Dielectric constant as function

Several material properties exhibit a distinct change over the range of Tg. These properties can be classified into three major categories—thermodynamic quantities (i.e., enthalpy, heat capacity, volume, and thermal expansion coefficient), molecular dynamics quantities (i.e., rotational and translational mobility), and physicochemical properties (i.e., viscosity, viscoelastic proprieties, dielectric constant). Figure 34 schematically illustrates changes in selected material properties (free volume, thermal expansion coefficient, enthalpy, heat capacity, viscosity, and dielectric constant) as functions of temperature over the range of Tg. A number of analytical methods can be used to monitor these and other property changes and... 

LIG. 34 Schematic illustrations of changes in selected material properties (free volume, thermal expansion coefficient, enthalpy, heat capacity, viscosity, and dielectric constant) as functions of temperature over the range of Tg. 

The reflectivity of bulk materials can be expressed through their complex dielectric functions e(w) (i.e., the dielectric constant as a function of frequency), the imaginary part of which signifies absorption. In the early days of electroreflectance spectroscopy the spectra were often interpreted in terms of the dielectric functions of the participating media. However, dielectric functions are macroscopic concepts, ill suited to the description of surfaces, interfaces, or thin layers. It is therefore preferable to interpret the data in terms of the electronic transitions involved wherever possible. 

Measurements of D carried out at a selected temperature (20°C) as a function of the concentration of organic solvent from 10 to 100% have been published elsewhere (Douzou, 1977a,b). There is a marked proportional decrease in the dielectric constant as the concentration of organic solvent is increased. This effect is very pronounced in the case of methanol and MPD and less pronounced for dimethylformamide and polyols. Adding 50% of most of the organic solvents selected decreases the di-... 

Fig. 6.74. The dielectric constant as a function of the distance from the electrode and the ordering of the dipole water molecules.

The symmelrical loss-frequency curve predicted by this simple theory is commonly observed for simple substances, but its maximum is usually lower and broader because of the existence of more than one relaxation time. Various functions have been proposed to represent the distribution of relaxation times. A convenient representation of dielectric behavior is obtained, according to the method of Cole and Cole, by writing the complex dielectric constant as... 

Fig. 20. The real part of the microwave frequency (10 GHz) dielectric constant as a function of sodium metal concentration at 298 K in sodium-ammonia solutions. Note the break in the ordinate. [Adapted from Mahaffey and Jerde (117) used with permission from the American Physical Society, Reviews of Modern Physics.]...

Finally, other models [8-10] define the dielectric constant as a function of the point in space around the solute and solve the three-dimensional electrostatic problem, usually by a finite differences method. 

Figure 13 Dielectric constant as a function of flow ratio (N20/SiH4).10...

If we measure the dielectric constant as a function of temperature, then, it should be a linear function of 1 /T and from the constants of the curve we can find both the electronic polarizability ao and the dipole moment... 

Fig. 3 Magnetodielectric effect in YMn03 (left scale, full line H = 0 dotted line H = 7 T) and in HoMnOj (right scale, full line H = 0 dotted lines H - 3,5,7 T from top to bottom). Inset relative change of the dielectric constant as a function of the magnetic field for H0M11O3 at 4.5 K (from ref, 22).

Fig. 6 (a) Temperature variation of magnetization of BiMn03 at 500 Oe. Inset shows the hysteresis loops at 75 and 45 K, (b) P-E hysteresis loops of polycrystalline BiMnO, (from ref. 13). Isothermal (c) magnetization and (d) field-induced change in dielectric constant as a function of a magnetic field at different temperatures (from ref. 30). 

Fig 2.27. Differential dielectric constant as a function of field that is near an ion. (Reprinted from B. E. Conway, Ionic Hydration in Chemistry and Biophysics, Elsevier, New York, 1981.)... 

This broken-down region near the ion was the subject of mathematical discussion by Webb as early as 1926, by Conway et al., and by Booth, whosepaper also can be considered seminal. Grahame made an attempt to simplify Booth s equation for the dielectric constant as a function of field strength, and a diagram due to him is shown in Fig. 2.27. 

The ionization constant should be a function of the intrinsic heterolytic ability (e.g., intrinsic acidity if the solute is an acid HX) and the ionizing power of the solvents, whereas the dissociation constant should be primarily determined by the dissociating power of the solvent. Therefore, Ka is expected to be under the control of e, the dielectric constant. As a consequence, ion pairs are not detectable in high-e solvents like water, which is why the terms ionization constant and dissociation constant are often used interchangeably. In 1ow-e solvents, however, dissociation constants are very small and ion pairs (and higher aggregates) become important species. For example, in ethylene chloride (e = 10.23), the dissociation constants of substituted phenyltrimethylanunonium perchlorate salts are of the order 10" . Overall dissociation constants, expressed as pXrx = log Xrx, for some substances in acetic acid (e = 6.19) are perchloric acid, 4.87 sulfuric acid, 7.24 sodium acetate, 6.68 sodium perchlorate, 5.48. Acid-base equilibria in acetic acid have been carefully studied because of the analytical importance of this solvent in titrimetiy. 

Figure 8. Comparison of the solvent dielectric constant as the function of ionic strength as predicted from the AMSA theory [77] against experimental data [76] for aqueous solutions of nitrate and formate salts.

Measurements of dielectric constant as a function of frequency. These dielectric dispersion measurements permit the estimation of the relaxation times or rotary diffusion constants which characterize the rotary Brownian movement of the protein molecule. 

F. Booth, Dielectric Constant As a Function of the Applied Held, 7. Chem. Phys. 19 1451(1951). 

Values of e, n and ve and Hamaker constants for two identical types of a material in a vacuum, which are calculated from Equation (567) by taking e3 = 1 and 3 = 1, are given in Table 7.1. Unfortunately, the lack of material constants, such as the dielectric constant, as a function of frequency for most of the substances, and also the complexity of the derived formulae have hampered the general use of the Lifshitz model. However, Lifshitz theory made possible the advent of the first theories on the stability of hydrophobic colloids as a balance between London attraction and electrical double-layer repulsion. Later, these theories were further elaborated by Derjaguin and Landau, and independently by Verwey and Overbeek. The general theory of colloidal stability (which is beyond the scope of this book) is based on Lifshitz theory and has become known as the DLVO theory, by combining the initials of these four authors. 

---