A numerical Kramers-Kronig transform for the calculation of dielectric relaxation losses free from Ohmic conduction losses

 A numerical Kramers–Kronig transform is described which allows the calculation of dielectric relaxation losses from dielectric constant data measured at a limited set of frequencies differing by a factor of 2. Conversion formulas for both the central frequencies and for frequencies near the edges of the experimental frequency window are derived. The approach used can be extended easily to measurement frequencies with a different logarithmic spacing. Using this conversion, relaxation and dissipative, conduction losses can be separated. In this way Ohmic conduction processes and simultaneously occurring relaxation processes like dipole or space-charge relaxations can be analysed independently. The results of some simulations and of calculations on experimental data for poly(vinyl-chloride) are used to illustrate the potentials of the ɛ′ to ɛ″ conversion. Received: 17 May 1996 Accepted: 16 August 1996     

On the relation between W'/W index, hyper-Wiener index, and Wiener numbers

It is shown analytically that the W'/W index, the hyper-Wiener index, and the Wiener number are closely related graph-theoretical invariants for acyclic structures. A general analytical expression for the hyper-Wiener index of a tree is derived too.     

On the relation of the non-linear dielectric effect to the kerr effect: closing a gap

A simple and uniform procedure is used to determine the non-linear dielectric effect in static fields, for probing fields with frequency either below or above the rotational relaxation region. Contributions from the permanent moment and the linear and non-linear polarizability of non-interacting particles are considered. A quantitative link with the Kerr effect is established. The different weight of contributions due to anisotropic polarizability and hyperpolarizability in both effects is emphasized.     

The relation between the nonlinear dielectric effect and solvent polarity

The relation between solvent polarity expressed through the Dimroth-Reichardt spectroscopic parameter E _T (30) and the nonlinear dielectric effect (NDE) expressed through the parameter /E² is demonstrated where is a change in the electric permittivity of a solvent in an external strong electric field E. Both E _T (20) and /E², determined in quite different ways, are extremely sensitive to the dielectric properties of a solvent which depend on molecular interactions. Linear correlations between /E² and E _T (30) have been found for n-alkanols representing hydrogenbond donor solvents, and for halogenobenzenes which are dipolar, aprotic, weakly-associated solvents.Part of this work was presented at The 22^nd International Conference on Solution Chemistry in Linz, Austria, July 1991.     

Size dependent index of refraction and absorption of a spherical metal cluster

Size-dependent optical properties of large metal clusters are studied on the example of spherical sodium clusters. The model is based on the fact, that a sphere filled with free-electron gas forms a cavity with size dependent eigenfrequencies of the optically excitable TM plasmons. Therefore the dielectric function of the system gains the resonant character. The dielectric function defines the size-dependent indices of absorption and of refraction.     

Determination of density and index of refraction of ozonides of sodium and potassium

Summary The densities and indices of refraction of sodium and potassium ozonides were determined.We consider it our pleasant duty to express our thanks to G. B. Bokii for assistance in the work.     

The relation between dilatometric and dielectric glass-transition temperatures

A simple method has been developed for extracting the “static” glass-transition temperature of a polymer from dielectric relaxation data. Only the temperature of the loss maximum and the activation energy at 1 kHz are required for the procedure.     

Influence of the dielectric constant on ion-pair and ion-ligand complex formation

The effect of dielectric constant on ion association of triethylammonium picrate and methylimidazolium picrate and on ion-ligand complex formation between the cations Et₃NH⁺ and MeImH⁺ and 1-methylimidazole was investigated from conductance data carried out in nitrobenzene-benzene mixtures (34.8K _A satisfy in first approximation the relation logK _A 1/D. The center-to-center distance å has been calculated and compared to the value obtained for nonhydrogenbonded ion pairs. The ion-ligand association constantK ₁ ⁺ increases as the dielectric constant of the medium decreases. Plots of logK ₁ ⁺ against 1/D give straight lines, the slopes of which are consistent with the predictions of a theory that interprets the effect of the dielectric constant in terms of changes in the polarization energy of the solvent around the complexed and the uncomplexed ions. For these interactions, the complexed ions can be approximated as charged spheres, the volume of which is equal to that of the bare ion plus the volume of the ligand.     

Numerical analysis of complex dielectric mixture formulae

As a continuation of our earlier work (Ref. [9]) the complex (frequency dependent) dielectric behaviour of some mixture formulae are studied numerically. These include matrix-inclusion type formulae (as the Wagner-Sillars or the Bruggeman-Boyle equations), mean-field statistical mixture formulae (as the Böttcher-Hsu equation) and symmetrical integral formulae (as the Looyenga equation). The frequency dependent dielectric properties are first calculated for a model system at various particle shapes, field orientations and volume fractions. After this, the validity of these equations is checked on typical sets of experimental data. For low loss powders, the Böttcher and Looyenga equations are suggested; for emulsions, suspensions and filled polymers, the matrix-inclusion type formulae give acceptable results in most cases, while for metal-insulator composites mean-field statistical mixture formulae have to be used, as they are capable of describing the percolation phenomenon.     

