Polarizability and dielectric constants

Solvent polarity and temperature also influence ihe results. The dielectric constant and polarizability, however, are of little predictive value for the selection of solvents relative to polymerization rates and behavior. Evidently evety system has to he examined independently. In cationic polymerization of vinyl monomers, chain transfer is the most significant chain-breaking process. The activation energy of chain transfer is higher than that of propagation consequently, the molecular weight of the polymer increases with decreasing temperature. 

Finally, Shannon obtained 61 sets of ionic polarizabilities for 129 oxides and 25 fluorides using the Clausius-Mosotti equation and least square refinements, and suggested the periodic table of ionic polarizabilities. Therefore the dielectric constant of materials with compositional changes can be successfully predicted by Equation 22.17 and Equation 22.18. Erom another arrangement of Equation 22.16, the theoretical dielectric constant can be obtained from the total ionic polarizabilities in Equation 22.19. Erom Equation 22.17 through Equation 22.19, the theoretical values of dielectric constant and polarizabilities can be obtained as well as the measured values ... 

Shepard, R. 1949. Dielectric constants and polarizabilities of ions in simple crystals and barium titanate. Physical Review, 76(8) 1215-1219. 

The refractive index of a compound oxide or a multi-component glass may be roughly estimated by using the Lorenz-Lorentz formula (Clausius-Mosotti s formula in terms of the dielectric constant and polarizability) which gives the relation between the refractive index and polarizability of materials described as equation (31-1). 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

Linear absorption and fluorescence spectra for the series of symmetrical cationic polymethines with 5-butyl-7,8-dihydrobenzo[ /]furo 2,3 /lindolium terminal groups are shown in Fig. 14 for solvents of different polarity. It is known that the polarity of solvents can be characterized by their orientational polarizability, which is given by Af = (e- l)/(2e + 1) — (n2 - l )/(2n2 +1), where e is the static dielectric constant and n is the refractive index of the solvent [41], Calculated A/values... 

Methods for determining permanent dipole moments and polarizabilities can be arbitrarily divided into two groups. The first is based on measuring bulk phase electrical properties of vapors, liquids, or solutions as functions of field strength, temperature, concentration, etc. following methods proposed by Debye and elaborated by Onsager. In the older Debye approach the isotope effects on the dielectric constant and thence the bulk polarization, AP, are plotted vs. reciprocal temperature and the isotope effect on the polarizability and permanent dipole moment recovered from the intercept and slope, respectively, using Equation 12.5. 

In the equation s is the measured dielectric constant and e0 the permittivity of the vacuum, M is the molar mass and p the molecular density, while Aa and A (po2) are the isotope effects on the polarizability and the square of the permanent dipole moment respectively. Unfortunately, because the isotope effects under discussion are small, and high precision in measurements of bulk phase polarization is difficult to achieve, this approach has fallen into disfavor and now is only rarely used. Polarizability isotope effects, Aa, are better determined by measuring the frequency dependence of the refractive index (see below), and isotope effects on permanent dipole moments with spectroscopic experiments. 

The very high ionization potential and the low polarizability of the fluorine atom imply that fluorinated compounds have only weak intermolecular interactions. Thus, perfluoroalkylated compounds have very weak surface energies, dielectric constants, and refracting indexes. 

Many attempts have been made to correlate the enantioselective properties of enzymes with structure and/or process conditions [61, 70-73]. Attempts to correlate the effect of a particular medium on the enantioselectivity of an enzyme-catalyzed reaction with physico-chemical descriptors of the solvent have also been reported by a number of groups [22, 59, 64, 74]. Correlations with solvent size [75], dielectric constant [59], polarizability, electron pair acceptance index [76], logP [17],... 

These effects are related to the electric properties of the reacting molecules, like their dipole moments and polarizability, as well as to solvent properties, like their dielectric constants and viscosity. 

The valence bond method with polarizable continuum model (VBPCM) method (55) includes solute—solvent interactions in the VB calculations. It uses the same continuum solvation model as the standard PCM model implemented in current ab initio quantum chemistry packages, where the solvent is represented as a homogeneous medium, characterized by a dielectric constant, and is polarizable by the charge distribution of the solute. The interaction between the solute charges and the polarized electric field of the solvent is taken into account through an interaction potential that is embedded in the... 

