Thermoelastic inversion point

One of the most remarkable properties of a strip of rubber is that, for a particular fixed length, the force of extension is independent of temperature  

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From the dynamic mechanical investigations we have derived a discontinuous jump of G and G" at the phase transformation isotropic to l.c. Additional information about the mechanical properties of the elastomers can be obtained by measurements of the retractive force of a strained sample. In Fig. 40 the retractive force divided by the cross-sectional area of the unstrained sample at the corresponding temperature, a° is measured at constant length of the sample as function of temperature. In the upper temperature range, T > T0 (Tc is indicated by the dashed line), the typical behavior of rubbers is observed, where the (nominal) stress depends linearly on temperature. Because of the small elongation of the sample, however, a decrease of ct° with increasing temperature is observed for X < 1.1. This indicates that the thermal expansion of the material predominates the retractive force due to entropy elasticity. Fork = 1.1 the nominal stress o° is independent on T, which is the so-called thermoelastic inversion point. In contrast to this normal behavior of the l.c. elastomer... 

Results of force-temperature experiments for a PAA solution on rubber are shown in Figure 2. For the first cycle, the initial load is that of the rubber since the coating is still in the liquid state and cannot support a load. At this load the rubber is just below its thermoelastic inversion point and its contribution to the force change is negligible. 

Note that since (8H/dL)TP 0, an ideal rubber has a thermoelastic inversion point. 

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. 

Fig. 7.4. Observation of a thermoelastic inversion point for natural rubber The temperature dependence of the force at constant extension exhibits a reversal in slope. Measurements by Anthony et al.[74]...

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. 

These observations are confirmed in Fig. 14.4. The negative slope at low elongations arises from the predominance of thermal expansion when elongation, and hence f, is low. Note that there is an intermediate elongation, the thermoelastic inversion point, at which force is essentially independent of temperature, where thermal expansion and entropy contraction balance. 

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