Polarization macroscopic electric

The coupling between strain and electrical polarization that occurs in many crystals provides a means for generating acoustic waves electrically. When die structure of a crystal lacks a center of inversion symmetry , the application of strain changes the distribution of charge on the atoms and bonds comprising the crystal in such a manner that a net, macroscopic, electrical polarization of the crys-... 

Fig. 5. Pulsed-nozzle FT microwave measurements. A molecule-radiation interaction occurs when the gas pulse is between mirrors forming a Fabry-Perot cavity. If the transient molecule has a rotational transition of frequency vm falling within the narrow band of frequencies carried into the cavity by a short pulse (ca. 1 (is) of monochromatic radiation of frequency v, rotational excitation leads to a macroscopic electric polarization of the gas. This electric polarization decays only slowly (half-life T2 = 100 (is) compared with the relatively intense exciting pulse (half-life in the cavity t 0.1 (is). If detection is delayed until ca. 2 (is after the polarization, the exciting pulse has diminished in intensity by a factor of ca. 106 but the spontaneous coherent emission from the polarized gas is just beginning. This weak emission can then be detected in the absence of background radiation with high sensitivity. For technical reasons, the molecular emission at vm is mixed with some of the exciting radiation v and detected as a signal proportional to the amplitude of the oscillating electric vector at the beat frequency v - r , as a function of time, as in NMR spectroscopy Fourier transformation leads to the frequency spectrum [reproduced with permission from (31), p. 5631.

The ferroelectric materials show a switchable macroscopic electric polarization which effectively couples external electric fields with the elastic and structural properties of these compounds. These properties have been used in many technological applications, like actuators and transducers which transform electrical signals into mechanical work [72], or non-volatile random access memories [73]. From a more fundamental point of view, the study of the phase transitions and symmetry breakings in these materials are also very interesting, and their properties are extremely sensitive to changes in temperature, strain, composition, and defects concentration [74]. 

Preceding the reports on elastomers, piezoelectricity in chiral smectic C phases of low-molar weight molecules or of polymers has usually been observed. The special property is that the system possesses macroscopic electrical polarization without an external field, so it is classified as ferroelectric. 

We know that the quadratic-in-field coupling of an electric field to the dielectric tensor craitributes to the free energy density with the term g = —EaE / n. When liquid crystals possess macroscopic electric polarization P (spontaneous or induced by some external, other than electric field factors), then an additional, linear-in-field term gE = PE is added to the free energy density. One of such a source of the macroscopic electric polarization is orientational distortion of a liquid crystal. 

The excitonic model was carried further by Turkevich and Cohen (1984a. 1984b) who proposed the stabilization of an excitonic insulator state. This is an insulator in which the hybridized (6s-6p) state actually becomes the ground state so that the system acquires a macroscopic electrical polarization due to the dipoles. Under these conditions, the fluid... 

The oscillating electric field of the light wave induces electric dipoles by the passage through a dielectric medium, which leads to a macroscopic electric polarization of the medium. In the case of less intensive light the dipole moments are linear and the resulting macroscopic polarization P is... 

The macroscopic electric polarization has several microscopic origins. 

As implied by the trace expression for the macroscopic optical polarization, the macroscopic electrical susceptibility tensor at any order can be written in temis of an ensemble average over the microscopic nonlmear polarizability tensors of the individual constituents. 

This idea is elegant for its simplicity and also for its usefulness. While often in phenomenological theories of materials, control of parameters with molecular structure would provide useful properties, but the parameters are not related in any obvious way to controllable molecular structural features. Meyer s idea, however, is just the opposite. Chemists have the ability to control enantiomeric purity and thus can easily create an LC phase lacking reflection symmetry. In the case of the SmC, the macroscopic polar symmetry of this fluid phase can lead to a macroscopic electric dipole, and such a dipole was indeed detected by Meyer and his collaborators in a SmC material, as reported in 1975.2... 

Remember that e = D/E, where the displacement vector is given by D = E -F 4 rP (CGS units), E being the macroscopic electric held and P the macroscopic polarization. Considering a density of atoms N, the macroscopic polarizahon is P = N (p) = 7Vq (Eioc> (where the symbol ( ) indicates an average valne) and so D = E + dTriVa (Eioc>. Now assnming (Eioc) = E, we obtain ... 