For further progress it is necessary to specify how E varies with D, or how P depends on Ea. For this purpose, we introduce the constitutive relations D - e(T,V)E or P - ot0(T,V)F0, where e is the dielectric constant and a0 is a modified polarizability. (Conventionally, the polarizability is defined through the relation P - oE, but no confusion is likely to arise through the introduction of this variant.) Note several restrictions inherent in the use of these constitutive relations. First, the material under study is assumed to be isotropic. If this is not the case, e and c 0 become tensors. Second, the material medium must not contain any permanent dipole moments in the preceding constitutive relations P or E vanishes when E0 or D does. Third, we restrict our consideration to so-called linear materials wherein e or a0 do not depend on the electric field phenomena such as ferroelectric or hysteresis effects are thus excluded from further consideration. These three simplifications obviously are not fundamental restrictions but render subsequent manipulations more tractable. Finally, in accord with experimental information available on a wide variety of materials, e and aQ are considered to be functions of temperature and density assuming constant composition, these quantities vary with T and V. 

In the liquid phase, calculations of the pair correlation functions, dielectric constant, and diffusion constant have generated the most attention. There exist nonpolarizable and polarizable models that can reproduce each quantity individually it is considerably more difficult to reproduce all quantities (together with the pressure and energy) simultaneously. In general, polarizable models have no distinct advantage in reproducing the structural and energetic properties of liquid water, but they allow for better treatment of dynamic properties. 

Table 1 Mean dielectric constants and molar polarizabilities of simple oxides...

As discussed in the previous section, the dielectric properties of materials at microwave frequencies are strongly dependent on the ionic polarization. Theoretical dielectric constants of materials can be obtained from the dielectric polarizabilities of composing ions through the understanding of crystal structure. Let us consider the basic relationships between the dielectric polarizabilities and dielectric constants and how the control of dielectric properties and the search for new materials can be achieved by the additive rule. 

Therefore the dielectric constants and TCFs of PCCN and PCMT with compositional variation of the A-site cations are closely related to the bond valence of the A-site as well as ionic polarizability. With an increase in calcium content, the bond valence of the A-site decreases and A-site ions rattle easily, which results in an increase in the dielectric constant of specimens. Also, the TCP of PCCN and PCMT increases with an increase in the bond valence of the A-site. 

Hydrophobicity, from the greek hydro water and phobia aversion, is a term referring to the way a molecule likes or does not like water. A compound with a high hydrophobicity will not be water soluble. It is ap-olar. Conversely, a compound with a low hydrophobicity is said to be hydrophilic or polar. It is likely to be water soluble. In between the two extremes, the hydrophobicity varies. A scale is needed. The problem is that the hydrophobicity, or the polarity of a compound, depends on several parameters such as the dipole moment, the dielectric constant, the polarizability, the proton donor or acceptor character, or even the boiling point to molecular mass ratio. Since the end of the nineteenth century, the octanol-water partition coefficient, P i, was used with success as a measure of hydrophobicity. The log is the convenient scale. Compounds with a positive log Po/w value are more and more hydrophobic or apolar as the value increases. Compounds with a negative log value are hydrophilic or polar [1]. 

The role of the medium, in which contacting and pull-off are performed, has been mentioned but not considered so far. However, the surroundings obviously influence surface forces, e.g., via effective polarizability effects (essentially multibody interactions e.g., by the presence of a third atom and its influence via instantaneous polarizability effects). These effects can become noticeable in condensed media (liquids) when the pairwise additivity of forces can essentially break down. One solution to this problem is given by the quantum field theory of Lifshitz, which has been simplified by Israelachvili [6]. The interaction is expressed by the (frequency-dependent) dielectric constants and refractive indices of the contacting macroscopic bodies (labeled by 1 and 2) and the medium (labeled by 3). The value of the Hamaker constant Atota 1 is considered as the sum of a term at zero frequency (v =0, dipole-dipole and dipole-induced dipole forces) and London dispersion forces (at positive frequencies, v >0). 

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