Anisotropic fine term

The isotropic g and a values are now replaced by two 3x3 matrices representing the g and A tensors and which arise from the anisotropic electron Zeeman and hyperfine interaction. Other energy terms may also be included in the spin Hamiltonian, including the anisotropic fine term D, for electron-electron interactions, and the anisotropic nuclear quadrupolar interaction Q, depending on the nucleus. Usually the quadrupolar interachons are very small, compared to A and D, are generally less than the inherent linewidth of the EPR signal and are therefore invisible by EPR. They are readily detected in hyperfine techniques such as ENDOR and HYSCORE. All these terms (g. A, D) are anisotropic in the solid state, and must therefore be defined in terms of a tensor, which will be explained in this section. 

Teeth fulfill very specific functions and it can be safely assumed that the tooth structure is finely tuned for this purpose. The dentin structure is clearly anisotropic, with all the mineralized fibrils being located on one plane, and all the tubules oriented perpendicular to this plane. It is therefore most surprising that in terms of microhardness, dentin is isotropic. This has recently been confirmed in a careful study in which root dentin microhardness was measured at the same precise location in three orthogonal directions [33],... 

As mentioned in Chapter 1 high field ESR gives a better spectral resolution of anisotropic g-factors, and allows simpler analysis than is possible at X-band of spectra with large zero-field (another term is fine structure) and hyperfine splittings. These features, (l)-(3) below, are the most important in general applications, but some other characteristics of high field ESR are also of relevance [2] ... 

Alternating copolymers of acrylates and styrenes have, in effect, two rotational states per main chain bond. The splittings in the fine structure of the methoxy protons of methyl acrylate and methyl methacrylate repeat units is shown to arise from the anisotropic aromatic shielding, as modified by conformational probabilities. When C shifts are treated, the y effect between carbon atoms 3 bonds apart is usually deemed the only factor sensitive to conformation, though other possible terms have been considered. ... 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

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