On the complex refractive index of N-doped TiO2 nanospheres and nanowires in the terahertz spectral region

In this paper, the terahertz (THz) transmission measurement technique was applied to characterize titanium dioxide (TiO₂) nanospheres and nanowires subjected to thermal treatments under various conditions. Differences in the spectral features of the nanospheres and nanowires were observed due to treatment and annealing of the samples in different gas atmospheres. The observations made can be explained based on the formation of new phonon bands and/or widening of the phonon bands due to polymorphism. A singly subtractive Kramers Kronig dispersion relation was utilized to estimate the frequency-dependent real refractive index of the various samples, having a priori unknown sample thickness, from the absorbance data.     

Distance and exposure dependent effective dielectric function

In an effort to develop a dielectric screening function for molecular dynamics simulations of biomolecules in implicit solvent, effective dielectric constants (D(eff)) for a large number of atom pairs in a typical globular protein are calculated by continuum electrostatics. Plots of D(eff) versus the intercharge distance are in general sigmoidal with the characteristics of the curve depending on the distance of the two charges from the dielectric boundary and, secondarily, on the extent to which the area surrounding each charge is occupied by solvent (the "exposure"). The D(eff) values were fitted to an empirical, analytical function of these parameters that reproduces the data reasonably well, although considerable scatter exists in the range of D(eff) from 30 to 80. In the system used for parameterization, the mean square deviation of electrostatic interaction energies with this function is 0.48 kcal/mol, compared to 1.45 for an analytical Generalized Born model and 1.52 for the linear distance-dependent dielectric model. When tested in other proteins of varying size and compactness, the present function is superior to both of the above models, except for a fully unfolded polypeptide chain, where the Generalized Born model is superior.     

On the atomic refraction of nitrogen in certain organophosphorous compounds

Conclusions In calculating the molecular refraction of organophosphorus compounds containing one or several tertiary amide groups in the molecular, the atomic refraction of nitrogen should apparently be assumed equal to 2.4.     

Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements

The cavity enhanced Raman scattering spectrum recorded from an aerosol droplet provides a unique fingerprint of droplet radius and refractive index, assuming that the droplet is homogeneous in composition. Aerosol optical tweezers are used in this study to capture a single droplet and a Raman fingerprint is recorded using the trapping laser as the source for the Raman excitation. We report here the retrieval of the real part of the refractive index with an uncertainty of ± 0.0012 (better than ± 0.11%), simultaneously measuring the size of the micrometre sized liquid droplet with a precision of better than 1 nm (< ± 0.05% error). In addition, the equilibrium size of the droplet is shown to depend on the laser irradiance due to optical absorption, which elevates the droplet temperature above that of the ambient gas phase. Modulation of the illuminating laser power leads to a modulation in droplet size as the temperature elevation is altered. By measuring induced size changes of <1 nm, we show that the imaginary part of the refractive index can be retrieved even when less than 10 × 10(-9) with an accuracy of better than ± 0.5 × 10(-9). The combination of these measurements allows the complex refractive index of a droplet to be retrieved with high accuracy, with the possibility of making extremely sensitive optical absorption measurements on aerosol samples and the testing of frequently used mixing rules for treating aerosol optical properties. More generally, this method provides an extremely sensitive approach for measuring refractive indices, particularly under solute supersaturation conditions that cannot be accessed by simple bulk-phase measurements.     

An interlayer model for the complex dielectric constant of composites

The complex dielectric constant of a composite with an interlayer was studied as a function of the volume fractions and the properties of the filler, the interlayer, and the matrix. The theoretical approach is analogous to the calculation of the shear modulus, the bulk modulus, and the termal expansivity of particulate filled polymers using the interlayer model (IM).An analytical expression describing the influence of an interlayer on the generalized dielectric constant of the composite as a function of the volume fraction and interlayer properties is derived.In the case of a composite with non-conductive constituents, the equations for static and oscillatory electric fields are similar. When conductive constituents are present, the complex dielectric constants have to be replaced by the generalized complex dielectric constants.For a composite of non-conductive materials, without interlayer, the obtained relation reduces to the classical Rayleigh equation. In the case of a composite with conductive constituents, also without interlayer, the complete solution of Wagner's theory is found. Special attention has been paid to the case of a water interlayer in a glass-bead filled non-conductive matrix material.     

On the dielectric constant of nonpolar fluids

Referring to a recent paper in this journal of Stell and Rushbrooke the deviation from the Clausius-Mossotti relation for the static dielectric constant of a nonpolar fluid is discussed. In particular a number of coefficients in the dielectric virial expansion have been evaluated for a hard-sphere system.     

On the dielectric constant of nonpolar fluids

We discuss the recent work of Wertheim on the dielectric constant of nonpolar fluids, and also present some new calculations on the Kirkwood-Yvon theory. These serve to emphasise the prime importance of the state dependence of the effective polarisability in interpreting deviations from the Clausius-Mossotti theory for real dense fluids.     

Effect of refraction index and thickness of the light guide in the position-sensitive gamma-ray detector using compact PS-PMTs

We constructed a position-sensitive gamma-ray detector consisting of an array of BGO scintillators, a light guide and compact PS-PMTs. The effects of refractive index and thickness of the light guide of a glass plate on the detector performance were investigated. A light guide with higher refractive index and smaller thickness is found better for a good spatial resolution.