Dielectric constant,

Dielectric constants of substances vary widely and can be measured with considerable accuracy. Despite the potentialities of this technique for kinetic studies, it has been little used. (As an example, see Melville et who followed vinyl 

Letort, Thesis, University of Paris, 1937 J. Chim. Phys., 34 (1937) 206 Bull. Soc. Chim. France, 9 (1942) 1. 

4 For a discussion see K. J. Laidler, Chemical Kinetics, 2nd edn., McGraw-Hill, New York, 1965, p. 17. 

Benson, The Foundation of Chemical Kinetics, McGraw-Hill, New York, 1960. 

Semenov, Some Problems in Chemical Kinetics and Reactivity, Vol. 2, (transl. by M. Boudart), Princeton Univ. Press, Princeton, N. J., 1958, p. 10. 

Dielectric constant is more useful than electrical conductivity in characterizing coal and is a measure of the electrostatic polarizability of the dielectric coal (Chatterjee and Misra, 1989). The dielectric constant of coal is believed to be related to the polarizability of the Ji-electrons in the clusters of aromatic rings within the chemical structure of coal (Chapter 10). 

Like conductivity, dielectric constant is strongly dependent on water content. Indeed, the dielectric constant can even be used as a measure of moisture in coal. Meaningful dielectric constant measurements of coal require drying to a constant dielectric constant and several forms of coal are used for dielectric constant measurements. These include precisely shaped blocks of coal, mulls of coal in solvents of low dielectric constant, or blocks of powdered coal in a paraffin matrix. 

The dielectric constant varies with coal rank (Chatteijee and Misra, 1989). The theorem that the dielectric constant is equal to the square of the refractive index (which is valid for nonconducting, nonpolar substances) holds only for coal at the minimum dielectric constant. The decreasing value of dielectric constant with rank may be due to the loss of polar functional groups (such as hydroxyl or carboxylic acid functions) but the role of the presence of polarizable electrons (associated with condensed aromatic systems) is not fully known. It also appears that the presence of intrinsic water in coal has a strong influence on the dielectric properties (Chatterjee and Misra, 1989). 

Knowledge of coal properties is an important aspect of coal characterization and has been used as a means of determining the suitability of coal for commercial use for decades, perhaps even centuries. In fact, the molecular characterization of coal (Chapter 10) is seen to be of little, or no, by some consumers. 

The analysis of coal ash (Chapter 8) for environmentally hazardous trace elements is but one example of how the data might be used. The mineral portion of coal has been ignored for too many years. It must be considered an integral part of the coal structure and so the ash (and its contents) must also be given consideration when a use is designed for coal. 

The dielectric constant of a material is defined as the ratio of the capacitance of a particular capacitor containing the material to that of the same capacitor when the material is removed and replaced by air. 

The dielectric varies with frequency and generally increases with temperature. The values quoted in Table 5.5 are typical room temperature values measured at a frequency of 1 kHz. 

When designing a capacitor, it is desirable to include a material with a high dielectric constant because more power can be stored in a given volume. Conversely, materials with low dielectric constants are preferred for applications involving high frequencies to minimize electric losses. 

Apparatus Available from ATS FAAR for Determining the Electrical Properties of Polymers 

Method ATS FAAR Measurement Units Test Suitable for Meeting the Following Standards 

The dielectric constant r,i is defined to be the ratio of the applied field Sq to the field inside the material, f and from Eq. (4-21), the dielectric constant is given by 

A field o applied to a dielectric gives rise to a smaller field within the material. The difference is calculated by noting that the polarization inside, P = causes a surface charge density P and a resulting opposing field 0 - = 4tiP. 

It is also a familiar result of electromagnetic theory that the refractive index, n (the ratio of the speed of light in vacuum to the speed of light in the material), is given by 

Here also we have performed the sum over bonding orbitals to write the result in terms of the electron density N. 

It would have been tempting at some stage in this argument to use the sum rule, Eq. (4-14), to eliminate the matrix elements. This cannot be done without making corrections (Phillips, 1970), because the sum is over all states k not just the empty ones. In addition, the fact that the energy diflerence enters the sum rule 

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. 

For fluids, this is computed by a statistical sampling technique, such as Monte Carlo or molecular dynamics calculations. There are a number of concerns that must be addressed in setting up these calculations, such as 

Whether an adequate sampling of phase space is obtained Whether the system size is large enough to represent the bulk material Whether the errors in calculation have been estimated correctly 

Another way to obtain a relative permitivity is using some simple equations that relate relative permitivity to the molecular dipole moment. These are derived from statistical mechanics. Two of the more well-known equations are the Clausius-Mossotti equation and the Kirkwood equation. These and others are discussed in the review articles referenced at the end of this chapter. The com- 

Experimental methods are applicable for a wide range of frequencies. High-frequency measurements employ commercially available dielectric constant meters, Q-meters, and so on the impedance bridge method is widely employed at low frequencies. The levels of the frequencies applied experimentally are very important for data interpretation and comparison. 

