Polarization of Dielectrics

Exposing a dielectric material to an electric field (E, D) always leads to polarization, i. e. a separation of electric charges forming a macroscopic dipole moment (Pe) characteristic to the system and the applied electric field (E, D) applied, cp. Fig. 6.8  

Here (Nt) is the number of particles , i. e. molecules, atoms, or ions included in the system and Pe the averaged (molecular) dipole moment per particle. For weak electric fields (E IV/cm) pe is proportional to the electric field strength (E) giving 

Here s is a numerical shape factor being s = 1/3 for simple cubic crystals and freely rotating molecules [6.22, 6.24], For non-polar admolecules (p = 0) numerical values of a = aj i can be determined by combined dielectric and, for example, gravimetric measurements (cp. examples given in Sect. 3.2). For polar admolecules the same is true at least at low frequencies (v 1 MHz) of the electric field where often um tton and hence can be neglected compared to Oori- For both types of admolecules numerical data of (a) are between their values for the gas and the liquid phase of the adsorptive and normally depend on the amount adsorbed, i. e. degree of saturation. Hence they can give an indication of the nature of the site where the admolecule is adsorbed and also on the structure of the sorbate phase [6.3]. 

According to Clausius and Mossotti [6.1-6.3, 6.22, 6.24] the polarization (P) can be represented for static electric fields (E = const) as 

Here 8rs is the static relative dielectric permittivity of the system. For gases, where 8rs 1, Eq. (6.35) reduces to 

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Figure 11.2 Partial neutralization of charge by polarization of dielectric for a charge at the interface of two different dielectrics.

The total polarization of dielectric material results from all the contributions discussed above. The contributions from the lattice are called intrinsic contributions, in contrast to extrinsic contributions. 

The application of an alternating electric field causes polarization of dielectrics in the low-freqnency regions of the field. As the frequency increases, the polarization does not follow the changes in the electric field. The dielectric constant of the dielectric materials decreases with the frequency increase by the space charge, dipole, ionic, and/or electronic polarization mechaifisms. The dielectric loss is the maximnm at the dispersed frequencies (f, as shown in Figure 22.2. 

As we mentioned above, the electrokinetic mechanisms, which includes electrophoresis, DEP, ACEO, electrothermal effect, and electro-orientation, are main driving force for particle manipulation using an optoelectrofluidic device. In addition, we could also observe the electrostatic interactions due to the polarization of dielectric particles like cells. 

There are two mechanisms by which microwaves interact with reaction mixtures [7]. Polarization of dielectric material arises when the distribution of an electron cloud is distorted or physical rotation of molecular dipoles occurs. For generation of heat on irradiation with microwaves, at least one component of a reaction mixture must have a dipole moment. Compounds with high dipole moments also have large dielectric constants, e. The selectivity of microwave irradiation is clear when comparing the heating of water and hexane. Water, a polar solvent, has a high dielectric constant and therefore heats rapidly on microwave irradiation whereas hexane, a nonpolar solvent, heats very slowly. 

FIGURE 19 Polarization of dielectric materials in an electric field is indicated by the ellip-soids. The material with the greater dielectric coastant (upper half) exhibits greater polarization, indicated by the larger dipoles, (b) The net charge due to polarization. 

The concept and theoretical considerations of the sample behavior, which responds to the temperature oscillation is, thus, quite similar to the sample behavior responding to other oscillation, such as polarization of dielectrics to alternating electric field and deformation of viscoelastic substances to dynamic mechanical stress, and these would also be applicable to other thermoanalytical... 

Dielectric displacement— dependence on electric field intensity and polarization (of dielectric medium)... 

Bdttcher C J F 1973 Theory of Dielectric Polarization (Amsterdam Elsevier)... 

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... 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

The Born model is based on electrostatic interactions, dielectric permitivity, and orbital overlaps. It has the advantage of being fairly straightforward and adaptable to computational methods. The free energy for the polarization of the solute is expressed as... 

Polarization which can be induced in nonconducting materials by means of an externally appHed electric field is one of the most important parameters in the theory of insulators, which are called dielectrics when their polarizabiUty is under consideration (1). Experimental investigations have shown that these materials can be divided into linear and nonlinear dielectrics in accordance with their behavior in a realizable range of the electric field. The electric polarization PI of linear dielectrics depends linearly on the electric field E, whereas that of nonlinear dielectrics is a nonlinear function of the electric field (2). The polarization values which can be measured in linear (normal) dielectrics upon appHcation of experimentally attainable electric fields are usually small. However, a certain group of nonlinear dielectrics exhibit polarization values which are several orders of magnitude larger than those observed in normal dielectrics (3). Consequentiy, a number of useful physical properties related to the polarization of the materials, such as elastic, thermal, optical, electromechanical, etc, are observed in these groups of nonlinear dielectrics (4). 

The dielectric permittivity as a function of frequency may show resonance behavior in the case of gas molecules as studied in microwave spectroscopy (25) or more likely relaxation phenomena in soUds associated with the dissipative processes of polarization of molecules, be they nonpolar, dipolar, etc. There are exceptional circumstances of ferromagnetic resonance, electron magnetic resonance, or nmr. In most microwave treatments, the power dissipation or absorption process is described phenomenologically by equation 5, whatever the detailed molecular processes. 

