Polarization of a dielectric

We can further describe the polarization, P, according to the different types of dipoles that either already exist or are induced in the dielectric material. The polarization of a dielectric material may be caused by four major types of polarization electronic polarization, ionic (atomic) polarization, orientation polarization, and space-charge (interfacial) polarization. Each type of polarization is shown schematically in Figure 6.24 and will be described in succession. In these descriptions, it will be useful to introduce a new term called the polarizability, a, which is simply a measure of the ability of a material to undergo the specific type of polarization. 

All these contributions are very low and they may, in most cases, be neglected. The polarization of a dielectric adsorbent by an adsorbed dipole may, similarly, be neglected. 

Problem 1.5. Show that for t the contribution to the polarization of a dielectric solvent that arises from the orientation of permanent dipoles is given by... 

The spontaneous polarization of a dielectric depends strongly on T, this is the pyroelectric effect that we use for infrared (IR) detection (e.g., intruder alarms and thermal imaging). 

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 ... 

The macrosoopic polarization of a dielectric, P, is the average dipole moment per unit volume or charge per unit area. The connection between the definitions can be gained from the sketoh ... 

On the contrary, when the time-dependent electric field varies on a time scale faster than the relaxation time of one or more molecular degrees of freedom there is not time to reach at any moment a time-dependent polarization which is in equilibrium with the electric field. In this regime, which is called non-equilibrium polarization, the actual value of polarization will also depend values of the electric field at previous time, and the relation between the polarization of a dielectric medium and the time-dependent polarizing field is phenomenologically described in terms of the whole specuiim of the dielectric permittivity as a function of the frequency co of the oscillating electric field. 

Just as the permittivity and polarization of a dielectric is dependent on the applied field, so is the refractive index that is... 

Briefly explain how the charge storing capacity of a capacitor may be increased by the insertion and polarization of a dielectric material between its plates. 

Figure 18.31 Schematic representations of (a) the charge stored on capacitor plates for a vacuum, (b) the dipole arrangement in an unpolarized dielectric, and (c) the increased charge-storing capacity resulting from the polarization of a dielectric material.

Polarization of a dielectric medium-dependence on dielectric constant and electric field intensity... 

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.

The proper quantum mechanical treatment of the electric polarization of a dielectric material and of the orbital magnetization of a magnetic material is rather subtle. To illustrate the main complication arising in the context of DFT, let us consider a homogeneous electric field E = -V >, entering the Hamiltonian via the corresponding electric potential... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

Table 8-2 lists several physical properties pertinent to our concern with the effects of solvents on rates for 40 common solvents. The dielectric constant e is a measure of the ability of the solvent to separate charges it is defined as the ratio of the electric permittivity of the solvent to the permittivity of the vacuum. (Because physicists use the symbol e for permittivity, some authors use D for dielectric constant.) Evidently e is dimensionless. The dielectric constant is the property most often associated with the polarity of a solvent in Table 8-2 the solvents are listed in order of increasing dielectric constant, and it is evident that, with a few exceptions, this ranking accords fairly well with chemical intuition. The dielectric constant is a bulk property. 

A more thorough analysis shows that one should not expect the electric dipole moment to remain constant, because real molecules have polarizability. The polarization of the dielectric in the electric field of the molecule itself gives rise to a reaction field, which tends to enhance the electrical asymmetry. 

Solution 9.1. The energetics of this reaction in water is known from experimental information (Chapter 7). In order to estimate the corresponding energetics in a non polar site we start by expressing the electrostatic energy of a given state in a solvent of a dielectric constant d by (see Ref. 8a of Chapter 4). 

Here e is the dielectric constant of the gas, F the strength of the applied field, N the number of molecules in unit volumes, n the permanent electric moment of a molecule, and a the coefficient of induced polarization of a molecule cos 9 is the average value of cos 9 for all molecules in the gas, and cos 9 is the time-average of cos 9 for one molecule in a given state of motion, 6 being the angle between the dipole axis and the lines of force of the applied field. 

Arranging the solvents in separation-strength order, the so-called eluotropic series appeared. This term, introduced by Trappe, was related to the experience with bare silica, where a strong solvent is able to move polar solutes on a polar stationary phase. Later this was improved by the discovery of a direct proportion between the elution strength and the dielectric constant. Because silica is hydrophilic and highly polar, there was a correlation between the eluotropic series and the polarity of a solvent [16,18]. 

The electric polarization of the solvent has three components electronic, atomic (i.e., translational and vibrational), and orientational. The polarization of a nonpolar solvent is almost entirely electronic this leads to e 2. Polar solvents can have much larger dielectric constants, e.g. is 13.9 for 1-pentanol, 37.7 for methanol, and 78.3 for water.50... 

As mentioned above, the PCM is based on representing the electric polarization of the dielectric medium surrounding the solute by a polarization charge density at the solute/solvent boundary. This solvent polarization charge polarizes the solute, and the solute and solvent polarizations are obtained self-consistently by numerical solution of the Poisson equation with boundary conditions on the solute-solvent interface. The free energy of solvation is obtained from the interaction between the polarized solute charge distribution and the self-... 

After these preliminary remarks, the term polarity appears to be used loosely to express the complex interplay of all types of solute-solvent interactions, i.e. nonspecific dielectric solute-solvent interactions and possible specific interactions such as hydrogen bonding. Therefore, polarity cannot be characterized by a single parameter, although the polarity of a solvent (or a microenvironment) is often associated with the static dielectric constant e (macroscopic quantity) or the dipole moment p of the solvent molecules (microscopic quantity). Such an oversimplification is unsatisfactory. 

Dielectric constant (or relative permittivity), er, is an indication of the polarity of a solvent, and is measured by applying an electric field across the solvent between... 

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