Permittivity, correlation with

Figme 2.3.18 shows that the relative permittivity correlates with molecular weight. It is only with aliphatic hydrocarbons that the relative permittivity increases slightly as the molecular weight increases. The relative permittivity of alcohols, esters, and ketones decreases as their molecular weight increases, but only alcohols and ketones have the same relatiorrship. The relative permittivities of esters are well below those of alcohols and ketones. 

A further problem is that ion association, that is, the tendency of oppositely charged ions to form pairs or larger aggregates in solution, becomes increasingly important as the temperature rises unless the density is kept constant this is because ion association is inversely related to the dielectric constant (relative permittivity) of the medium, which is correlated with density for a given solvent. Helgeson and co-workers have attacked these problems theoretically for aqueous solutions up to 1000 °C.28 For our purposes, it is enough to note that quantitative treatment of ionic reactions in sub- and supercritical aqueous solutions is extremely difficult at present, and likely to remain so for some time. 

The values of AN are also included in Table 1.5.6) The solvent acidity increases with the increase in the AN value. Here, it should be noted that neither DN nor AN can be correlated with the relative permittivity of the corresponding solvents. 

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. ... 

Returning to our problem, we remark that the temperature dependences of such parameters as, for example, the Debye relaxation time td(7 ) (which determines the low-frequency dielectric spectra), or the static permittivity s are fortunately known, at least for ordinary water [17], As for the reorientation time dependence t(T), it should probably correlate with in(T), since the following relation (based on the Debye relaxation theory) was suggested in GT, p. 360, and in VIG, p. 512 ... 

In contrast to dielectric losses permittivity is not, in general, sensitive to small amounts of impurities and for homogeneous dielectrics values can be calculated as described in Section 2.7.1, and the various mixture rules allow good estimates to be made for multiphase dielectrics. For Ba- and Sr-based dielectrics having the perovskite structure the variation of permittivity with temperature, which determines rf (see Eq. (5.37)), can be correlated with the tolerance factor t (see Section 2.7.3) [13] providing guidance for tailoring ceramics to have xf = 0. 

Extending the media used for the Menschutkin reaction to protic solvents such as alcohols leads to an even worse correlation, as shown in Fig. 5-12 for the quaternization of l,4-diazabicyclo[2.2.2]octane with (2-bromoethyl)benzene studied in a total of thirty-six solvents [65], The group of protic solvents is separated from the assembly of non-HBD solvents, each group showing a very rough but distinct correlation with the function of relative permittivity. Such behaviour has also been observed for several other Menschutkin reactions [60, 61],... 

The polarity of the solvent exerts an appreciable effect on some of the hfc constants for pyridinyl radicals The effects have been correlated with the solvent polarity parameters, Z-value and Er(30)-value and a theory relating the shifts to the permittivity of the solvent has been published... 

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

The connection of dipole correlation with angular-momentum correlation cannot be quite so direct for a non-linear molecule. Rahman and Stillinger have published a detailed molecular-dynamics study of a water model containing 216 model molecules in a cube with periodic boundary conditions, at a density of 1 kg dm . The short-time behaviour of the molecules is dominated by librations at 1—2 x 10 Hz. They ve Cole-Cole plots of the electric permittivity estimated by applying an analysis due to Nee and Zwanzig to the computed molecular-correlation function. However, this application is uncertain in view of the... 

Djakovic-Sekulic et al. " separated eight anilides of 2,2-dimethylpropanoic acid, nine anilides of benzoic acid, and nine anilides of ot-phenyl acetic acid by RP-18 HPLC using mixtures containing methanol and water in volume proportions 6h-4, 6.5h-3.5, and 7-1-3 as the mobile phases. The log k values of investigated anilides have been correlated with the dipole moments ( raph) or permittivities (Emph) of the mobile phases applied, with numerical values of one topological index from among those based on the distance matrix R, W, A, B, B) or on the adjacency matrix (M, M, x with... 

