Polarization in Dielectrics

As stated previously, the electrical and optical properties are primarily determined by the dielectric material s abihty to form electric dipoles in the presence of an electric field. An electric dipole can be thought of as a positive and a negative charge q separated by some distance d and the dipole moment is defined as p = qd. 

Macroscopically, the resulting electrical displacement, D = E = oE + P/ where s is the permittivity, P is the polarization, which is defined as the dipole moment per unit volume, and So is the permittivity of a vacuum = 8.85 x 10 farads/m (Coulomb/V-m). For an anisotropic crystal, is a tensor of rank two, but here we consider only isotropic materiab, so s will be a scalar. 

It is convenient to define a relative dielectric constant r = / o- Then StE = E + P/so, P = sq (sr —1) E = sqxE, where the electric susceptibility x = Sr — l. The susceptibility relates the amount of polarization to the applied field, or as the name suggests, tells how susceptible a material is to being polarized by an electric field. 

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The theory of electronic polarization in dielectric media [25] provides the framework for the derivation of a free energy functional that meets the requirements set forth in the Introduction. In particular, the additional free energy of the system due to a polarization P(r) can be expressed as [26] ... 

Chipman, D. M. (2006). New formulation and implementation for volume polarization in dielectric continuum theory, /. Chem. Phys. 124, pp. 224111 1-10. 

Piezoelectric The generation of electricity or of electric polarity in dielectric crystals subjected to mechanical stress and, conversely, voltage. 

An alternative approach that avoids many of the problems associated with electric polarization in dielectrics is TD-DFT. In the time-dependent case, the time change of the polarization induces a current, which may be considered an ultra-nonlocal functional of the charge density, and has been successfully used as an alternative additional variable for the description of dielectric properties of both solids and molecular systems. 

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

Electron transfer reaction rates can depend strongly on tire polarity or dielectric properties of tire solvent. This is because (a) a polar solvent serves to stabilize botli tire initial and final states, tluis altering tire driving force of tire ET reaction, and (b) in a reaction coordinate system where the distance between reactants and products (DA and... 

Finally, the dielectric properties of a nonpolar polymer are modified by inclusion of even small amounts of a polar comonomer. In coatings applications the presence of polar repeat units in an otherwise nonpolar polymer reduces the tendency for static buildup during manufacture, printing, and ultimate use. On the other hand, in dielectric applications this increases the power loss and must be kept to a minimum, even to the exclusion of polar initiator fragments. 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

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. 

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

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. 

With polar molecules the value of the dielectric constant is additionally dependent on dipole polarisation and commonly has values between 3.0 and 7.0. The extent of dipole polarisation will depend on frequency, an increase in frequency eventually leading to a reduction in dielectric constant. Power factor-frequency curves will go through a maximum. 

The insulating properties of polyethylene compare favourably with those of any other dielectric material. As it is a non-polar material, properties such as power factor and dielectric constant are almost independent of temperature and frequency. Dielectric constant is linearly dependent on density and a reduction of density on heating leads to a small reduction in dielectric constant. Some typical data are given in Table 10.6. 

The central role of the concept of polarity in chemistry arises from the electrical nature of matter. In the context of solution chemistry, solvent polarity is the ability of a solvent to stabilize (by solvation) charges or dipoles. " We have already seen that the physical quantities e (dielectric constant) and p (dipole moment) are quantitative measures of properties that must be related to the qualitative concept of... 

Ferroelectric materials are capable of being polarized in the presence of an electric field. They may exhibit considerable anomalies in one or more of their physical properties, including piezoelectric and pyroelectric coefficients, dielectric constant, and optoelectronic constant. In the latter case, the transmission of light through the material is affected by the electric field, which produces changes in refractive index and optical absorption coefficient. Varying the applied field changes the phase modulation. 

In dielectric materials (oxides, semiconductors, halides, polymers, and he like), polarizability correlates with hardness. For metals, this is not the case. However, the frequencies of the collective polarizations known as plasmons are related to mechanical hardness. 

In dielectric materials there can be both permanent and induced polarization domains. The walls between these domains may also act as barriers to dislocation motion. They tend to have larger energies than magnetic domain walls so they may have more effect on hardness (McColm, 1990). 

The objective of this first part of the book is to explain in a chemically intelligible fashion the physical origin of microwave-matter interactions. After consideration of the history of microwaves, and their position in the electromagnetic spectrum, we will examine the notions of polarization and dielectric loss. The orienting effects of the electric field, and the physical origin of dielectric loss will be analyzed, as will transfers between rotational states and vibrational states within condensed phases. A brief overview of thermodynamic and athermal effects will also be given. 

The properties of HF reflect the strong hydrogen bonding that persists even in the vapor state. As a result of its high polarity and dielectric constant, liquid HF dissolves many ionic compounds. Some of the chemistry of HF as a nonaqueous solvent has been presented in Chapter 10. Properties of the hydrogen halides are summarized in Table 15.9. 

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