Dielectric inhomogeneities

Source Formulae derived in Section 5 of G. H. Weiss, J. E. Kiefer, and V. A. Parsegian, "Effects of dielectric inhomogeneity on the magnitude of van der Waals interactions," J. Colloid Interface Sci., 45, 615-625 (1973) Equation numbers in [ ] from that paper. yp here is "n" in source paper. 

The results for the density profiles (in mole/dm3 unit) are shown in Fig. 8. Comparing the results to Fig. 7 of [41] (where a similar geometry was used but without dielectric boundaries), it can be seen that the presence of dielectric inhomogeneity has a large effect on the charge distribution in the channel. In our earlier study [41] both the Ca++ and Na+ ions were concentrated in the center of the filter. On the contrary, our present results indicate that the Ca++... 

Furthermore, the impedance of a depressed Nyquist plot due to surface roughness, dielectric inhomogeneities and diffusion is defined as the Cole-Cole impedance formula [33-36]. Hence,... 

A novel optimization approach based on the Newton-Kantorovich iterative scheme applied to the Riccati equation describing the reflection from the inhomogeneous half-space was proposed recently [7]. The method works well with complicated highly contrasted dielectric profiles and retains stability with respect to the noise in the input data. However, this algorithm like others needs the measurement data to be given in a broad frequency band. In this work, the method is improved to be valid for the input data obtained in an essentially restricted frequency band, i.e. when both low and high frequency data are not available. This... 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

The capacitance determined from the initial slopes of the charging curve is about 10/a F/cm2. Taking the dielectric permittivity as 9.0, one could calculate that initially (at the OCP) an oxide layer of the barrier type existed, which was about 0.6 nm thick. A Tafelian dependence of the extrapolated initial potential on current density, with slopes of the order of 700-1000 mV/decade, indicates transport control in the oxide film. The subsequent rise of potential resembles that of barrier-layer formation. Indeed, the inverse field, calculated as the ratio between the change of oxide film thickness (calculated from Faraday s law) and the change of potential, was found to be about 1.3 nm/V, which is in the usual range. The maximum and the subsequent decay to a steady state resemble the behavior associated with pore nucleation and growth. Hence, one could conclude that the same inhomogeneity which leads to pore formation results in the localized attack in halide solutions. 

Characteristic properties of SCFs include variable density, dielectric constant viscosity, and cage strength, local inhomogeneity, high diffusion rate, high miscibility with gaseous substances, and high sensitivity of all properties to added substances. All... 

E. F. Kuester and D. C. Chang, Propagation, attenuation and dispersion characteristics of inhomogeneous dielectric slab waveguides, IEEE Trans Microwave Theory Tech. 23, 98-106 (1975). 

One aspect of the research will examine equilibrium aspects of solvation at hydro-phobic and hydrophilic interfaces. In these experiments, solvent dependent shifts in chromophore absorption spectra will be used to infer interfacial polarity. Preliminary results from these studies are presented. The polarity of solid-liquid interfaces arises from a complicated balance of anisotropic, intermolecular forces. It is hoped that results from these studies can aid in developing a general, predictive understanding of dielectric properties in inhomogeneous environments. 

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

The notion of homogeneity is not absolute all substances are inhomogeneous upon sufficiently close inspection. Thus, the description of the interaction of an electromagnetic wave with any medium by means of a spatially uniform dielectric function is ultimately statistical, and its validity requires that the constituents—whatever their nature—be small compared with the wavelength. It is for this reason that the optical properties of media usually considered to be homogeneous—pure liquids, for example—are adequately described to first approximation by a dielectric function. There is no sharp distinction between such molecular media and those composed of small particles each of which contains sufficiently many molecules that they can be individually assigned a bulk dielectric function we may consider the particles to be giant molecules with polarizabilities determined by their composition and shape. 

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