Relative permittivity, definition

The failure of the solvent relative permittivity to represent solute/solvent interactions has led to the definition of polarity in terms of empirical parameters. Such attempts at obtaining better parameters of solvent polarity by choosing a solvent-dependent standard system and looking at the changes in parameters of that system when the solvent is changed e.g. rate constants of solvent-dependent reactions or spectral shifts of solvatochromic dyes) are treated in Chapter 7. 

It is obvious that such a definition of solvent polarity cannot be measured by an individual physical quantity such as the relative permittivity. Indeed, very often it has been found that there is no correlation between the relative permittivity (or its different functions such as l/sr, (sr — l)/(2er + 1), etc.) and the logarithms of rate or equilibrium constants of solvent-dependent chemical reactions. No single macroscopic physical parameter could possibly account for the multitude of solute/solvent interactions on the molecular-microscopic level. Until now the complexity of solute/solvent interactions has also prevented the derivation of generally applicable mathematical expressions that would allow the calculation of reaction rates or equilibrium constants of reactions carried out in solvents of different polarity. 

The influence of solvents on the ionization equilibrium is related to their electrostatic and their solvation properties. The value of the ionization constant of an analyte is closely determined, in practice, by the pH scale in the particular solvent. It is clear that it is most desirable to have a universal scale which is able to describe acidity (and basicity) in a way that is generally valid for all solvents. It is, in principle, not the definition of an acidity scale in theory which complicates the problem it is the difficulty of approximating the measured values in practice to the specifications of the definition. The pH scale, as is common in water, is applicable only to some organic solvents (i.e., mainly those for which the solvated proton activity is compatible with the Brpnsted theory of acidity). The applicability of an analog to the pH scale in water decreases with decreasing relative permittivity of the solvents and with their increasing aprotic character. 

In general, less polar solutes dissolve best in solvents with low values, and the higher values favor dissolution of polar molecules. However, the involvements of specific interactions, especially hydrogen bonding, do not allow definite trends to be established which relate the extent to which a solute is dissolved to the polarity of the solute and the relative permittivity of the solvent (Snyder, 1978). 

But pay particular attention what is important is that this definition of the relative permittivity is independent of any assumption that the dielectric is composed of atoms or molecules, and so requires no discussion of the medium at the microscopic level. 

Solvents can be classified as polar, non-polar and apolar, with the definitions being as above. However, a more general classification uses the relative permittivity. There are high relative permittivity solvents such as (at 25°C) ... 

Together with the definition of the dielectric constant (relative permittivity), e = 1+ 4ny, this leads to ... 

The definitions of lEC 50 [18], the International Electrotechnical Vocabulary, are abstruse and of little use in every day work. The notes to the definition of Relative permittivity" are more valuable In the case of. .. alternating fields of sufficiently low frequency, the relative permittivity. .. is equal to the ratio of the capacitance of... 

Introduction of complex capacity C requires introduction of the notion of complex relative permittivity e, to which it is proportionate by definition ... 

The effect of a solvent can actually be considered as the resultant of two components a macroscopic effect depending on the dielectric permittivity of the solvent as an environmental continuum, and specific interactions related to the formation of definite associates. The former effect predominates in solvents of low relative permittivity, containing no donor or acceptor groups. It can be taken into account with appropriate model calculations, e.g., on the basis of the Onsager reaction space model. 

Dielectric constant Also called relative permittivity or K. Represented by the variables and k. A measure of a material s ability to store charge under the influence of an applied electric field. Values are given in comparison to a perfect vacuum or "free space, which has a dielectric constant of 1 by definition. 

Cheng et al. demonstrated an LC droplet-based microlens driven by DEP force [7]. LC is a high dielectric medium and thus may be potentially actuated by DEP forces. Based on the relative permittivity e//= 16.5 and conductivity o = 5 X 10 (Q m) 1 for the LC MDA2625 (Merck), the factor a/((nei,8o) is calculated to be 5 x 10 at an operation frequency of 1 kHz. By definition of dielectric material of o/Ccoe eo) 1, LC thus behaves as a dielectric medium. Using this DEP mechanism Cheng s group demonstrated the adjustment of the focal length of the liquid crystal droplet lens. 

These assumptions are rather severe but they do not seem to affect significantly the accuracy of the theory. The second assumption implies that ions have no volumes although they do have a radii which, moreover, increases with hydration. The last assumption is definitely not correct for water. The relative permittivity decreases much nearer the surface in addition, ions may dehydrate on a surface. 

