Dielectric polarization mechanism electronic

The application of an electric field E across a linear dielectric material results in polarization P or the separation of positive and negative charges. The relative dielectric constant k is a measure of the capacity of a solid to store charge relative to vacuum and is related to the extent to which the charges in a solid polarize. Atomically there are four main polarization mechanisms electronic, ionic, dipolar, and space charge. 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

The Marcus treatment uses a classical statistical mechanical approach to calculate the activation energy required to surmount the barrier. It assumes a weakly adiabatic electron transfer process and non-equilibrium dielectric polarization of the solvent (continuum) as the source of activation. This model also considers the vibrational contributions of the inner solvation sphere. The Hush treatment considers ion-dipole and ligand field concepts in the treatment of inner coordination sphere contributions to the energy of activation [55, 56]. 

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],... 

Fundamental properties, such as the van der Waals volume, cohesive energy, heat capacity, molar refraction and molar dielectric polarization, are directly related to some very basic physical factors. Specifically, materials are constructed from assemblies of atoms with certain sizes and electronic structures. These atoms are subject to the laws of quantum mechanics. They interact with each other via electrical forces arising from their electronic structures. The sizes, electronic stmctures and interactions of atoms determine their spatial arrangement. Finally, the interatomic interactions and the resulting spatial arrangements determine the quantity and the modes of absorption of thermal energy. 

The dielectric properties of a material are determined by the polarizability of its molecules. There are three primary contributions to the electric polarization of a dielectrics electronic, ionic and dipole reorientation - related (Uchino, 2000). The intensity with which each mechanism occurs depends on the frequency of applied electric field. The electronic polarization causes a displacement of the electrons with respect to the atomic nuclei and can follow alternating field with the frequencies up to - lOi Hz. The ionic polarization relies on a displacement of the atomic nuclei relative to one another and responds up to lO - lO Hz. Both mentioned polarization mechanisms are related to the non-polar molecules. The third mechanism associated with the dipole reorientation is valid only in the case of polar molecules. It can follow with the frequency of alternating electric field up to 10 - lO Hz. The dielectric permittivity of a material represents the ratio of the capacitance of a plane condenser filled with the dielectric to that of the same condenser under vacuum and is to calculate from the expression ... 

Insulator and capacitor applications depend on the dielectric properties of ceramics, that is, on their polarization response to an applied electric field. The four polarization mechanisms which describe the displacement of charged species in ceramics are (1) electronic polarization—the shift of the valence electron cloud with respect to the nucleus (2) ionic or atomic polarization— movement of cation and anion species (3) dipolar polarization—perturbation of the thermal motion of ionic or molecular dipoles and (4) interfacial polarization—inhibition of charge migration by a physical barrier. Further discussion of polarization phenomena may be found in Reference 1. 

Generally, the literature shows that for pol)timides the dielectric constant decreases gradually with increasing frequency. This variation is attributed to the frequency dependence of the polarization mechanisms which include the dielectric constant. The magnitude of the dielectric constant is dependent on the ability of the polarizable emits in a polymer to orient fast enough to keep up with the oscillations of an alternating electric field. At optical frequencies (approx. 10 Hz), only the lowest mass species, the electrons, are efficiently polarized. At lower frequencies, the atomic polarization of nuclei, which move more slowly, also, contribute to the dielectric constant. Atomic polarization of induced... 

Insulator Dielectrics. Insulator thick film dielectrics are multiphase materials. The electronic, ionic, and interfacial polarization mechanisms all contribute to the dielectric constant of glass-ceramic materials. Electronic polarization is directly proportional to the density of electrons in the glass-ceramic. Thus, dielectrics based on glasses containing oxides of high atomic number elements (e.g., lead) or high density exhibit high dielectric constants. 

Possible polarization types include electronic (Figure 18.32a), ionic (Figure 18.32h), and orientation (Figure 18.32c) not all types need be present in a particular dielectric. For alternating electric fields, whether a specific polarization type contributes to the total polarization and dielectric constant depends on frequency each polarization mechanism ceases to function when the applied field frequency exceeds its relaxation frequency (Figure 18.34). 

