6,7). This will normally be the case when a rather narrow range of experimental temperatures is used or the reference temperature is significantly greater than the glass transition temperature. A least squares treatment of log versus 1/T will lead to a shift function of the form... 

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