The glass to rubber transition

Most PHAs are partially crystalline polymers and therefore their thermal and mechanical properties are usually represented in terms of the glass-to-rubber transition temperature (Tg) of the amorphous phase and the melting temperature (Tm) of the crystalline phase of the material [55]. The melting temperature and glass transition temperature of several saturated and unsaturated PHAs have been summarized in Table 2. 

The temperature dependence of the compliance and the stress relaxation modulus of crystalline polymers well above Tf is greater than that of cross-linked polymers, but in the glass-to-rubber transition region the temperature dependence is less than for an amorphous polymer. A factor in this large temperature dependence at T >> TK is the decrease in the degree of Crystallinity with temperature. Other factors arc the reciystallization of strained crystallites ipto unstrained ones and the rotation of crystallites to relieve the applied stress (38). All of these effects occur more rapidly as the temperature is raised. 

As the temperature is raised the thermal agitation becomes sufficient for segmental movement and the brittle glass begins to behave in a leathery fashion. The modulus decreases by a factor of about 10- over a temperature range of about I0-20°C in the glass-to-rubber transition region. 

Observed Tg s vary from -123°C for polyfdimelhyl siloxane) (1-43) to 273°C for polyhydantoin (11-2) polymers used as wire enamels and to even higher temperatures for other polymers in which the main chain consists largely of aromatic structures. This range of behavior can be rationalized, and the effects of polymer structure on Tg can be predicted qualitatively. Since the glass-to-rubber transition... 

Many relatively slow or static methods have been used to measure Tg. These include techniques for determining the density or specific volume of the polymer as a function of temperature (cf. Fig. 11-1) as well as measurements of refractive index, elastic modulus, and other properties. Differential thermal analysis and differential scanning calorimetry are widely used for this purpose at present, with simple extrapolative eorrections for the effects of heating or cording rates on the observed values of Tg. These two methods reflect the changes in specific heat of the polymer at the glass-to-rubber transition. Dynamic mechanical measurements, which are described in Section 11.5, are also widely employed for locating Tg. 

The development of a maximum in tan 5 or ihe loss modulus at the glass-to-rubber transition is explained as follows. At temperatures below Tg the polymer behaves elastically, and there is little or no flow to convert the applied energy into internal work in the material. Now It, the energy dissipated as heat per unit volume of material per unit time because of flow in shear deformation, is... 

The onset of the Tg is near 175°C. This composite, which is 45° carbon-fiber-reinforced, shows a dynamic storage modulus of the epoxy matrix in the glassy-state of ca. 15 GPa. At the onset of the glass-to-rubber transition (see Figure 6), the modulus drops gradually from 15 GPa (175°C) to about 3 GPa (300°C) as the rubbery plateau is reached. 

Modulus-temperature relations for amorphous polymers in static test reveal a sharp drop of modulus in the glass-to-rubber transition region (see Figure 1.19). Since the storage modulus G (oj) behaves like a modulus measured in a static test, it decreases in the glass transition region. However, the loss modulus G"((jj) and tan 6 go through a maximum under the same conditions. 

In the same studies, Moehlenpah et al (1970, 1971) obtained master curves for the stress relaxation of their epoxy systems, at least into the glass-to-rubber transition region (Figure 12.4), and demonstrated similar behavior of both the stress relaxation modulus and the tensile modulus as a function of strain rate. As with the strain rate studies mentioned, no effect of filler type on the WLF shift factor was observed. All solid fillers increased the modulus of the system, the fibers being more effective than the spheres. The bubbles, as expected (Nielsen, 1967a), decreased the modulus. 

For solids which are purely elastic tan S equals zero. Metals, for example, conform fairly closely to this ideal another good example of a low-damping solid is quartz. Polymers on the other hand have values of S of the order of several degrees in certain temperature ranges (for instance the glass to rubber transition) 8 may approach 30°. This very high damping is frequently of use technically (4.N.3). 

Gladfelter and co-workers probed polymer viscoelastic relaxations with temperature-controlled FFM (272,273). The dependence of the mean value of the friction force on temperature was reported to be correlated to the glass-to-rubber transition and/or secondary relaxation mechanisms in films of PMMA, poly(ethylene terephthalate) (PET), and PS. Viscoelastic mechanical losses were thought to be the dominant contribution to friction, which were found to obey the time-temperature superposition principle. Interestingly, the surface Tg s and values for the activation energy measured for the /3-relaxation at the surface were lower than those of the bulk material. 

We assign the sharp rise in friction at elevated RH to the glass-to-rubber transition. It is well known that both PVOH and gelatin are plasticized by absorbed water. ] At approximately 60% RH a moisture content of 8% is expected in PVOH. This would shift the glass transition from around 80 C in anhydrous PVOH to 20-22°C, i.e. room temperature, as used in the present experiment. Thus above 60% RH, large-scale molecular motions in response to shear and compressive stresses (tip) will dissipate strain energy. Enhanced energy dissipation is measurable as an abrupt... 

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