Anisotropy other physical properties

Other physical properties. Anisotropy of thermal and electrical conductivity, coefficient of thermal expansion, elasticity, and dielectric constant may also provide information on internal structure. These properties, however, have so far been little used in structure determination, because they are less easily measured than those already considered consequently not very much experimental evidence is available for the purpose of generalizing on the relations between such properties and structural features. For further information on these subjects, see Wooster (1938), Nye (1957). 

The constants of proportionality d and e are called piezoelectric stress and strain coefficients. The stress and strain forces are represented by matrix quantities, and the coefficients are tensor quantities. A tensor mathematically represents the fact that the polarization can depend on the stress or strain in more than one direction. This is also true for the relationship between the stress or strain and the electric field. Many other physical properties in crystals also exhibit this nature, which is called anisotropy. Thus when a property is anisotropic, its value depends on the direction of orientation in the crystal. For the direct piezoelectric effect, the total polarization effect is the sum of these two contributions, an applied electric field and applied mechanical force. Based on the relationship between the electric displacement and the electric polarization it is then possible to write equations that relate the displacement D to the applied stress or strain. Electric displacement is the quantity that is preferred in experiment and engineering. 

Other physical properties related to chain dimensions were also studied by Yamakawa and collaborators, who evaluated the mean-square dipole moment (j/) of various types, the optical anisotropy, the electric birefringence, the electric dichroism, and the Kerr constant for the HW chain. If the chain has type A dipoles, (j/ is proportional to R ), that is,... 

Due to the clear correlation between molecular properties which can be calculated by computational methods and the physical properties of the nematic phase, the dielectric anisotropy (Ae) and the birefringence (An) can be predicted with reasonable accuracy by molecular modeling [28]. On the other hand, the viscoelastic terms and Kj, K2, are currently not really predictable, even if some recent results based on neural networks [3b], Monte Carlo simulations [29] and molecular mechanics approaches [30] give rise to some careful optimism (Figures 4.8 and 4.9). 

The responsiveness of the irradiated molecule to the CPL is more formally known as the g (or anisotropy) factor the relative difference of the extinction coefficients exhibited by an enantiopure compound to right and left CPL [49-51]. Thus, the success of the method is dependent on a basic physical property of the molecule as well as the conditions used [52, 53], meaning that, Hke aU the other processes described in this book, the appHcabihty of the method of the separation of enantiomers varies depending on the structure of the molecule under consideration and the conditions (such as solvent) that may be employed. 

The performed research showed that any residual deformation in clay soils is a result of displacement and redirection of structural elements on contacts. Deformational processes on contacts as a rule are accompanied by the changing number of contacts, their area, and the forces of interaction between structural elements. This results in alteration of strength, deformational, filtrational and other system parameters and in the appearing of anisotropy of physical and mechanical properties. 

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