Polarons Definitions

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

Because the polaron maintains its shape while moving we may take nY=F ti-Vdtla), with a being the lattice constant, 3.4 A, and F ) being a continuous function. We may then take d l/Jdt=F n), where F )=dF/d. Using the definition of mobility iu=Vdl , where B is the electric field strength, we may also write dEldt=ev/liu. Equating this form of (dEldt) with Eq. 20 we obtain... 

The ET processes under discussion here correspond by definition to pure ET, in which molecular or medium coordinates may shift (the polaron response) [17], but no overall bonding rearrangements occur. More complex ET processes accompanied by such rearrangements (e.g., coupled electron/proton transfer and dissociative ET) are of great current interest, and many theoretical approaches have been formulated to deal with them, including quantum mechanical methods based on DC treatment of solvent [31,32],... 

On the basis of a definite analogy between e tx and F-centers we may expect the appearance under certain conditions of (e tr)2- particles of the type of F -centers. From the polaron model (57) it follows that the bipolaron (two electrons localized in a common polarization well) can not exist. In accordance with the work of Vinetskii and Giterman (63), in some cases the formation of the bipolarons becomes energetically possible in the result of interaction of the polarization wells of two separate polarons. However, the saving in energy for such bipolaron states is not large and hence they will not be stable in liquids under room temperature. Actually, up to the present time a series of attempts have been made to detect (e aq)2 in the irradiated liquid water but these attempts were not successful. The polaron theory (57) predicts that F -centers (two electrons in the anionic vacancy) may be stable. For this it is necessary that the ratio e/n2 (e and n2 are the static and optical dielectric constants, n—refraction index) should be more than 1.5. Evidently, in the glassy systems under consideration this requirement is fulfilled. 

Still there is no chance to find some experimental criterion for checking each of the described theories. It should be stressed that the polaron model of the cavity with the localized electron is definitely proved by the volume expansion of ammonia when adding the alkali metal to it (38). Besides, on the basis of any of the cavity theories it becomes comparatively easy to explain the results of investigation of e tr photoannealing—i.e., the dispersion of the trap depths, and temperature dependence of ExmaX of the electrons. In this connection it is rather desirable to find some approach to determining the sizes of the cavities for the electrons in the irradiated polar systems, as it has been done for the metal-ammonia solutions. 

Figure 13.31. (a) HREELS spectra of undoped a6T and a6T with increasing doping level (for definition compare Figure 13.30). (b) HREELS spectra of undoped a6T, pure FeCL, and doped a6T (9%). The doited lines indicate the positions of the polai on levels. The inset shows these polaron stales, the optically allowed (0.5 eV, l.l eV) and the forbidden (1.7 eV) transitions [119]. 

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