The Glass Temperature

FIGURE 1 Schematic plots of the variation of volume V and enthalpy H with temperature. The uppermost line represents cooling from equilibrium liquid at a more rapid rate Q. The line in the middle represents cooling at a slower rate Q2. The thin lines are extrapolations of the glass lines to higher temperatures. Their intersections with the equilibrium liquid line (thicker dashed line) define the glass temperatures, T Qi) and The downward pointing arrow indicates 

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Many of the most floppy polymers have half-melted in this way at room temperature. The temperature at which this happens is called the glass temperature, Tq, for the polymer. Some polymers, which have no cross-links, melt completely at temperatures above T, becoming viscous liquids. Others, containing cross-links, become leathery (like PVC) or rubbery (as polystyrene butadiene does). Some typical values for Tg are polymethylmethacrylate (PMMA, or perspex), 100°C polystyrene (PS), 90°C polyethylene (low-density form), -20°C natural rubber, -40°C. To summarise, above Tc. the polymer is leathery, rubbery or molten below, it is a true solid with a modulus of at least 2GNm . This behaviour is shown in Fig. 6.2 which also shows how the stiffness of polymers increases as the covalent cross-link density increases, towards the value for diamond (which is simply a polymer with 100% of its bonds cross-linked. Fig. 4.7). Stiff polymers, then, are possible the stiffest now available have moduli comparable with that of aluminium. 

Polymers, too, creep - many of them do so at room temperature. As we said in Chapter 5, most common polymers are not crystalline, and have no well-defined melting point. For them, the important temperature is the glass temperature, Tq, at which the Van der Waals bonds solidify. Above this temperature, the polymer is in a leathery or rubbery state, and creeps rapidly under load. Below, it becomes hard (and... 

Creep of polymers is a major design problem. The glass temperature Tq, for a polymer, is a criterion of creep-resistance, in much the way that is for a metal or a ceramic. For most polymers, is close to room temperature. Well below Tq, the polymer is a glass (often containing crystalline regions - Chapter 5) and is a brittle, elastic solid -rubber, cooled in liquid nitrogen, is an example. Above Tq the Van der Waals bonds within the polymer melt, and it becomes a rubber (if the polymer chains are cross-linked) or a viscous liquid (if they are not). Thermoplastics, which can be moulded when hot, are a simple example well below Tq they are elastic well above, they are viscous liquids, and flow like treacle. 

The glass temperature, T, you will remember, is the temperature at which the secondary bonds start to melt. Well below the polymer molecules pack tightly together, either in an amorphous tangle, or in poorly organised crystallites with amorphous... 

MPa. The temperature, normalised by the glass temperature T, is plotted linearly on the horizontal axis it runs from 0 (absolute zero) to 1.6 (below which the polymer decomposes). 

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. 

It was pointed out in Chapter 3 that the glass temperature is dependent on the time scale of the experiment and thus will be allocated slightly different values... 

The dielectric properties of polar materials will depend on whether or not the dipoles are attached to the main chain. When they are, dipole polarisation will depend on segmental mobility and is thus low at temperatures below the glass transition temperatures. Such polymers are therefore better insulators below the glass temperature than above it. 

Poly(vinyl acetate) is too soft and shows excessive cold flow for use in moulded plastics. This is no doubt associated with the fact that the glass transition temperature of 28°C is little above the usual ambient temperatures and in fact in many places at various times the glass temperature may be the lower. It has a density of 1.19 g/cm and a refractive index of 1.47. Commercial polymers are atactic and, since they do not crystallise, transparent (if free from emulsifier). They are successfully used in emulsion paints, as adhesives for textiles, paper and wood, as a sizing material and as a permanent starch . A number of grades are supplied by manufacturers which differ in molecular weight and in the nature of comonomers (e.g. vinyl maleate) which are commonly used (see Section 14.4.4)... 

Glass Temperature. The glass temperatures for a substantial number of polyurethane elastomers, similar to those discussed herein, were found (1 ) to increase linearly with the concentration of urethane moieties, [U]. For the present elastomers prepared using LHT-240 and TIPA, [U] should be 1.10 and 1.15 moles/kg, respectively. Their glass temperatures should be about —57°C, indicated by the previous data. 

Also termed glass temperature or Tg. The temperature at which the stiffness of an elastomer subjected to low temperatures changes most rapidly. If the glass temperature is close to the operational temperature the material will be leathery in its behaviour rather than rubber-like. Approximate glass transition temperatures for different polymers are NR -70 °C SBR -52 °C HR -75 °C PCP -40 °C and silicone rubber -85 °C. 

In aqueous solutions with small molecules the relaxation is slow (0.1 to 0.5 s), while tSSR of ice is very small (some 10 3 s) [ 1.36]. Close to the glass temperature of a substance the relaxation time does not decrease exponentially, and thus a different means of description must be used [3.9]. 

In attempts to better understand dendrimer intramolecular morphology, considerable attention was devoted to the fractional free volume near the glass temperature [40, 49, 50], Because all of the studies were performed within the WLF temperature range, the data were analyzed using the equation... 

Values of the fractional free volumes at the glass temperature were calculated for PBzEs and PAMAMs from fg = /ref + (Tg — 7 ref)/2.303C1° [53], and the results obtained are listed in Table 14.2 and shown (for PAMAMs) as C in Figure 14.12. It can be seen from these data that fg appears to be independent of... 

The systematic changes in the glass temperatures illustrated in Table 1 indicate quantitatively the changes in the composition within each phase. The random copolymer equation can be used to estimate the composition within each phase ... 

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

The glass transition temperatures of polymethylpentenes by DSC measurements are generally in the room temperature range, from 20°C up to 30°C. The glass temperatures by DTMA measurements can be higher, depending on the frequency. 

D. Axelson The glass temperature usually increases with increasing frequency. However, in the present problem our conclusions are based on the correlation time, which is a frequency-independent quantity. 

D. Axelson These spectra were obtained at 57.9 MHz, but that s not the problem. We can measure correlation times regardless of the frequency. The correlation time at the glass temperature is very long. From a measurement of the correlation time we should be able to tell whether it is a true glass. In all these cases the correlation times are six to nine orders of magnitude lower than can possibly exist in a glass. For this reason I think the correlation between the NMR measurement and dielectric relaxation and dynamic mechanical do not relate one to one because of the frequency effects in the other measurements. 

D. Axelson As we have already pointed out, the correlation time is frequency-independent. The longest correlation time that we have measured is about 10" s. Whether the results correlate well with the glass temperature depends on the value one accepts for linear and branched polyethylene. Those values have been a controversial matter. 

D. Axelson Carbon-13 NMR allows for the measurement of the average correlation time for each individual carbon atom. For the glass temperature problem we are obviously only concerned with the correlation time of the backbone carbons. 

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