The dielectric constant of coal is strongly dependent on coal rank (van Krevelen, 1961 Speight, 1994, and reverences cited therein). For dry coals the minimum dielectric constant value is 3.5 and is observed at about 88% w/w carbon content in the bituminous coal range. The dielectric constant increases sharply and approaches 5.0 for both anthracite (92% carbon) and lignite (70% carbon). The Maxwell relation which equates the dielectric constant to the square of the refractive index for a polar insulators generally shows a large disparity even for strongly dried coal. 

The dielectric constant rarely correlates with reaction rate, but is a useful parameter to keep in mind as it influences other properties, such as ion pairing, which can be important in determining chemical reactivity. Some values are shown in Table 12.2. 

The dielectric constant e of a material is essentially a measure of how effectively it concentrates the electrostatic lines of flux when placed in an electric 

Dong et al. (2004) found a qualitative correlation between e of the solvent and the quality of electrospun nanofibers for PMMA (at a concentration of lOOmg/mL) (Table 4.2), illustrating the effectiveness of high-e solvents (Dong et al. 2004). Similar qualitative observations have been made for other polymers such as PCL (Lee, K. H., et al. 2003b), PMMA 

TABLE 4.2 The effect of the dielectric constant e of the solvent on electrospinning of PMMA at a concentration of lOOmg/mL  

To a good approximation, the relation of the dielectric constant of a liquid, to its density, p, is given by the Clausius-Mossotti equation (Stratton, 1941)  

The Clausius-Mossotti equation is based on the assumption that the polarization induced by the external electric field is proportional to the field strength, or that 

Data from Bokov, O.G. and Naberukhin, Y.I., /. Chem, Phys., 75,2357, 

Pergamon Press, Elmsford, NY, 1973 Gee, N., Shinsaka, K., Dodelet, J.P., and Freeman, G.R., /. Chem. Thermodyn., 18,221,1986 Landolt-Bomstein, in Zahlenwerte und Funktwnen aus Naturwissenshaften und Technik, Vol. 6, Made-lung, O., Ed., Springer-Verlag, Berlin, 1991 Rechowicz, M., Electric Power at Low Temperatures, Clarendon Press, Oxford, 1975. 

The nonlinear dielectric effect (NLDE) is then characterized by the quantity 

Since LTCCs are basically composite structures of glass and crystals, controlling their dielectric constant depends largely on the combination of constituent materials of the composite and its material composition (volume fraction of the constituent materials). In addition, the dielectric constant of 

The dielectric constant of the materials themselves depends on the contribution of electrons or ions with regard to polarizability and their dipole orientation, and the following relationship obtains between polarizability No and relative permittivity s per unit volume. 

N number of molecules per unit volume, a polarizability, e relative permittivity. 

The total polarizability of the dielectric is expressed as the sum of each polarizability feature. 

In the composite, the dielectric constant is determined by the dielectric constant and volume fraction of the constituent material, and the complex form of the constituent material [31]. Table 2-5 shows the 4 different models of mixing rules for complex forms of the constituent materials. LTCC ceramics, being of the type with ceramic particles distributed in a glass matrix, fit the Maxwell model well. In order to achieve a lower dielectric 

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

Use a constant dielectric of 1.0 with TIP3P water molecules in a periodic box. Because of the parameterization of TIP3P molecules, using a distance-dependent dielectric or a value other than 1.0 gives unnatural results. 

A distance-dependent dielectric constant is commonly used to mimic the effect of solvent in molecular mechanics calculations, in the absence of explicit water molecules. 

The increasing use of physical data in laboratory work has also led to developments in the technique of determining the dielectric constant. This constant is an especially useful quantity when the mixture contains water (diel. const. 80) or other components having widely different values. Examples are the mixtures acetic acid (diel. const 6.13)-acetic anhydride (22.2) and methanol-toluene. In the latter system the azeotroj)e has a dielectric constant of 26.8, whilst methanol and toluene have values of 33.8 and 2.37, respectively [65]. The dielectric constant has also proved convenient for determining toluene in benzene, in spite of the fact that the difference in the figures for these two com x nents is only 0.08 units. 