It was pointed out earlier that the Gibbs energy of transfer of simple monatomic ions such as Na and CU is not related in any simple way to the dielectric permittivity of the solvent. On the other hand, for the alkali metal cations is correlated with solvent basicity. A plot of this quantity for the Na ion against the solvent s donor number DN is shown in fig. 4.15. Although the correlation is not excellent, it shows a clear trend in which AtrG° becomes more negative as DN increases. This is exactly what one expects because the ability of the solvent to stabilize the cation in solution increases with increase in solvent basicity. 

Namely, the LDL is in some respect similar to our LIB fraction regarding its connection with the HB network and dominance in contribution to the low-frequency spectrum (described by the first term in (39)), in particular, to the static permittivity 8S. However, in contrast to RAK, it is hardly reasonable to bring this fraction into correlation with the HB network itself due to the almost free libration of the dipoles in an intermolecular (hat) potential. On the other hand, it is reasonable to assign the VIB fraction to the HB network, which in our simplified calculation scheme is modeled by a dimer of oppositely charged water molecules connected by a hydrogen bond. Thus, in our opinion... 

It can be seen from the data that, as expected, the equilibrium constants are dependent on the solvent. The ratio of the stepwise stability constants is similarly solvent-dependent. The logarithms of the first stepwise equilibrium constants exhibit a reciprocal correlation with the Gutmann donicities of the solvents they therefore reflect the stabilities of the solvate complexes governed by the donicity of the solvent. On the other hand, the logarithm of the second stepwise equilibrium constant of the iodide ion association appears to be inversely proportional to the relative permittivity of the solvent. 

By presenting the joint occurrence of the double (donor and acceptor) effects of the solvents, this model also explained why it was not possible to describe solvent effects in these systems by means of a single empirical parameter. It is obvious that the standard AG values for dissolution, for example, could not give a linear correlation with parameters predominantly reflecting a single type of effect, e.g., the Kosower Z value, the Reichardt Ej value, the DN value, the AN value, the relative permittivity of the solvent alone. Even in systems where one of the effects is so predominant that the system can be described more or less with a single parameter, only calculations in which the other parameters are also taken into... 

The MO measurements provide information about the angular distribution of molecules in the x, y, and z film coordinates. To extract MO data from IR spectra, the general selection rule equation (1.27) is invoked, which states that the absorption of linearly polarized radiation depends upon the orientation of the TDM of the given mode relative to the local electric field vector. If the TDM vector is distributed anisotropically in the sample, the macroscopic result is selective absorption of linearly polarized radiation propagating in different directions, as described by an anisotropic permittivity tensor e. Thus, it is the anisotropic optical constants of the ultrathin film (or their ratios) that are measured and then correlated with the MO parameters. Unlike for thick samples, this problem is complicated by optical effects in the IR spectra of ultrathin films, so that optical theory (Sections 1.5-1.7) must be considered, in addition to the statistical formulas that establish the connection between the principal values of the permittivity tensor s and the MO parameters. In fact, a thorough study of the MO in ultrathin films requires judicious selection not only of the theoretical model for extracting MO data from the IR spectra (this section) but also of the optimum experimental technique and conditions [angle(s) of incidence] for these measurements (Section 3.11.5). 

Thirteen barbiturates have been separated by RP-HPTLC with 13 mobile phases (methanol-water in different volume compositions). The Rm values of barbiturates investigated have been correlated with the selected traditional structural descriptors, with the partition coefficients of the compounds, and with the dipole moments (/Xmph) or with the permittivities (emph) of the mobile phases applied. The most accurate prediction of the Rm values of the... 

The 7 m values of cis- and tra/i5-9-octadecenoic and 11-octadecenoic acids in aU the applied stationary phases and mobile phases could also be correlated with dipole moments (or permittivities) of mobile phases, with the impregnation percentages of stationary phases, and with numerical values of one topological index (IT, A, B, 7b) or electrotopological state of oxygen atoms. ... 

For PB the dipole moments are located on the vinyl side group aud the cis group. The partial charges, however, are small and that was the reason we did not include Coulomb forces into our MD simulation. Consequently, there can be no correlations due to the local dipole moment occurring in om simulation trajectory. We then have to see, how well our results for the dielectric permittivity agree with the experiments [22]. To this end we reinsert partial charges into the simulated trajectory. We know that we have to find... 

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