Localization length Subject

In other words, the local deformation energy is quadratic in the local curvature k s) when expanded to the lowest order in k. Conformations with Rlocal deformation energy greater than k T per unit length. Subjecting this model to thermal fluctuations results in the wormlike chain model. ... 

Electronic conduction in insulating materials has been a subject of considerable interest in the quest to understand charge transport in the thin film layers of organic electronic devices. In typical dielectric materials, the electronic states near the Fermi level are usually localized states, and the electron wave functions decay exponentially over a distance known as the localization length. In constrast, metals have a high, generally uniform density of states, whereas semiconductors have well-separated conduction and valence bands (separated... 

The combined effects of a divalent Ca counterion and thermal treatment can be seen from studies of PMMA-based ionomers [16]. In thin films of Ca-salts of this ionomer cast from methylene chloride, and having an ion content of only 0.8 mol%, the only observed deformation was a series of long, localized crazes, similar to those seen in the PMMA homopolymer. When the ionomer samples were subject to an additional heat treatment (8 h at 100°C), the induced crazes were shorter in length and shear deformation zones were present. This behavior implies that the heat treatment enhanced the formation of ionic aggregates and increased the entanglement strand density. The deformation pattern attained is rather similar to that of Na salts having an ion content of about 6 mol% hence, substitution of divalent Ca for monovalent Na permits comparable deformation modes, including some shear, to be obtained at much lower ion contents. 

The question of electronic conductivity in the polyphosphazenes inevitably raises questions regarding the electronic structure of the phosphazene linkage.7-12 This matter has been the subject of controversy in the literature, but experimentally the situation is now well known.4,13 In spite of the fact that the phosphazene backbone is fully conjugated, bond equalized and possesses bond lengths which are indicative of partial double bond character, the evidence suggests that these are localized systems. 

Heteroindacenes have been prepared and studied by Hafner and co-workers.198 199 The syntheses of 1,3,5,7-tetra-te/t-butyl-4-azaindacene, its AA-oxide, and l,3,5,7-tetra-tot-butyl-4-phospha-s-indacenes have been recently reported (Scheme 66).200 The 12-jt-electron delocalized systems have been studied by dynamic NMR and X-ray and were subjected to molecular orbital calculations, and there is strong evidence of electron delocalization. However, X-ray crystallographic data for 4-phospha-s-indacene 164 and the 4-7V-oxide 164 show that there is a dual orientation in the crystal this disorder with two different orientations of the molecule does not allow for conclusions regarding bond lengths or delocalization, and the mediated structures show a D2h symmetry rather than C2h with localized double bonds. 

After a listing of some general definitions relating to crystalline polymers (Section 1), the subject is divided into sections dealing, successively, with local structural arrangements at the scale of a few bond lengths (Section 2), morphological aspects (Section 3), molecular conformation within polymer crystals (Section 4) and, finally, kinetic aspects of crystallization (Section 5). An alphabetical index of terms is provided for the convenience of the reader. 

It is certainly more constant than that of sediments being introduced into the basin. This fact is due to the greater mobility of material in solution which tends to even out local fluctuations in concentration through the action of waves and currents. The sediment is much less subjected to such a mechanical homogenization process and tends, therefore, to attain equilibrium by localized mineral reaction. The type of thermodynamic system operative is most likely to be "open", where each point of sediment has some chemical variables fixed by their concentration in the sediment (inert components due to their low solubility in the solution) and other chemical components, which are soluble, have their concentration in the sediment a function of their activity in the aqueous solution. The bulk composition of the resulting sediment will be largely determined by the composition of the waters in which it is sedimented and the length of time it has reacted with this environment. The composition of the aqueous solution is, of course, determined to a minor extent by these reactions. 

In many cases, the study of kinetics concerns itself with the paths and rates adopted by systems approaching equilibrium. Thermodynamics provides invaluable information about the final state of a system, thus providing a basic reference state for any kinetic theory. Kinetic processes in a large system are typically rapid over short length scales, so that equilibrium is nearly satisfied locally at the same time, longer-length-scale kinetic processes result in a slower approach to global equilibrium. Therefore, much of the machinery of thermodynamics can be applied locally under an assumption of local equilibrium. It is clear, therefore, that the subject of thermodynamics is closely intertwined with kinetics. 

The Mills-Nixon hypothesis had, as its foundation, certain differences in the chemical behaviour of indan (3) and tetralin (4) from which a localization of the aromatic 7r-bonds was predicted to occur in the direction depicted by la rather lb. The original experimental evidence upon which the effect was based was shown to be erroneous, but calculations at various levels of theory indicated that aromatic bond localization should exist and become more pronounced as the size of the annelated ring decreases In essence one can recognize that the structure of benzene has a symmetry such that both Kekule structures must contribute equally. With Q tetralin (4) (and the lower homologues) no such symmetry requirement exists and ring annelation could induce bond length alternation within the arene nucleus. As the strain imposed by the fused ring increases, the Mills-Nixon effect should increase. The hypothesis has been the subject of considerable discussion and the controversy is far from settled. 

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