Permittivity coefficient

Table 3.6 lists, as far as could be gleaned from the literature, the values of the vapor/liquid surface potentials Aj, the field dependence of the permittivity coefficient p (Eq. 2.13), the theoretical limiting slopes of the apparent molar volumes, Sy, the molar diamagnetic susceptibility, /, and the mean electrostriction volumes, of solvents at ambient temperatures. 

The compounds K5Nb3OFi8 and Rb5Nb3OFi8 display promising properties for their application in electronics and optics. The compounds can be used as piezoelectric and pyroelectric elements due to sufficient piezo- and pyroelectric coefficients coupled with very low dielectric permittivity. In addition, the materials can successfully be applied in optic and optoelectronic systems due to their wide transparency range. High transparency in the ultraviolet region enables use of the materials as multipliers of laser radiation frequencies up to the second, and even fourth optical harmonic generation. 

Substrate material Price per unit area (arb. units) Dielectric permittivity of insulator Maximum working temperature (K) Resistivity of dielectric layer (fl-cm) Density (g/cm3) Linear expansion coefficient x i[Pg.490]

Here the atoms in the system are numbered by i, j, k, l = 1,..., N. The distance between two atoms i, j is ry, q is the (partial) charge on an atom, 6 is the angle defined by the coordinates (i, j, k) of three consecutive atoms, and 4> is the dihedral angle defined by the positions of four consecutive atoms, e0 is the dielectric permittivity of vacuum, n is the dihedral multiplicity. The potential function, as given in equation (6), has many parameters that depend on the atoms involved. The first term accounts for Coulombic interactions. The second term is the Lennard-Jones interaction energy. It is composed of a strongly repulsive term and a van der Waals-like attractive term. The form of the repulsive term is chosen ad hoc and has the function of defining the size of the atom. The Ay coefficients are a function of the van der Waals radii of the... 

When nonnegligible concentrations of the electrolyte are present in the organic solvent, ion-ion interactions superimpose on the ion-solvent ones, or the secondary medium ejfect. Although an equation similar to Eq. (2.43) may be used for determining the activity coefficient in the new medium, it is necessary to employ the appropriate value of A in this equation that depends on the relative permittivity of the medium A(org) = A(aq)(eaq/e ,g) Unless very water-rich mixed solvents are used, different numerical values of the parameters in the denominator and the second term on the right-hand side of Eq. (2.43) have to be employed. 

A common sitnation is that the electrolyte is completely dissociated in the aqueons phase and incompletely, or hardly at all, in the organic phase of a ternary solvent extraction system (cf. Chapter 3), since solvents that are practically immiscible with water tend to have low valnes for their relative permittivities e. At low solnte concentrations, at which nearly ideal mixing is to be expected for the completely dissociated ions in the aqneons phase and the undissociated electrolyte in the organic phase (i.e., the activity coefficients in each phase are approximately nnity), the distribntion constant is given by... 

The fifth letter in the Greek alphabet hence, used to denote the fifth in a series (for example, the fifth methylene carbon in a fatty acid). 2. Symbol for molar absorption coefficient or extinction coefficient. 3. Symbol for permittivity (cq refers to permittivity of a vacuum refers to relative permittivity). 4. s, Symbol for degree of activation (lUB (1982) Eur. J. Biochem. 128, 281). 5. 8i, Symbol for degree of inhibition. 6. Symbol for efficiency. 7. Symbol for linear strain. 8. Symbol for emit-tance. 

The temperature coefficient of the natural logarithm of the relative permittivity of water is -0.0046, and insertion into equation (2.39) gives ... 

The values of ds in seven dipolar aprotic solvents have been reported to be 80 + 5 pm for cations and 44 4 pm for anions [10]. The MSA is also used in treating ionic activity coefficients in a recent study [11], the change in solvent permittivity with electrolyte concentration was taken into account in addition to the change in ionic radius, and excellent agreements were obtained between the experimental and theoretical results for 1 1 electrolytes of up to 2.5 M. 

The influence of ionic strength on yCii is great in solvents of lower permittivities. When we compare ionic activities in different solvents, we have to consider this activity coefficient, in addition to the transfer activity coefficient yt. However, in reality, the influence of is usually negligibly small compared to that of yt. 

In 1985, the IUPAC Commission of Electroanalytical Chemistry defined the pH for solutions in organic solvents of high permittivity and in water-organic solvent mixtures [15]. According to them, the pH is conceptually defined by Eq. (3.26), where m shows the molality and yrn the activity coefficient ... 

When the permittivities of solvents S and R are very different, this affects the De-bye-Hiickel activity coefficient of M+ (9) in Chapter 2). If necessary, the effect should be estimated (or eliminated) using the Debye-Hiickel theory. 

The problem of triple ion formation has been studied in detail, because it is related to lithium battery technologies [18]. In some cases, however, the occurrence of the minimum in the log A-log c curve, as observed in Fig. 7.2, is not attributed to triple-ion formation but is explained by ion-pair formation only. The increase in log A at high electrolyte concentrations is attributed either to the increase in the distance of closest approach of ions, the increase in the solution permittivity, or the decrease in the activity coefficient of the ion-pairs. Although there is still some controversy, it seems certain that triple ions are actually formed in many cases. 

The temperature and frequency dependence of the complex dielectric permittivity a for both 2-chlorocydohexyi isobutyrate (CCHI) and poly(2-chlorocyclohexyl acrylate) (PCCHA) is reported. The analysis of the dielectric results in terms of the electric modulus suggests that whereas the conductive processes in CCHI are produced only by free charges, the conductivity observed in PCCHA involves both free charges and interfacial phenomena. The 4x4 RIS scheme presented which accounts for two rotational states about the CH-CO bonds of the side group reproduces the intramolecular correlation coefficient of the polymer. 

The effect of changing the dielectric constant is shown for ions of radius 4.0A in Figure 5, where the values of D correspond to those for the solvents methanol, water, and N-methylpropionamide. The upward turn of log y at higher concentrations is exaggerated when D is low, which is again in qualitative agreement with some experimental observations (2) the effect is attributed to mutual polarization of ions, which is more effective when the permittivity is low. On an intuitive basis it might have been expected, erroneously, that the polarization would lower the activity coefficients, which could be the reason why ionic polarization has received so little attention in interionic theory. 

A jumpwise volume change in the transition correlates with a jumpwise change in the shear equilibrium modulus, the refractive index, the stress-optical coefficient and in the components of complex permittivity e and complex modulus G. ... 

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