Figures 12a and 12b show the dielectric constant (c ) as a function of frequency of LNMO and LCMO ceramics at different temperatures. It can be observed that the dielectric constant of both ceramics decreases as frequency increases. The decrease in the dielectric constant with increase in frequency can be explained by the behavior on the basis of electron happing from Fe to Fe ions or on basis of decrease in polarization with the increase in frequency. Polarization of a dielectric material is the quantity of the contributions of ionic, electronic, dipolar, and interfacial polarizations [63]. At low frequencies, polarization mechanism is keenly observed at low frequencies to the time var)ing electric fields. As the frequency of the electric field increases, different polarization contributions are filter out under leads to the decrement in net polarization under dielectric constant. Similar behavior has also been reported by different investigators earlier in the literature [60, 64]. The physical, magnetic, and dielectric properties of LMNO and LCMO are summarized in Table 1.

In general, the dielectric constant is a complex quantity, k = k — Ik". The dielectric constant k is controlled by the conductivity at very low frequencies, and by various polarization mechanisms at higher frequencies. Electronic polarization and molecular dipole moments can be estimated from the refractive indices and dielectric constants. The dissipation factor D = k" k of a dielectric is sensitive to charge carriers and reorientable dipoles. Accurate loss measurements are capable of detecting free-carrier concentrations of 10 /cm. Various contributions to the loss can be separated by determining the dependence on temperature and frequency. 

Another disadvantage of the Marcus theory is associated not with the Born approximation for an isotropic dielectric but with the nature of the dynamic description of the medium adopted in this theory. Dielectric polarization is divided only into two parts, viz. electronic polarization and the remaining polarization, the entire slower part being described in the same way. A more detailed analysis shows, however, that such an approach is not rigorous and that a part of polarization of the medium behaves quantum-mechanically. 

Relates to the deformation type of polarization and appears as a result of the displacement of an atomic electron shell relative to the nucleus which, accordingly, leads to an induced dipole moment. Certainly, such a polarization mechanism takes place in all systans containing atoms, i.e., in all dielectrics however, in a pure state it can be seen in the case of nonpolar homo-atomic molecules and atoms. 

The frequency dependence explains why the dielectric permeability of water measured in a static electric field is 81, but at optic frequencies is only 1.77 in the first case all polarization mechanisms are participating in the polarization but in the latter case only electron polarization takes place. 

The dielectric constant is a measure of the ease with which charged species in a material can be displaced to form dipoles. There are four primary mechanisms of polarization in glasses (13) electronic, atomic, orientational, and interfacial polarization. Electronic polarization arises from the displacement of electron clouds and is important at optical (ultraviolet) frequencies. At optical frequencies, the dielectric constant of a glass is related to the refractive index k =. Atomic polarization occurs at infrared frequencies and involves the displacement of positive and negative ions. 

The treatment of electrostatics and dielectric effects in molecular mechanics calculations necessary for redox property calculations can be divided into two issues electronic polarization contributions to the dielectric response and reorientational polarization contributions to the dielectric response. Without reorientation, the electronic polarization contribution to e is 2 for the types of atoms found in biological systems. The reorientational contribution is due to the reorientation of polar groups by charges. In the protein, the reorientation is restricted by the bonding between the polar groups, whereas in water the reorientation is enhanced owing to cooperative effects of the freely rotating solvent molecules. 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

There is greatly renewed interest in electron solvation, due to improved laser technology. However it is apparent that a simple theoretical description such as implied by Eq. (9.15) would be inadequate. That equation assumes a continuum dielectric with a unique relaxation mechanism, such as molecular dipole rotation. There is evidence that structural effects are important, and there could be different mechanisms of relaxation operating simultaneously (Bagchi, 1989). Despite a great deal of theoretical work, there is as yet no good understanding of the evolution of free-ion yield in polar media. 

Electron transfer processes induce variations in the occupancy and/or the nature of orbitals which are essentially localized at the redox centers. However, these centers are embedded in a complex dielectric medium whose geometry and polarization depend on the redox state of the system. In addition, a finite delocalization of the centers orbitals through the medium is essential to-promote long-range electron transfers. The electron transfer process must therefore be viewed as a transition between two states of the whole system. The expression of the probability per unit time of this transition may be calculated by the general formahsm of Quantum Mechanics. 

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