Mean anisotropy

The matrices Hf and G 7 describe the mutual influences of the particles of the chain and depend not only on the direction of particle motion in comparison with direction of chain in the vicinity of the particle labelled a (the local anisotropy) (see equation (3.13)), but also on the mean anisotropy of the medium (the global anisotropy). 

Typically, one sees normahzed principal axes, a mean shape factor, and a mean anisotropy degree specihed for an elhpsoid. Often, the elhpsoid is characterized by its overall shape with respect to its three radii. Oblate elhpsoids (disk-shaped) have a = b> c prolate elhpsoids (cigar-shaped) have a = b < c and scalene elhpsoids have three unequal sides (a > h > c). In a sphere, of course, a = b = c. 

Table 40.7 summarizes some values of directional permeability available in the literature for different species. Depending on the experimental apparatus and the protocol nsed by the authors, some data are missing in the papers. For example, it is not always easy to calculate the permeability ratios from permeability value, or vice versa. Choong et al. (1974), for example, have reported the permeability values for sapwood and heartwood for the longitudinal direction, but not for the transverse directions. Only the mean anisotropy ratio is available in this paper. Perre (1992) and Perre et al. (2002) have used an experimental procedure to determine the longitudinal permeability and the anisotropy ratio on the same sample. In these instances, they just obtained the ratios and decided not to calculate the transverse permeability accordingly. 

If the variation of anisotropy degree with confining pressure is known, it is advisable to select the mean anisotropy degree over the confining pressure range of the application (e.g. deep tunnels) when using equation 6, which yields more accurate results. 

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

Experimental determinations are far from straightforward, especially if the molecule has little or no symmetry. The mean value can be deduced from the refractive index of a gas, whilst Kerr effect experiments give some idea of the anisotropy. 

Gelbart (1974) has reviewed a number of theories of the origins of the depolarized spectrum. One of the simplest models is the isolated binary collision (IBC) model of McTague and Bimbaum (1968). All effects due to the interaction of three or more particles are ignored, and the scattering is due only to diatomic collision processes. In the case that the interacting particles A and B are atoms or highly symmetrical molecules then there are only two unique components of the pair polarizability tensor, and attention focuses on the anisotropy and the incremental mean pair polarizability... 

A problem with studies on inert gas is that the interactions are so weak. Alkali halides are important commercial compounds because of their role in extractive metallurgy. A deal of effort has gone into corresponding calculations on alkali halides such as LiCl, with a view to understanding the structure and properties of ionic melts. Experience suggests that calculations at the Hartree-Fock level of theory are adequate, provided that a reasonable basis set is chosen. Figure 17.7 shows the variation of the anisotropy and incremental mean pair polarizability as a function of distance. 

Figure 17.7 Anisotropy (doited) and mean incremental pair polarizability...

Theories of the oxidation of tantalum in the presence of suboxide have been developed by Stringer. By means of single-crystal studies he has been able to show that a rate anisotropy stems from the orientation of the suboxide which is precipitated in the form of thin plates. Their influence on the oxidation rate is least when they lie parallel to the metal interface, since the stresses set up by their oxidation to the pentoxide are most easily accommodated. By contrast, when the plates are at 45° to the surface, complex stresses are established which create characteristic chevron markings and cracks in the oxide. The cracks in this case follow lines of pores generated by oxidation of the plates. This behaviour is also found with niobium, but surprisingly, these pores are not formed when Ta-Nb alloys are oxidised, and the rate anisotropy disappears. However, the rate remains linear it seems that this is another case in which molecular oxygen travels by sub-microscopic routes. 

Viovy,J.L. and Monnerie, L. Fluorescence Anisotropy Technique Using Synchroton Radiation as a Powerful Means for Studying the Orientation Correlation Functions of Polymer Chains. Vol. 67, pp. 99—122. 

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