Static dielectric polarizability

Polarizability (Static Dielectric Polarizability) is a measure of the linear response of the electronic cloud of a chemical species to a weak external electric field of particular strength. 

PollockEL, Alder BJ, Patey GN (1981) Static dielectric properties of polarizable Stockmayer fluids. Physica A Stat Theor Phys 108(1) 14—26... 

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... 

Separation of Electronic and Nuclear Motions. The polarizabilities of the ground state and the excited state can follow an electronic transition, and the same is true of the induced dipole moments in the solvent since these involve the motions of electrons only. However, the solvent dipoles cannot reorganize during such a transition and the electric field which acts on the solute remains unchanged. It is therefore necessary to separate the solvent polarity functions into an orientation polarization and an induction polarization. The total polarization depends on the static dielectric constant Z), the induction polarization depends on the square of the refractive index n2, and the orientation polarization depends on the difference between the relevant functions of D and of n2 this separation between electronic and nuclear motions will appear in the equations of solvation energies and solvatochromic shifts. 

Dipole-Dipole Interaction. The first of the four terms in the total electrostatic energy depends on the permanent dipole moment of the solute molecule of radius a (assuming a spherical shape) immersed in a liquid solvent of static dielectric constant D. The function f(D) = 2(D - l)/(2D + 1) is known as the Onsager polarity function. The function used here is [f(D) — f(n2)] so that it is restricted to the orientational polarity of the solvent molecules to the exclusion of the induction polarity which depends on the polarizability as of the solvent molecules, related to the slightly different Debye polarity function q>(n2) according to... 

There are two parameters which appear to be of major importance in determining the occurrence and observability of electron solvation. The first is the polarizability of the liquid, as expressed by its dielectric behavior. On the basis of theory, which will be discussed later, a necessary condition for electron solvation appears to be that the static dielectric constant of the liquid be substantially greater than one. The second parameter, which seems at present to be unpredictable, is the natural lifetime of the solvated electron—i.e., its lifetime with respect to reaction with the solvent itself. 

In the language of reciprocal space, nonlocal metal response refers to the dependence of the metal dielectric constant on the wavevector k of the various plane waves into which any probing electric fields can be decomposed. Such an effect is often mentioned in reports on SERS, but it is usually neglected. One of the oldest papers addressing the importance of nonlocal effects on the polarizability of an adsorbed molecule is the article by Antoniewicz, who studied the static polarizability of a polarizable point dipole close to a linearized Thomas-Fermi metal [63], The static dielectric constant eTF(k) of such a model metal can be written as ... 

E. L. Pollock, B. J. Alder and G. N. Patey, Static dielectric properties of polarizable Stock-mayer fluids, Physica A, 108 (1981) 14—26. 

The same formula applies if the electron polarizability is replaced by the total polarizability, and the optical dielectric constant is replaced by the static dielectric constant, provided attention is then restricted to nonpolar materials. 

In contrast to the silver halides for which the use of the static dielectric constant in Eq. (57) yields good agreement, for PbF2 with its high static dielectric constant a value more typical for this structure ( ficafj ) had to be used. Since at the small distances involved the full static permittivity is not operative, the neglect of the high static polarizability of the lead ion makes sense. (Similarly the interaction... 

First, consider a very dilute gas of molecules [16]. The conventional theory of the static dielectric susceptibility % of such a gas invokes the notion of polarizable molecules with permanent dipole moments that are partially aligned by the external electric field . Standard techniques of statistical thermodynamics produce the Langevin-Debye formula for x Per molecule that reads... 

It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water s dielectric constant of s = 78 T5,i85,i96 holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.. 

Several conclusions can be drawn from Table 3. First, in accordance with the two-state model, /So and jSj all increase with decreasing HOMO-LUMO gap. Second, the intrinsic second-order polarizability of p-nitroaniline is increased by two-thirds when the solvent is changed from p-dioxane to methanol or A-methylpyrrolidone, even when the values are corrected for the differences in (A ). As we have adopted the value for p-nitroaniline in dioxane as a standard, it should therefore be noted that molecules that truly surpass the best performance of p-nitroaniline should have a second-order polarizability of l. p-nitroaniline (dioxane). As a third conclusion, there is a poor correlation between and the static reaction field as predicted by (91). This is in part due to the fact that the bulk static dielectric constant, E° in (89), differs from the microscopic dielectric constant. For example, p-dioxane has long been known for its anomalous solvent shift properties (Ledger and Suppan, 1967). Empirical microscopic dielectric constants can be derived from solvatochromism experiments, e.g. e = 6.0 for p-dioxane, and have been suggested to improve the estimation of the reaction field (Baumann, 1987). However, continuum models can only provide a crude estimate of the solute-solvent interactions. As an illustration we try to correlate in Fig. 7 the transition energies of p-nitroaniline with those of a popular solvent polarity indicator with negative solvatochromism. 

Here a,- is the polarizability of the ith sublattice and e is the static dielectric constant. 

Static dielectric properties of icosahedral and Stone-Wales rounded fullerenes, optimized with the REBO2 potential [D.W. Brenner, J. Phys. Cons. Matter 14, 783 (2002)], are studied using a Gaussian renormalized monopole-dipole interaction model. The molecular polarizability of icosahedral and spherical (with defects) fullerenes is found to vary linearly with the cube of the mean radius of the molecules. The local electric field of spherical fullerenes varies on average with the same law as that obtained with a continuous metallic sphere submitted to an external static uniform electric field. 

Here, co and Ss are the optical and the static dielectric constants of the solution the former appears because the contribution from the electronic polarizability has been subtracted. Dqx and D ed are the dielectric displacements when the reactant is in the reduced and in the oxidized form, respectively. The integral is to be performed over the space filled by the solution. When the reactant is close to the electrode surface, image terms arise, which contrihute to the displacement. 

Whether CT is possible depends on the polarity of the solvent, as measured by the dielectric constant. There are essentially two important dielectric constants one for slow processes or the static dielectric constant (Cj) and the other for very fast processes (faster than any reorganization process), referred to as or the dielectric constant at infinite frequency. of a compound can be obtained by measuring the capacitance of a condensator where the compound is used as a dielectricum. is obtained by measuring molecular polarizability. The higher the frequency of the applied electric field, the slower are the motions in the medium to follow the variations in the field. For example, a water molecule has a certain rotation time and when the field frequency is too fast, the water molecule no longer moves with the field. When the frequencies applied correspond to UV frequencies, (for all practical purposes) is measured. One may show that = n, where n is the refractive index. 

Measurements of the (static) dielectric permittivity (ers) of a sorbent/sorbate system allow the determination of the product of the specific polarizability of the molecules adsorbed (a ) and the Gibbs excess mass of the adsorbate (mQ ) Indeed we have from Sect. 2.2, Eq. (6.47)... 

The Clausius-Mossotti equation provides a means of correlating the macroscopic dielectric property with the microscopic property—the number of molecules per unit volume and the molecule polarizability. The dielectric property varies with temperature is because the number of the molecule per unit volume changes due to the material thermal expansion. For non-polar liquid materials used in ER fluids, it is acceptable to assume that only the static dielectric constant and the number of the molecules per unit volume N are dependent of temperature. Differemiating the Clausius-Mossotti equation shown in Eq. (26) with respect to temperature T for both sides, one may obtain... 

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