Symmetric effects external field

Effects Due to Polarization of Counterion Distribution.—We consider first spherical particles (of radius a) with a layer of counterions which are freely mobile on the surface, but which cannot escape into the solvent because of the strong attractive forces of the highly charged partide. Without external manipulations, a symmetrical distribution of counterions can be assumed. After application of an external field, a displacement of counterions will occur which leads to some asymmetry of the distribution. The final equilibrium is determined by the opposing effects of the field and the diffusion of counterions, which tends to restore a random distribution. It can be shown that the phenomenon may be quantitatively described by a frequency-dependent complex surface conductivity... 

An external field may have a secondary effect, namely, the induced moment y may cause certain vibratory motions, which in the undisturbed molecule are symmetrical, to become unsymmetrically anhar-monic. Here by symmetric anharmonic vibrations we mean those for which the energy O is an even function of the distance x ... 

The process giving rise to this asymmetry is called the relaxation effect, and the time taken for the ion to build up its new ionic atmosphere is called the relaxation time. As the ion moves, the build up and decay are occurring continuously. Since the process is a relaxation phenomenon, then the build up of the asymmetry in the ionic atmosphere under the influence of the external field and the decay of the asymmetry to the symmetrical ionic atmosphere once the external field is removed will be first order processes. The overall rate constant for a first order relaxation process can be shown to be given by feoveraii = buildup + decay, and the relaxation time is given by t = l/(fcbuiidup + decay)- This applies even if the rate constants for build up and decay are different. This has the consequence that the same relaxation time is applicable to both build up and decay. 

Cross term due to (i) An applied external field has an indirect effect on the solvent through the ions. The force exerted on the moving central ion by the solvent in between the ions of the ionic atmosphere is dependent on the ionic distribution in the ionic atmosphere. Hence the interaction between the ions and the solvent will be determined by the interactions between the ions themselves. If the symmetrical distribution is perturbed by the externally applied field this will have an effect on the interactions between an ion and the solvent, and this will result in an additional solvent flow about the ion. For a calculation of the electrophoretic effect this asymmetry should be considered, but in this derivation it is not and it is assumed that the symmetrical distribution given by Equation (12.3) can be used. This added effect is considered in more advanced treatments (see Section 12.10). 

Between 1929 and 1935, several perturbations in the CO A1 and N2 B2E+ states were studied in magnetic fields up to 36 kG (Crawford, 1929, 1934 Watson, 1932 Parker, 1933 Schmid and Gero, 1935). Lines were observed to split, to broaden symmetrically and asymmetrically, to gain or lose intensity each line was a special case. Spectral resolution and sensitivity were seldom adequate to resolve individual M-components. Although many qualitative features were satisfactorily explained, several perturbing states were conclusively but incorrectly assigned, and no quantitative theory of the effect of an external field on perturbed line positions, shapes, and intensities emerged. 

In Fig. 1.4b, symmetric BHB bonds are considered. The less basic is B, the weaker and longer is the H bond. Simultaneously, two minima appear and the energy barrier br increases (Fig. 1.3a, b). The polarization effect is due to the central anion atom P for H2P04 and to the external field in the chloroaurate. 

For all but spherically symmetrical molecules, van der Waals forces are anisotropic. The polarizabihties of most molecules are different in different molecular directions because the response of electrons in a bond to an external field will usually be anisotropic. A consequence of this effect is that the dispersion force between two molecules will depend on their relative molecular orientation. In nonpolar liquids, the effect is of minor importance because the molecules are essentially free to tumble and attain whatever orientation is energetically favorable. However, in sohds, hquid crystals, and polar media, the effect can be important in determining the relative fixed orientation between molecules, thereby affecting or controlling specific conformations of polymers or proteins in solution, critical transition temperatures in liquid crystals and membranes, and so on. Repulsive forces in polar molecules are also orientation dependent, and are often of greater importance in controlling conformations and orientations. 

Generally, the piezoelectric effect could exist just in non-centrosymmetrical crystallographic symmetry classes. Mechanical stress/strain as a second-rank symmetrical tensors are basically centrosymmetrical external fields. If the materials crystallographic symmetry include cerrtre of symmetry operation, the resulting symmetry of material subjected to such field is also cerrtrosymmetrical (see Neuman s Law in Nye (1985)). Therefore, piezoelectric effect is excluded. Centrosymmetrical crystal stays centrosymmetrical even after the application of the mechanical stress and no polar direction for the polarization vector might exist in such stmcture. 

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