In Slevogt s dielectrometer, the Multidekameter , the frequencj is not restricted to a single value, but can be varied between 100 kilocycles and 12 megacycle.s [66]. Grant [67] has described a recording dielectrometer that appears suitable for distilla- 

Arrangement for measuring the dielectric constant during distillation (Oehme) 

A dielectric is an insulating material, which polarizes under the application of an electric field. The extent to which a material can be polarized creating a separation between the boimd positive and negative charges is expressed by the dielectric constant or relative permittivity (x, e or k). The microscopic origin of 

For a specific material, the dielectric response can be strongly influenced by the specific crystal structure pertaining to the material. This is easily imderstood, because the phase determines the local environment of the atoms or ions. An example of this is given by the 8b phase of niobia (Nb20s), which has a layered structure without metal-oxygen bonds to connect the layers, leading to large interatomic distances. As a consequence, a lower polarizability normal to these layers is observed. Such an effect of anisotropy is seen neither in the 8a nor in the p phase of niobia [4j. 

Furthermore, the dielectric constant for solid solutions can be predicted as well, based on the assumption of a crystal structure identical to the individual components. In the example of NbTaOs, it was found that the average calculated permittivity (54) was identical to the arithmetic mean of the individual composing oxides, and a mean value for the dielectric constant was also found experimentally. It should be noted though that experimental values and calculated permittivities for crystals containing vacancies were found to be much lower than permittivities calculated for the perfect crystal. As crystal imperfections are often difficult to avoid in practice, this may be extrapolated to other material systems. 

1 Introduction. The use of electrical measurements has been fairly important in the study of H bond association. In the main, this is the result of three facts (1) the experimental quantities are readily obtained (2) dipole moments calculated from the measured quantities have directionally additive properties and therefore can often allow a choice between various possible structures (3) dielectric dispersion studies permit separation of the several kinds of rearrangements that occur. The experimental determinations have increased in complexity as more extensive ranges of frequency are scanned in studying dielectric dispersion, as biological and polymeric substances become of interest, and as improved theories demand more accurate data. The advantage of the directional aspects of the dipole vector is somewhat nullified by extraneous effects of the solvent and of parts of the molecule not involved in H bonding. 

The classical treatment of nonpolar dielectric materials is expressed by the Clausius-Mossotti equation. Polar materials in nonpolar solvents are better handled by Debye s modification, which allows for the permanent dipole of the molecule. Onsager made the next major step by taking into account the effect of the dipole on the surrounding medium, and finally Kirkwood treated the orientation of neighboring molecules in a more nearly exact manner. (See Table 2-1.) The use of these four theoretical expressions can be quickly narrowed. Because of their limitations to nonpolar liquids or solvents, the Clausius-Mossotti and Debye equations have little application to H bonded systems. Kirkwood s equation has great potential interest, but in the present state of the theory of liquids the factor g is virtually an empirical constant. The equation has been applied in only a few cases. 

The Onsager equation is the one most used for H bonded systems. For solutions, the experimentally determined dielectric constant is commonly plotted in terms of polarization (see Table 2-1) against concentration. Extrapolation to infinite dilution gives and hence the dipole moment. The last steps require knowledge of the electronic (Pe) and atomic (P ) polarizations. The value of Pe is usually found from refractive index values, and Pa (fortunately small) is estimated or 

NAME OF EQUATION DATE PUBLISHED EQUATION USEFUL FOR 

Clausius- Mossotti 1850-1880 3M if - 1) 4rNd (e + 2) Nonpolar gases and liquids 

According to Equation (4-1) the activity coefficient is made up of two terms, one of which is the transfer activity coefficient y,. This term may be regarded as resulting from the specific interactions of solute and solvent and the nonspecific (electrostatic) effects from differences in dielectric constant. In this section we consider the electrostatic effects, and in the next section specific interaction effects. 

Transfer activity coefficient The electrostatic, or nonspecific, contribution to the transfer activity coefficient can be obtained by estimating the free-energy change involved in transferring a sphere of radius r and charge Zfi from one solvent to another of different dielectric constant. According to the Bom equation, when 1 mole 

The chemical potential is the partial molal free energy, and by modifying Equation (2-3), we obtain 

In (4-6), i is 8.3145 x 10 ergs/deg-mole. The radius r is usually estimated to be equal to the crystal radii and should not be confused with the ion-size parameter used in Debye-Hiickel calculations. 

EXAMPLE 4-1 Calculate the expected electrostatic contribution to the transfer activity coefficient from differences in dielectric constant for ethanol and water (dielectric constants 24.3 and 78.3) at 25°C for a 1 1 electrolyte with an average ionic radius of 1.5 x 10 cm. 

Any compound with a nonsymmetrical distribution of charge or electron density will possess a permanent dipole moment, /v, whereas a molecule with a centre of symmetry will have no permanent dipole moment. Dipole moment is proportional to the magnitude of the separated charges, z, and also the distance between those charges, l. 

As well as these permanent dipole moments, random motion of electron density in a molecule leads to a tiny, instantaneous dipole, which can also induce an opposing dipole in neighbouring molecules. This leads to weak intermolecu-lar attractions which are known as dispersive forces or London forces, and are present in all molecules, ions and atoms - even those with no permanent dipole moment. Dispersive forces decrease rapidly with distance, and the attractions are in proportion to 1/r6, where r is the distance between attracting species. 

