Thermoelastic inversion effect

The data in Fig. 5.18 were obtained at a fairly high extension (350 percent). When the experiment is repeated at lower extensions the slope of the curve decreases and below about 10 percent extension it becomes negative. This is caused by a reduction in stress due to thermal expansion of the rubber as the temperature is increased and it is known as the thermo-elastic inversion effect. If the effective change in extension due to thermal expansion is allowed for then the thermoelastic inversion effect disappears and the stress increases proportionately with temperature at low extensions as well as high extensions. 

No thermoelastic inversion should appear in the force-temperature coefficient at constant elongation a, inasmuch as the effect of ordinary thermal expansion is eliminated by fixing a instead of the length L as the temperature is varied. As the elongation approaches unity, both the force and its temperature coeffi.cient df/dT)p,a must van-... 

Experiments performed at lo i/er elongations (or compressions) belovi/ the so-called thermoelastic inversion point lead to decreasing o-values i/ith increasing temperature because the thermal expansion of the samples predominates the effect of the retractive force. 

Thus, the Gough-Joule effect can be understood as the manifestation of the thermoelastic inversion when seen from a different viewpoint. 

One might think at first that the energetic part of the force, could be derived also from a temperature dependent measurement of the force on the basis of Eq. (7.6). In fact, direct application of this equation is experimentally difficult since the volume does not remain constant under the normally given constant pressure conditions. Indeed, thermal expansion is observed and this is also the reason for the occurrence of a thermoelastic inversion point . It shows up in temperature dependent measurements on rubbers which are kept at a fixed length. Figure 7.4 shows a series of measurements which were performed at different values of A. For high extensions, we find the signature of ideal rubbers, i.e. an increase f T. For low extensions, on the other hand, thermal expansion over compensates this effect, and then even leads to a decrease of the force. 

The linear expansion of (71) reveals that the position of the thermoelastic inversion is insensitive to internal energy effects and depends principally upon thermal expansion. 

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