When applied to solvents, this rather iU-defined term covers their overall solvation capabihly (solvation power) for solutes (i.e., in chemical equilibria reactants and products in reaction rates reactants and activated complex in light absorptions ions or molecules in the ground and excited state), which in turn depends on the action of aU possible, nonspecific and specific, intermolecular interactions between solute ions or molecules and solvent molecules, excluding such interactions leading to definite chemical alterations of the ions or molecules of the solute. Occasionally, the term solvent polarity is restricted to nonspecific solute/solvent interactions only (i.e., to van der Waals forces). With respect to this definition of polarity, when discussing dipolar molecules, the dipolarity (rather than polarity) of solvents should be considered. Molecules with a permanent dipole moment are dipolar (not polar). Molecules, which are lacking permanent dipole moment should be called apolar (or nonpolar). In literature, the terms polar and apo-lar are used indiscriminately to characterize a solvent by its relative permittivity as well as its permanent dipole moment, even though dipole moments and relative permittivities are not directly related to each other. 

The buzzword polarity , derived from the dielectric approach, is certainly the most popular word dealing with solvent effects. It is the basis for the famous rale of thumb ""similia similibus solvuntuf" ( like dissolves like"") apphed for discussing solubility and miscibility. Unfortunately, this rale has many exceptions. For instance, methanol and toluene, with relative permittivities of 32.6 and 2.4, respectively, are miscible, as are water (78.4) and isopropanol (18.3). The problem lies in exactly what is meant by a like solvent. Originally, the term polarity was meant to be an abbreviation of static dipolarity and was thus associated with solely the dielectric properties of the solvent. Later on, with the advent of the empirical solvent parameters, it has assumed a broader meaning, sometimes even that of the overall solvating power. With this definition, however, the term polarity is virtually superfluous. 

The present evidence is thus that kinetic effects may account for half or more of permittivity decreases of ionic solutions and this may be an important factor in determing the amplitude of the Y dispersion in conducting biopolymer solutions and lead to revisions in estimated nature and amount of bound water. The effect may also have some bearing on dielectric properties of cell interiors and membranes if these have appreciable conductances. It would seem premature to attempt definitive answers to such questions until the relative importance of static and kinetic effects in presumably simpler ionic solutions has been better established experimentally in comparison with theory which treats them self-consistently. 

It should be noticed that, in many theoretical works, the term solvent polarity is defined by the values of the relative electric permittivity, also called dielectric constant. However, such a definition is by no means precise. The existence of hydrogen bonds (H-bonds) between solute and solvent molecules is one of the important limitations of the use of the continuum models based on the theory of dielectrics. In modern physical chemistry of solutions in order to quantitatively describe the solvatochromism phenomenon various empirical scales of the polarity are used. The exhaustive reviews on this topic have been presented by Reichardt [1, 2],... 

It is clear that the frequency of the metal-solvent band decreases with increase in the size of the alkali metal, that is, with decrease in the field due to the charge on the ion. When ion pairing is absent, the value of the frequency is independent of the nature of the anion. This is definitely the case in DMSO, which strongly solvates cations because of its high donor number. In addition, the relatively high permittivity of this solvent reduces the influence of long-range ion-ion interactions. 

Before focusing on PLCs, let us quote the basic definitions [89]. The relative dielectric permittivity e is the ratio of the capacities of a parallel plate condenser measured with and without (in vacuum) the dielectric material placed between the plates. If s is independent of the field strength, it is called dielectric constant. Polymers are typically dielectric, so that— in contrast to electric conductors—there is a certain reversal of the relative positions of the electric charges after the removal of the field. If no permanent dipoles are present in the material, then the following Maxwell relation is valid ... 

If an c-wave is incident on a hybrid NLC cell, all three interaction mechanisms (orientation, thermal, and thermoorientation ) will occur simultaneously. We will use Eq. (17) and the corresponding expressions for the perturbation of the permittivity tensor to estimate the relative contributions of these mechanisms to the nonlinear phase shift. For the orientation and thermo-orientation mechanisms, Sen efe-k =Sa sin 10 S0. We readily find an expression for 30 for the orientation mechanism from Eq. (4a) by setting = 0, = const, and E z0 (for definiteness we consider a normally indicent e-wave). For the thermal mechanism of nonlinearity,... 

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