Dynamic properties of rubber: the glass transition temperature.

The glass transition temperature 

As stated previously, the glass transition temperature (Tg) is the temperature below which molecular rotational motion ceases. A similar cessation of rotational motion occurs when a crystallizable polymer is taken below its crystalline melt temperature (Tm). When going below the Tm, the polymer immediately changes from a rotating disordered state to a rigid highly ordered state with a large reduction in entropy. The Tm occurs over a narrow temperature range and the only thing that widens it is the presence of impurities which interfere with crystallization. When going below the Tg, a polymer changes from a rotating disordered state to a rigid disordered state with no accompanying change in entropy. The Tg occurs over a much wider temperature range than the Tm. The reason for this difference is that with the Tg, the resistance to rotation rapidly increases over the entire temperature range until it is high enough to inhibit almost all rotational motion. The Tg usually encompasses about a 5[degrees]C to 20[degrees]C temperature range.

The glass transition temperature can be detected by changes in the following:

* Mechanical properties

* Volumetric properties

* Thermodynamic properties 

* Electromagnetic properties

Many mechanical properties change when going through the Tg. Modulus, for example, increases by a factor of about 1000. Gehman Freeze is a measure of a rubber's torsional modulus, and is commonly used to estimate the Tg. The stress relaxation and creep properties also change dramatically. The dynamic properties, elastic modulus, loss modulus and tan & all exhibit large changes or reach peak values at the Tg. All of the dynamic properties of a non-crystalline polymer are determined by its Tg. This will be covered in more detail later.

Volume measurements, or dilatometry, is frequently used to determine a polymer's Tg (ref. 13). Figure 9 shows the effect of increasing temperature on the volume of a partially crystalline polymer (curve A). In going through the Tg, there is not a change in volume but an increase in the rate of change. The curve is continuous at the Tg but the first derivative is not. At the Tm, there is a definite change in volume due to the highly ordered reduced entropy conformation of the polymer chain in the crystalline state. The Tm entails a change in volume and is a first order transition; while the Tg entails a change in the rate of volume change and is a second order transition. If the polymer is heated above its Tm and cooled rapidly, crystallinity does not have time to set in and the polymer remains amorphous (curve B).

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The free volume concept has been used to explain the difference in the rate of volume change above and below the Tg. The free volume consists of holes or voids between the polymer segments. They are considered necessary for any type of rotational motion. Above the Tg, the free volume increases with increasing temperature with a resultant reduction in the resistance to rotational motion. Below the Tg, the free volume is at a constant value, which is small enough to hinder most rotational motion.

The effects of the Tg and the Tm on thermodynamic properties are illustrated in figure 10. The differential scanning calorimetry (DSC) curve shows a large change in heat capacity at the Tg and a peak value for the heat capacity at the Tm. The same type of curve would have been generated in the dilatometry experiment, had the coefficient of thermal expansion been plotted against temperature. When plotting enthalpy vs. temperature, the Tm and Tg exhibit the same first and second order transitions, as shown in the volume vs. temperature curve for the dilatometry experiment.

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Dielectric measurements can also be used to determine the Tg. The dielectric loss reaches a peak as does the loss modulus at the Tg. These dielectric measurements require the presence of polar groups on the polymer backbone.

All of the different methods of measuring the Tg show a variation of Tg with different cooling rates. The curves in figure 11 show that the Tg decreases with slower cooling of the polymer (ref. 14). This phenomenon can be explained by using the free volume theory. When a polymer is cooled, it is theorized that the individual segments assume extended chain conformations. These extended chain conformations reduce the free volume available for rotational motion. The formation of these extended chains, however, becomes a very slow process as the Tg is approached. If, therefore, a polymer is cooled at a fast rate, the temperature decrease is too fast to allow the free volume to reach a constant. Rotational motion is occurring while the measurements indicate that it has ceased. At a much slower cooling rate, there is ample time for the free volume to reach a constant value. A lower Tg value is therefore obtained at a slower cooling rate.

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Besides the glass transition associated with the rotational motion of the main chain, there also are transitions associated with the motion of other segments of a polymer. The transition due to the rotational motion of the main chain is usually at the highest temperature and is designated as the alpha Tg. Those associated with short sections of the main chain, or side groups, occur at lower temperatures. These are designated as beta and gamma Tgs in the order of decreasing temperature. Figure 12 shows the effect of alpha and beta Tgs on modulus and damping properties of polymethyl methacrylate (ref. 15). Here, the beta transition is due to the carbomethoxy side group.

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References

13. N. Bekkedahl, Forms of rubber as indicated by temperature-volume relationship, J. Res. Nat. Bur. Stand. 13, pp. 411-431 (1934).

14. J.J. Aklonis, W.J. MacKnight and M. Shen, Introduction to polymer viscoelasticity, Wiley Interscience (1972), p. 61.

15. L.E. Nielsen, Soc. Plastics Eng. J., 16, p. 525 (1960).