Anisotropy of polarisability

The usefulness of Frohhch s formula (2.53) is mainly restricted by our ignorance of the correlation factor g, which necessarily depends on the shapes of molecules and the disposition of the permanent dipoles within them, the anisotropy of pOlarisability and the presence of charge distributions of higher orders of symmetry. The theory gives us a good general understanding of the behaviour of polar materials, but deviations from the simple Debye equation (2.44) can often only be discussed in qualitative terms. 

The anisotropy of polarisability of the extended body is given by the expression... 

Fig. 1. Variation of the anisotropy of polarisability a — of a. DNA rod-like fragment with the nature and concentration of added salt.

A last point should not be forget in the comparison of dielectric and electrooptic measurements of the polarisability. The latter one measures in fact the anisotropy of polarisability (Xy — We have considered our result as giving ay and compared it to theories which neglect any transversal displacement of the counter-ions. While this is reasonable it doesn t means that transversal movements or end effects do not play a role in the value of the dielectric constant and its dispersion. 

One SEXAFS specific feature is the polarisation dependence of the amplitude. This derives from the high anisotropy of the surface and of ultrathin interfaces, that we may consider as quasi two dimensional systems. The relative orientation of the X-ray electric vector with respect to the surface (interface) normal does represent a preferential excitation for those atom pairs aligned along the electric vector e.g. with the electric vector perpendicular to the surface (interface) plane the EXAFS amplitude will be maximum for the atom pairs aligned normal, or almost normal to the surface (interface). The electric vector can be also aligned, within the surface plane, along different crystallographic directions. 

The anisotropy of the coil has been calculated for other models of the macromolecule. Expressions for the anisotropy coefficient are known in the case where the macromolecule has been represented schematically by a continuous thread (the persistence length model) (Gotlib 1964 Zgaevskii and Pokrovskii 1970) and also in the case where the microstructure of the macromolecules has been specified. In the latter case, the anisotropy coefficient of the macromolecule is expressed in terms of the bond polarisabilities and other microcharacteristics of the macromolecule (Flory 1969). 

The most common and easily applicable method of characterising liquid crystalline mesophases is polarisation microscopy. In this method, thin samples of the surfactant solution are viewed under a microscope between crossed polarisation filters. Due to optical anisotropy of liquid crystals they are birefringent. Hence, they give rise to a brightness in the microscope and show patterns that are very characteristic for the specific phases examples are shown in Figure 3.17. 

The anisotropy itself may be linear or circular, or a combination of both. In linear anisotropy the refractive index depends on the direction of polarised light. It is found in solid polymers under tension and in viscous polymeric liquids during flow (shear and elongation). The refractive index can also depend on the chirality of polarised light in this case one speaks of circular or elliptic anisotropy. Thus the so-called "optical activity" is circular birefringence its extinction analogue is circular dichroism. 

We shall now discuss in more detail the different phase types of polymers as far as data of birefringence, stress-optical coefficient and anisotropies in polarisability are available. 

Chirality of polarised light, 289 Chronological development of commercial polymers, 44 Circular anisotropy, 289 Clarity, 313, 316 Classification of composites, 843... 

The dielectric constants of an aligned nematic phase are dependent upon both the temperature and the frequency of the applied field at temperatures below the clearing point. The dielectric permitivity, j, measured parallel to all three axes above the clearing point in the isotropic liquid is the same. Therefore, the dielectric anisotropy of the same compound in the liquid state is zero, see Figure 2.10. The sign and magnitude of the dielectric constants and, therefore, the dielectric anisotropy are dependent upon the anisotropy of the induced molecular polarisability, Aa, as well as the anisotropy and direction of the resultant permanent molecular polarisation determined by permanent dipole moments. 

We can understand how anisotropy of electronic polarisation arises in molecules in terms of a simple diatomic molecule, consisting of two similar atoms of radius R at separation L, in an applied field E. 

Taking into account the possible anisotropy of the deformational polarisability of molecules requires that... 

These simulations demand better and more accurate water potentials to simulate complex phenomena, such as the vibrational dynamics, phase transitions and transport properties. The potential fimctions used in these calculations have gradually evolved, developing from very simple Lennard-Jones type with 3-point charges (e.g. BF [34]), 4-point charges (e.g. ST2 [5]), polarisable potentials (e.g. SK [35] DC [36] and NCC [37]) to the very complicated anisotropic multiple polarisable potential (ASP [38]). The process was also associated with a gradual increase in the anisotropy of these potentials. 

We must add a remark with regard to polarisability. In what precedes we have taken account only of the mean value of a over all directions—a procedure which, in the case of a gas, whose molecules ban rotate freely, is certainly permissible as a first approximation. But by suitable experiments we can also determine the anisotropy of the polarizability, and so also form for ourselves a picture of the anisotropy of the electron cloud. We have already mentioned (p. 230) that the polarizability is a tensor, and can be represented by the so-called ellipsoid of polarization (see fig. 3). This has the following... 

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