Thermally activated rotation

In contrast with the chain of coupled oscillators, the translational invariance of a chain of coupled rotors leads not to a continuous spectrum, but to two branches of tunneling states determined by Eqs. (7.83). These states are coherent, whereas the space-localized breather states (7.80) are incoherent. In this respect, the transitions between breather states are similar to thermally activated rotation of a single group, though the number of rotors lying within the breather envelope and participating in the collective motion is greater than unity ( 20). The above discussion of collective rotation, which is based on the paper of Fillaux and Carlile [1990], demonstrates that the spectrum of a chain of coupled rotors is much richer than the spectrum one can expect from the traditional band model. 

In this model,110 it was assumed that all C 2H bonds perform thermally activated rotational jumps within energy landscapes on the surface of a cone. Specifically, six basins were supposed to be separated by six energy barriers at positions 0, 60,..., 300° around the axis of the cone. For each cone, the barriers were drawn anew from the distribution of activation energies determined for TOL in DS.12,19 Further, it was assumed that all positions on the surface of the cone, except for the barriers, have the same energy, i.e., a random-barrier model was considered. The thermally activated jumps lead to a random new position in one of the two neighboring basins. This means that several back-and-forth jumps occur over relatively low energy barriers until relatively high barriers are crossed. In other words, many... 

There are several examples of catenanes where ring movements can be induced by external stimulations like simple chemical reactions or homogeneous or heterogeneous electron transfer processes [91-93], but only very few cases are reported in which the stimulus employed is light. It has been shown that in azobenzene-containing [2]catenanes like 31 + (Fig. 29) it is possible to control the rate of thermally activated rotation of the macrocyclic components by photoisomerization of the azobenzene moiety [119, 120]. Such systems can be viewed as molecular-level brakes operated by light. 

A useful means for compiling or comparing the results of a large number of experiments is to fit the observed populations to some distribution function. A reasonable first try for thermally activated processes would seem to be a Boltzmann function, where the population in a particular rotational level (J)... 

The end of the present Section aims both to summarize the just mentioned peculiarities of the non-steady-state transient kinetics of the tunnelling luminescence due to step-wise temperature changes, and to develop the theoretical basis for distinguishing two alternative reasons for the tunnelling luminescence temperature dependence thermally activated defect diffusion or rotation. 

A second difference from the continuum model is that large stresses near the reaction center should undergo thermally activated relaxation. According to the molecular mechanism of stress relaxation proposed above, such irreversible, or plastic, deformations occur in UP when the two decyl radicals back away from the reaction center by rotational translation along their long axes. In the process of making more room for the two new C02 molecules, each radical chain is driven into the adjacent interface between two layers of peroxide molecules. Introduction of a defect or a hole at the end of the peroxide chain should facilitate this motion and allow efficient relaxation of the stress. 

The dynamics of tunneling rotation of hindered rotors interacting with intra- and intermolecular vibrations has received much less attention than structural studies. Such interactions shift and broaden tunneling spectral lines and, when temperature is raised, lead to transitions from coherent tunneling to thermally activated hopping. 

This chapter is devoted to tunneling effects observed in vibration-rotation spectra of isolated molecules and dimers. The relative simplicity of these systems permits one to treat them in terms of multidimensional PES s and even to construct these PES s by using the spectroscopic data. Modern experimental techniques permit the study of these simple systems at superlow temperatures where tunneling prevails over thermal activation. The presence of large-amplitude anharmonic motions in these systems, associated with weak (e.g., van der Waals) forces, requires the full power of quantitative multidimensional tunneling theory. 

Activation by inelastic collisions is also called thermal activation. After a large number of collisions, a distribution over internal (rotational and vibrational) states will be established as given by the Boltzmann distribution at the given temperature. 

For the case of adsorbed complex molecules, which generally have a preferred orientation with respect to the substrate atomic lattice in their energy minimum configuration, the possibility of 2-D molecular rotations needs to be considered. These rotations require thermal activation, analogous to lateral transport. In the simplest case they imply the overcoming of a unique rotation energy barrier Er, which may be higher, equal or lower than the... 

In this section, we concentrate on the fundamental impact of particle size reduction on magnetization processes in individual particles. Although not directly related to coercivity, the classical effect of single domain particle formation is described. At small particle size, reversal by coherent rotation tends to be favoured with respect to nucleation/pinning-depinning finally thermal activation effects and macroscopic quantum tunnelling are discussed. 

Even below TB, the magnetization of nanoparticles may be strongly affected by thermal activation. Very small Co particles showing coherent rotation allowed thermal activation effects to be analyzed quantitatively [110]. From 40 mK up to 12 K, the coercive field was found to be a function of the expression theoretically expected for thermal activation, Tln(T/T0]213. 

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