Dispersion of dielectric constant

We have found that the proposed structure of water, based upon the centred pentagonal dodecahedron, accounts in a reasonably satisfactory way for several properties of water, including the dispersion of dielectric constant and the radial distribution curve as determined by x-ray diffraction. A detailed description of this work will be published later. 

Fig. 11. Effect of dielectric constant of dispersed particle on the ER effect in a polymer gel. The increment in shear storage modulus induced by an ac electric field of 0.4 kV/mm is plotted as a function of the real part of the dielectric constant of the particle...

Fig. 6. Maxwell-Garnett theory used for the prediction of dielectric constant containing dispersed regions of low dielectric polymer (e = 2.0,0) or air (e = 1.0, )...

Dipole-induced dipole interaction energies are proportional to the product of the square of the dipole moment and the polarizability a of the atom/group with which the ion interacts, divided by the product of the square of dielectric constant D and the sixth power of the distance between the dipole and the polarizable group. Dispersion interactions have energies that are proportional to the product of polarizabilities i and 2. divided by the sixth power of the distance between two polarizable atoms (or groups of atoms). 

As zero state of our system we chose that state in which all constituents are dispersed to infinite dilution within a dielectric of dielectric constant Dq (which value may or may not be chosen as D0 = 1). Then we obtain the contribution to the work function by imagining the system charged (in the way calculated above) at the given concentrations in a system of dielectric constant D and subsequently discharged at infinite dilution in a medium of dielectric constant Do. Adding over all species of particles we obtain an expression for the work function which can be written in the form... 

Molecular dipolar polarization was difficult to define from dielectric measurements. A large first dispersion in time for isothermal cures of Resin 5208 is attributed to charge migration in a viscous medium. High values of dielectric constant and dielectric loss factor are attributed to the formation of an ion double-layer and sample conductivity, respectively. Limited frequency data on a smaller second dispersion prevent unequivocal assignment of its relationship to molecular changes. 

Now, ice has a dielectric dispersion over the range 10 -10 Hz, and water over the range 10 Hz-10 Hz. Thus, the high rate of fall of dielectric constant with increased concentration for linear polyelectrolytes may come from the icelike structure of water in their vicinity. 

As an illustration consider the adsorption of molecules into zeolites, discussed in Chapter 2. If an adsorbate molecule or atom is immersed in a medium of dielectric constant z( ) instead of a vacuum, the dispersion selfenergy is modified, and now takes a form corresponding to eq. (3.1)... 

Measurements of dielectric constant as a function of frequency. These dielectric dispersion measurements permit the estimation of the relaxation times or rotary diffusion constants which characterize the rotary Brownian movement of the protein molecule. 

Figure 9. Dispersion surface of dielectric constant of thermoset derived from BCB-l monomer as a function of temperature.

Fig-1 Maxwell-Garnett theory used for the prediction of dielectric constant containing dispersed regions of air... 

Efforts at loading titanium oxide nanoparticles in PVA (commercially available from Nanophase) have been reported [65], In this report, titanium nanoparticles are dispersed in an aqueous solution of PVA with poly(melamine-co-formaldehyde). The solution is spun onto substrate and heated to generate a cross-Unked polymer-nanoparticle dielectric. A modest enhancement of dielectric constant is achieved for 600-nm thick films. Thin-film transistors using this composite show excellent pen-tacene mobility (> 0.2 cm V s ) and reasonable on/off ratios 10. Vj- —TV is reasonably high, suggesting static charge at the dielectric-semiconductor interface. 

The presence of dispersed particles may significantly affect the value of dielectric constant of disperse system. In some cases, e.g. in non-aggregated (non-flocculated) inverse emulsions (Chapter VIII,3), the dielectric constant is related to the volume fraction of droplets in the emulsion, VKi, by the Bruggerman relationship... 

In aqueous systems in which particles are surrounded by a well-developed double layer, such as in sols and emulsions, sharp increase in dielectric constant is observed at particular frequencies of external field. The observed unusually high values of dielectric constants typical for such systems (Fig. V-12) are due to the fact that particles move relatively to the surrounding ionic atmosphere as charges of high magnitude. At high frequencies of external field such motion becomes impossible, and dielectric constant assumes its normal values. The studies of such trends in dielectric constant are in the basis of dielectric spectroscopy, which is an effective method for investigation of disperse systems, and in particular of emulsions [15]. 

The simplicity of idealized electrostatic solvation models has led to the use of dielectric constant (e) and of the permanent dipole moment (p) as parameters of the so-called solvent polarity. However, the dielectric constant describes only the change in the electric field intensity that occurs between the plates of a condenser, when the latter is removed from vacuum and placed into a solvent. This induces a dipole moment in nonpolar solvent molecules and dipolar molecules are aligned. Hence, the dielectric constant describes only the ability of a solvent to separate electrical charges and orient its dipolar molecules. The intermolecular forces between solute and solvent molecules are, however, much more complicated in addition to the non-specific coulombic, directional, inductive and dispersion interactions, can also be present specific hydrogen bond, electron-pair donor (EPD)/electron-pair acceptor (EPA), and solvophobic interactions in solutions. 

Solvent Properties.—Dielectric Constant. The examination of the dependence of rate on dielectric constant remains a popular exercise, for substitution as well as for redox reactions. The small increase in the rate of hydrolysis of 2,4-dichlorophenyl phosphate on changing the solvent from 10% to 60% dioxan, i.e. on decreasing the dielectric constant markedly, is claimed to demonstrate dispersion of charge in transition-state formation. Other reactions of compounds of the ip-block elements where the effect of dielectric constant variation on rate is discussed include the semi-organic reactions of butyl-lithium with t-butyl peroxide and of formate with... 

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