Polyimides containing C—F bonds have been receiving strong attention (96—98). Fluorine-containing polyimides possess lower dielectric constant and dielectric loss because of reduced water absorption and lower electronic polarization of C—F bonds vs the corresponding C—H bonds. Fluorine-containing polyimides are often more soluble and readily processible without sacrificing thermal stabilities. The materials are appHed primarily iu... 

Solvent for Displacement Reactions. As the most polar of the common aprotic solvents, DMSO is a favored solvent for displacement reactions because of its high dielectric constant and because anions are less solvated in it (87). Rates for these reactions are sometimes a thousand times faster in DMSO than in alcohols. Suitable nucleophiles include acetyUde ion, alkoxide ion, hydroxide ion, azide ion, carbanions, carboxylate ions, cyanide ion, hahde ions, mercaptide ions, phenoxide ions, nitrite ions, and thiocyanate ions (31). Rates of displacement by amides or amines are also greater in DMSO than in alcohol or aqueous solutions. Dimethyl sulfoxide is used as the reaction solvent in the manufacture of high performance, polyaryl ether polymers by reaction of bis(4,4 -chlorophenyl) sulfone with the disodium salts of dihydroxyphenols, eg, bisphenol A or 4,4 -sulfonylbisphenol (88). These and related reactions are made more economical by efficient recycling of DMSO (89). Nucleophilic displacement of activated aromatic nitro groups with aryloxy anion in DMSO is a versatile and useful reaction for the synthesis of aromatic ethers and polyethers (90). 

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. 

For films on non-metallic substrates (semiconductors, dielectrics) the situation is much more complex. In contrast with metallic surfaces both parallel and perpendicular vibrational components of the adsorbate can be detected. The sign and intensity of RAIRS-bands depend heavily on the angle of incidence, on the polarization of the radiation, and on the orientation of vibrational transition moments [4.267]. 

Many other measures of solvent polarity have been developed. One of the most useful is based on shifts in the absorption spectrum of a reference dye. The positions of absorption bands are, in general, sensitive to solvent polarity because the electronic distribution, and therefore the polarity, of the excited state is different from that of the ground state. The shift in the absorption maximum reflects the effect of solvent on the energy gap between the ground-state and excited-state molecules. An empirical solvent polarity measure called y(30) is based on this concept. Some values of this measure for common solvents are given in Table 4.12 along with the dielectric constants for the solvents. It can be seen that there is a rather different order of polarity given by these two quantities. 

Although the effects of dielectric constant change and strain have a strong effect on the current during wave transit time, the current at a time about j transit time is close to the value for the linear relation. Thus, based on Eq. 5.7, the wavespeed can be computed from the measured current and the measured polarization data. The approximate agreement between currents calculated from the polarization data and the wavespeed data confirms that the wavespeed values currently available are reasonable. 

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]).

Fig. 5.21. The shock-induced polarization of polymers as studied under impact loading is shown. For the current pulse shown, time increases from left to right. The increase of current in time is due to finite strain and dielectric constant change. (See Graham [79G01]).

Rate increases with increasing polarity of solvent as measured by its dielectric constant e. (Section 8.12) Polar aprotic solvents give fastest rates of substitution solvation of Nu is minimal and nucleophilicity is greatest. (Section 8.12)... 

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. 

These can be determined experimentally to very high accuracy from the Stark effect and molecular beam studies. The experimental accuracy is far beyond the capabilities of ab initio studies. At the other extreme, the original route to these quantities was through studies of the dielectric polarization of species in solution, and there is currently interest in collision-induced dipole moments. In either case, the quantities deduced depend critically on the model used to interpret the experiment. 

The most common measure of polarity used by chemists in general is that of dielectric constant. It has been measured for most molecular liquids and is widely available in reference texts. However, direct measurement, which requires a nonconducting medium, is not available for ionic liquids. Other methods to determine the polarities of ionic liquids have been used and are the subject of this chapter. However, these are early days and little has been reported on ionic liquids themselves. I have therefore included the literature on higher melting point organic salts, which has proven to be very informative. 

An alternative method of studying the molecular motions of a polymeric chain is to measure the complex permitivity of the sample, mounted as dielectric of a capacitor and subjected to a sinusoidal voltage, which produces polarization of the sample macromolecules. The storage and loss factor of the complex permitivity are related to the dipolar orientations and the corresponding motional processes. The application of the dielectric thermal analysis (DETA) is obviously limited to macromolecules possessing heteroatomic dipoles but, on the other hand, it allows a range of frequency measurement much wider than DMTA and its theoretical foundations are better established. 

Metwally et al. [28] also studied the resin-catalyzed hydrolysis of ethyl formate in acetone-water mixtures at different temperatures. The experimental results indicated a linear dependence of the logarithm of rate constant on the reciprocal of the dielectric constant (Fig. 2). The decrease of dielectric constant may lower the concentration of the highly polar transition state and thereby decrease the rate [28]. 

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