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 

Nonpolar/polarizable Dipolar aprotic Dipolar protic 

In fact, tris(pyrrolidino)phosphane oxide has a donor number of 1.22. 

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Prepared from ethyne and ammonia or by dehydration of ethanamide. Widely used for dissolving inorganic and organic compounds, especially when a non-aqueous polar solvent of high dielectric constant is required, e.g. for ionic reactions. 

Clausius-Mosottf Jaw The molecular polarization (P) of a substance of molecular weight M, density d and dielectric constant O is ... 

CH3)2N]3P0. M.p. 4°C, b.p. 232"C, dielectric constant 30 at 25 C. Can be prepared from dimethylamine and phosphorus oxychloride. Used as an aprotic solvent, similar to liquid ammonia in solvent power but easier to handle. Solvent for organolithium compounds, Grignard reagents and the metals lithium, sodium and potassium (the latter metals give blue solutions). 

Added to these interactions are the electrostatic forces related to the dielectric constants and which are important when it is necessary to separate ionic components. 

By variation of ceramic volume fraction and selection of the best fitting PZT material we can as well adjust the dielectric constant of the piezocomposite within a wide range. Therefore, we can choose the best piezocomposite material for each probe type to get optimum pulse form and amplitude. 

Referring to Eq. V-69, calculate the value of C for a 150-A film of ethanol of dielectric constant 26. Optional Repeat the calculation in the SI system. 

Increasingly, dielectric measurements are being used to characterize the water content of emulsions. One model for the dielectric constant of a suspension, ... 

Dielectric Behavior of Adsorbed Water. Determination of the dielectric absorption of adsorbed water can yield conclusions similar to those from proton NMR studies and there is a considerable, although older literature on the subject. Figure XVI-7 illustrates how the dielectric constant for adsorbed water varies with the frequency used as well as with the degree of surface coverage. A characteristic relaxation time r can be estimated... 

Similar, very detailed studies were made by Ebert [112] on water adsorbed on alumina with similar conclusions. Water adsorbed on zeolites showed a dielectric constant of only 14-21, indicating greatly reduced mobility of the water dipoles [113]. Similar results were found for ammonia adsorbed in Vycor glass [114]. Klier and Zettlemoyer [114a] have reviewed a number of aspects of the molecular structure and dynamics of water at the surface of an inorganic material. 

The size of the exciton is approximately 50 A in a material like silicon, whereas for an insulator the size would be much smaller for example, using our numbers above for silicon dioxide, one would obtain a radius of only 3 A or less. For excitons of this size, it becomes problematic to incorporate a static dielectric constant based on macroscopic crystalline values. 

The quantity 1 + x is known as the dielectric constant, it is constant only in the sense of being independent of E, but is generally dependent on the frequency of E. Since x is generally complex so is the wavevector k. It is customary to write... 

At large distances, 0 and w.j r) qfljzry ssxt z is the macroscopic dielectric constant of the solvent. 

This shows that the dielectric constant e of a polar solvent is related to the cavity fimction for two ions at large separations. One could extend this concept to define a local dielectric constant z(r) for the interaction between two ions at small separations. 

Strong electrolytes are dissociated into ions that are also paired to some extent when tlie charges are high or the dielectric constant of the medium is low. We discuss their properties assuming that the ionized gas or solution is electrically neutral, i.e. 

Flere u. j(r,T,P) is the short-range potential for ions, and e is the dielectric constant of the solvent. The solvent averaged potentials are thus actually free energies that are fimctions of temperature and pressure. The... 

Stell G, Patey G N and H0ye J S 1981 Dielectric constant of fluid models statistical mechanical theory and its quantitative implementation Adv. Chem. Phys. 48 183... 

The are essentially adjustable parameters and, clearly, unless some of the parameters in A2.4.70 are fixed by physical argument, then calculations using this model will show an improved fit for purely algebraic reasons. In principle, the radii can be fixed by using tables of ionic radii calculations of this type, in which just the A are adjustable, have been carried out by Friedman and co-workers using the HNC approach [12]. Further rermements were also discussed by Friedman [F3], who pointed out that an additional temi is required to account for the fact that each ion is actually m a cavity of low dielectric constant, e, compared to that of the bulk solvent, e. A real difficulty discussed by Friedman is that of making the potential continuous, since the discontinuous potentials above may lead to artefacts. Friedman [F3] addressed this issue and derived... 

Onsager s original reaction field method imposes some serious lunitations the description of the solute as a point dipole located at the centre of a cavity, the spherical fonn of the cavity and the assumption that cavity size and solute dipole moment are independent of the solvent dielectric constant. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

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