Thermally activated mechanisms

Vol. 8 Thermally Activated Mechanisms in Crystal Plasticity by D. Caillard and... 

Different approaches were used to describe the yielding of polymers quantitatively. Some theories took into account the free volume fraction. Eyring considered thermally activated mechanisms, and Robertson s model was based on changes of chain conformations. Argon s and Bowden s models were based on a metallurgical approach and a dislocation theory. A brief summary of the existing yielding theories is presented. 

The to—1-Fe distance in the low temperature X-ray crystal structure [147], which corresponds to the distal state, is 8.5 A and in the conformation proposed by Jovanovic et al. [151], which corresponds to the proximal state, is 4.5 A. By defining the proximal state to be made of all conformations with w—1-Fe distances less than 6.5 A we obtain the population of the proximal state as a function of temperature shown in Fig. 5.3. The population of the proximal state is 32% at 260 K, increases with temperature and finally plateaus at 318 K with 90% of the population in the proximal state. Both proximal and distal states exist at all temperatures rather than a sharp conformational transition from distal to proximal state at a specific transition temperature, a gradual shift in population from distal to proximal state occurs with increase in temperature. These findings are in agreement with the thermal activation mechanism proposed by Jovanovic et al. [151]. The predicted midpoint of the transition from the distal to the proximal state is 268K (see Fig. 5.3), 20° higher than the observed transition temperature [151]. The increase in population of the proximal state with increasing temperature indicates that the proximal state is stabilized by conformational entropy [80]. 

Ef and both thermal activation and nuclear tunnelling mechanisms are consistent with these results. However, it was shown that for benzhydrols with Cl and Br as para substituents, where > 0 does not decrease with the increase in spin-orbit coupling [75], This rules out thermal activation mechanisms. 

KIE are particularly relevant in H abstractions (Table 11). The range of KIE observed is well reproduced by the theory. It may be surprising that a tunnelling mechanism can account for isotope elfects considered low even for thermal activation mechanisms. However, the low KIE are a direct consequence of Eq. (17) both CH and CO oscillators must tunnel through the energy barrier in the course of the reaction. 

Fig. 6.32, it is very dear that the smallest Ti addition (0.9 mol%) has marked effects on lowering Q for both steps of Reaction (6.15). However, further increases in Ti level have no effects, at least not on Q. The dramatic decrease in Q indicates a major discontinuous change in the thermally activated mechanism. Further increases in desorption kinetics accme with further increases in Ti level, but only through increases in the pre-exponential rate constant k [142]. 

It is well known that at low strain rate, deformation and fracture are controlled by thermally activated mechanism, and in at high strain rate. 

On the other hand the analysis of magnetic relaxation experiments on noninteracting fine y-Fe203 particles dispersed in a polymer revealed the persistence of a thermal activation mechanism down to very low temperatures. In some cases, for example, for experiments on Fe-AljOj, further measurements at lower temperatures are needed in order to have clear evidence of deviations from a thermally activated mechanism. 

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