Thermomechanical inversion

It can be easily demonstrated that for a Hookean body a thermomechanical inversion of the internal energy (AU = 0) must occur at the deformation... 

We see from Eq. (21) that the internal energy inversion occurs at compression of the system with a positive thermal expansivity and at extension with the negative one. Occurrence of the thermomechanical internal energy inversion in Hookean solids is a result of a different dependence of the work and heat on strain (Fig. 1). 

Since the values of P and a for solid polymers are usually in the range of 10 4 — 10-5 K-1, the thermomechanical inversion of the internal energy must occur at the deformation of a few percent7). 

Unlike the thermomechanical inversion of heat, the inversion of internal energy is possible only for chains with d In 0/dT 0. It is also evident from Eq. (48) that for d In 1 and vice versa. For values a = (6 — 10) x 10"4 K 1 and d In polymeric networks, XtJ = 1.3 — 2.2 for extension and X,j > 0.5 for compression. It must be emphasized that this thermomechanical inversion of internal energy is not connected with the stress-induced crystallization and arises from the different signs of inter- and intrachain contributions to the internal energy. The extreme of the internal energy occurs at the deformation... 

It is quite obvious that the thermomechanical inversions both of heat and internal energy must disappear at the condition of constant volume. 

We see that the relative change of entropy and internal energy at constant pressure is independent of the degree of twisting. This conclusion differs from that obtained for simple extension or compression. The entropic and energetic components in torsion are identical with the result for simple deformation. Equations (60) and (61) lead to the conclusion that there can be no thermomechanical inversions of heat and internal energy in torsion. 

The interchain effects in polymer networks are reflected in the thermomechanical inversion at low strains, which arises from a competition of intra- and interchain changes. Calorimetric studies of unidirectional deformation demonstrates this fact very obviously (Fig. 4). The point of elastic inversion of heat (Table 3) is dependent on the energy contribution and the thermal expansion coefficient in an excellent agreement with the prediction of Eq. (45). The value of (AU/W)VjT for the only one point of deformation, i.e. the inversion point, coincides with data obtained by a more general method (Fig. 3). 

An equivalent approach can be found in the determination of the elastic inversion on the f — T dependence 32-34 67>j Q = 2Data for NR obtained by both methods agree well. The energy contribution in EPR is negative and according to Eq. (37) a thermomechanical inversion of the internal energy should occur which is fully supported by the experimental findings (Fig. 4),... 

A surprising disappearance of the thermomechanical inversion of heat at elevated temperatures has been observed by Kilian 9,88). At 90 °C, the thermomechanical inversion in SBR and NR is found to disappeare in spite of the constant value of the thermal expansion coefficient. This means that the temperature dependence of elastic force should be negative from the initial deformations, which is in contradiction with experiment. This very unusual phenomenon was supposed to be closely related to rotational freedom which will continuously be activated above some characteristic temperature 9,88). 

Table 3. Thermomechanical inversions of heat 24-85-88( internal energy 24-85) and force 891 and related values of energy contribution...

TPs may provide some toughening for high-Tg networks without loss in thermomechanical properties the effect is modest below phase inversion and may increase significantly when bicontinu-ous morphologies are formed. 

Like the thermoelectric Seebeck effect, the thermomechanical effect implies the appearance of a pressure difference Ap = p2 - pi in the capillary connected vessels filled with a mobile substance—a hquid or gas— when the vessels are maintained at different temperatures with the temperature difference AT = T2 — Tj. The case of the vessels separated by a porous partition rather than one capillary is called thermoosmosis. The inverse phenomenon— the appearance of a temperature difference as a result of the pressure difference in the vessels—is called the mechanocaloric effect. 

As the parameters axial load, sliding velocity and mass moment of inertia have a direct influence on the thermomechanical conditions in the contact, they will referred to as primary stress parameters. Secondary stress parameters are the frequency of gear shifts - the inverse corresponds to the time... 

---