The dielectric constant is the electrostatic expression of the interaction of atoms and molecules with macroscopic electric fields rather than with the exceedingly strong fields of individual atoms and molecules. The interaction between the homogeneous outside field and electrically asymmetrical (polar) molecules results in a finite effect, since in these molecules the contributions of positive and negative charges do not cancel. 

As first realized by Meyer in 1974, when the molecules making up the C phase are non-racemic, the resulting chiral C phase can possess no reflection symmetry. Thus, the maximum possible symmetry of a C phase is C2, and the phase must possess polar order (21). One of the macroscopic manifestations of polar order can be a macroscopic electric dipole moment (the polarization P) associated with orientation of molecular dipoles along the polar axis. While the existence of polar order is not sufficient to assure an observable polarization (just as chirality does not assure optical activity), in fact many FLC materials do possess an observable P. 

We feel that these data in fact show that the o-nitroalkoxy functional array is indeed oriented along the polar axis in the FLC thin film as evidenced by the observed sign and magnitude of the macroscopic electric dipole moment of the film. This, of course, means that the molecular associated with this functional array must also be oriented along the polar axis of the film, which should therefore possess a substantial X(2). 

In this section, a simple description of the dielectric polarization process is provided, and later to describe dielectric relaxation processes, the polarization mechanisms of materials produced by macroscopic static electric fields are analyzed. The relation between the macroscopic electric response and microscopic properties such as electronic, ionic, orientational, and hopping charge polarizabilities is very complex and is out of the scope of this book. This problem was successfully treated by Lorentz. He established that a remarkable improvement of the obtained results can be obtained at all frequencies by proposing the existence of a local field, which diverges from the macroscopic electric field by a correction factor, the Lorentz local-field factor [27],... 

Hereby, the branches with E - and / -symmetry are twofold degenerated. Both A - and / d-modes are polar, and split into transverse optical (TO) and longitudinal optical (LO) phonons with different frequencies wto and wlo, respectively, because of the macroscopic electric fields associated with the LO phonons. The short-range interatomic forces cause anisotropy, and A - and / d-modcs possess, therefore, different frequencies. The electrostatic forces dominate the anisotropy in the short-range forces in ZnO, such that the TO-LO splitting is larger than the A -E splitting. For the lattice vibrations with Ai- and F -symmetry, the atoms move parallel and perpendicular to the c-axis, respectively (Fig. 3.2). 

Another limitation of the Poisson-Boltzmann approach is that the interaction between two surfaces immersed in water might not be exclusively due to the electrolyte ions. For instance, water has a different structure in the vicinity of the surface than in the bulk and the overlapping of such structures generates a repulsion even in the absence of electrolyte [20]. In this traditional picture, the hydration repulsion is not related to ion hydration actually it is not related at all to electrolyte ions. However, as recently suggested [21], this hydration interaction can still be accounted for within the Poisson-Boltzmann framework, assuming that the polarization is not proportional to the macroscopic electric field, but depends also on the field generated by the neighboring water dipoles and by the surface dipoles. 

Figure 4. (a) The electric potential (circles) as a function of the distance from the surface for the system described in the text. The continuous line represents a Spline interpolation, (b) The average polarization of a water molecule (squares) as a function of the distance from surface for the system described in text the macroscopic electric field (triangles) obtained through the numerical derivative of the potential is not proportional to the average polarization. 

In this paper a model was presented, which allowed one to calculate both the electric potential and the polarization between two surfaces, without assuming, as in the traditional theory, that the polarization and the macroscopic electric field are proportional. An additional local field, due to the interaction between neighboring dipoles, was introduced in the constitutive equation which relates the polarization to the local field. The basic equations were also derived using a variational approach. 

The average polarization of a water molecule, m(z), between two identical, charged parallel plates separated by a distance 2d is related to the macroscopic electric field, E(z), and to the local field produced by the neighboring dipoles via23... 

The traditional double-layer theory combines the Poisson equation with the assumption that the polarization is proportional to the macroscopic electric field, and uses Boltzmann distributions for the concentrations of the ions. The potential of mean force, which should be used in the Boltzmann distribution, is approximated by the mean value of the electrical potential. The macroscopic field E and the polarization P are related via the Poisson equation... 

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