Activation energies local motions

As in the case of G, the unrelaxed tensile modulus will be found more or less proportional to the cohesive energy density, whereas the relaxed modulus will depend sharply on the activity of local motions. 

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

Experimental mobility values, 1.2 X 10-2 cm2/v.s. for eam and 1.9 x 10-3 cm2/v.s. for eh, indicate a localized electron with a low-density first solvation layer. This, together with the temperature coefficient, is consistent with the semicontinuum models. Considering an effective radius given by the ground state wave-function, the absolute mobility calculated in a brownian motion model comes close to the experimental value. The activation energy for mobility, attributed to that of viscosity in this model, also is in fair agreement with experiment, although a little lower. 

NMR spectra and Tj measurements at different temperatures. The local polymer chain motion varies over a frequency range of 104-106 Hz in the nematic phase. The activation energy of this motion is found to increase with decreasing number ( ) of methylene units in the spacer, and exhibits odd-even fluctuations. In a study of a homologous series of main-chain LC polyesters, 13C CP/MAS and variable-temperature experiments reveal a conformation-ally more homogeneous and a less dynamic nature for the even-chained than for the odd-chained polymer structures.300... 

Fig. 1. The potential energy surface for the nuclear motion in the cases of electron localization on the core of the donor, Jl/ (q), and on the core of the acceptor, 7/r(<7). q is the nuclear coordinate, -tt,(q ) is the activation energy of the electron transfer in the case of the classical nuclear motion, J is the reaction exothermicity, and Er is the reorganization energy.

Inhomogeneous local packing, which leads to a broad distribution of the activation energy of both phenyl ring and carbonate group motions. This... 

At 60 °C, 50% of the ester groups, trapped in constrained environments with high activation energy barriers, do not performed 7r-flips at a frequency higher than 10 kHz and their motions are limited to restricted rotations (rocking) around the local chain axis with an average amplitude of 7°. 

However, the situation becomes already more complicated for ternary single crystals like lanthanum-aluminate (LaAlC>3, er = 23.4). The temperature dependence of the loss tangent depicted in Figure 5.3 exhibits a pronounced peak at about 70 K, which cannot be explained by phonon absorption. Typically, such peaks, which have also been observed at lower frequencies for quartz, can be explained by defect dipole relaxation. The most important relaxation processes with relevance for microwave absorption are local motion of ions on interstitial lattice positions giving rise to double well potentials with activation energies in the 50 to 100 meV range and color-center dipole relaxation with activation energies of about 5 meV. 

The lineshape changes observed for the amorphous fraction of the polymer between -128° and -60° (Figure 8) indicate some type of relaxation whose origin is similar to that just described. It appears that this process involves reorientation about the local chain axis and the rate of this process is 0.1 kHz at -80°C. The relaxation data of Figure 9 are consistent with this explanation and indicate that the rate of this motion is 30 kHz at -50°C. However, this process is coupled with a higher temperature process (see below) and does not give definitive lineshapes which are amenable to lineshape analysis. We can estimate that this relaxation has an activation energy of 16 5 kcal/mole. Therefore, we conclude that the process responsible for these results is the Y relaxation. 

The only allowed motion is the exchange of the vacancy with one of its neighboring atoms. The exchange rate depends on the local environment, i.e. on the relative position of the vacancy and the impurity atom. This takes into account the effect of the lattice stress induced by the tracer atom on the energy landscape observed by the vacancy. Each rate is simply proportional to the Boltzmann factor e-AE/kBT wjjere is the activation energy for the considered diffusional move and kBTis the thermal... 

Fluorescence Polarization under continuous excitation are presently developed. But these experiments need the a priori choice of a model of motion to be interpreted, and such models do not exist so far for the local dynamics in bulk polymers. This limitation is very troublesome, since experiments carried out on polymers in solution have shown that varying the choice of the model used in data treatment could lead to important discrepancies in the derived correlation times or activation energies. In the following, we will show how Fluorescence Anisotropy Decay may help to overcome this difficulty, and we will give some examples of original information that can be obtained using this technique in conjunction with the powerful synchrotron light source. 

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