The Dielectric Constant

The high-frequency dielectric constant is determined by the effects of electronic polarization. An accurate estimate of this property lends confidence to the modeling of the electronic polarization contribution in the piezoelectric and pyroelectric responses. The constant strain dielectric constants (k, dimensionless) are computed from the normal modes of the crystal (see Table 11.1). Comparison of the zero- and high-frequency dielectric constants indicates that electronic polarization accounts for 94% of the total dielectric response. Our calculated value for k ( x)) of 1.92 at 300 K compares favorably with the experimental value of 1.85 estimated from the index of refraction of the P-phase of PVDF.  

Reprinted with permission from Carbeck and Rutledge. Copyright 1996, Elsevier Science Ltd. 

H20 calculates to a dielectric constant (Dc) of 78.54 at 25°C, the highest of the ordinary solvents. Ethanol has D = 24.3 at 25°C. Given its high polarity, H20 easily engages in dipole-dipole and ion-dipole reactions. 

At neutral pH and 25°C, one water molecule in every 10 million becomes ionized through the bonding of one of its protons to another water molecule (Baianu, 1992a) West and Todd (1961) estimate one molecule in every 550 million. In practical terms, every 1 g mol (18 g) of pure H20 renders 10-7 g mol of hydrogen ion (10—7 g of H+) and 10-7 g mol of hydroxyl ion (1.7 X 10 6 g of OH ). In aqueous solution, H+ is hydrated to HsO+ (the 

---

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. 

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... 

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... 

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... 

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

Gray C G, Sainger Y S, Joslin C G, Cummings P T and Goldman S 1986 Computer simulation of dipolar fluids. Dependence of the dielectric constant on system size a comparative study of Ewald sum and reaction field approaches J. Chem. Phys. 85 1502-4... 

Here, E and s are the band gap energy and the dielectric constant of the bulk semiconductor, and p is the reduced 0 mass of the exciton system, 1/p = + 1/fffi,. The second tenn, proportional to /R, arises from a simple... 

Determine the dielectric constants for each of the faces between the grid points. 

T. Simonson. Accurate calculation of the dielectric constant of water from simulations of a microscopic droplet in vacuum. Chem. Phys. Lett, 250 450-454, 1996. 

Another way of calculating the electrostatic component of solvation uses the Poisson-Boltzmann equations [22, 23]. This formalism, which is also frequently applied to biological macromolecules, treats the solvent as a high-dielectric continuum, whereas the solute is considered as an array of point charges in a constant, low-dielectric medium. Changes of the potential within a medium with the dielectric constant e can be related to the charge density p according to the Poisson equation (Eq. (41)). 

Dick B G and A W Overhauser 1958. Theory of the Dielectric Constants of Alkali Halide Crj stals. Physical Review 112 90-103. 

The dielectric constant is concerned with the electrical properties of a material. The dielectric constant for a solid is a 3 x 3 matrix with different components according to the Cartesian axes. These elements are given by ... 

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. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

The dyes prepared in this way show a positive solvatochromism as the dielectric constant of the solvent increases, indicating that they possess a predominantly nonpolar structure. Substituents on the phenyl group in the 4-position of the selenazole ring have little influence on the absorption spectra. 

---