Effective permittivity of mixtures of anisotropic particles (original) (raw)
Related papers
Effective permittivity of dielectric mixtures
IEEE Transactions on Geoscience and Remote Sensing, 1988
In this paper, general mixing formulas are derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasi-static analysis, assuming the diameter of the inclusion particles to be much smaller than wavelength. The results are applicable to general multiphase mixtures, and the scattering ellipsoids of the different phases can have different sizes and arbitrary ellipticity distribution and axis orientation, i.e., the mixture may be isotropic or anisotropic. The resulting mixing formula is nonlinear and is especially suitable for iterative solutions. The formula contains a quantity called the apparent permittivity, and with different choices of this quantity, the result leads to the generalized Lorentz-Lorenz formula, the generalized Polder-van Santen formula, and the generalized coherent potential-quasicrystalline approximation formula. Finally, the results are applied to calculating the complex effective permittivity of snow and sea ice.
Electromagnetic Modeling of Dielectric Mixtures
Journal of Research Updates in Polymer Science, 2013
Electromagnetic modeling of dielectric materials allows us to study the effects of electromagnetic wave propagation and how such electromagnetic fields influence and interact with them. Dielectric materials are composites or mixtures, which often are made up of at least two constituents or phases. Modelling the electromagnetic behaviour of dielectric mixtures is crucial to understand how geometrical factors (shape and concentration), electromagnetic properties of inclusions and background medium, influence the permittivity of the overall material. The aim of this work is to develop new analytical models for dielectric mixtures, in order to describe their electromagnetic behaviour and design them with desired electromagnetic properties, for specific required applications. In particular, in this paper a new general expression for the effective permittivity of dielectric mixture is presented. The mixtures consist of inclusions, with arbitrary shapes, embedded in a surrounding dielectric environment. We consider the hosting environment and the hosted material as real dielectrics, both of them as dispersive dielectrics. The proposed analytical models simplify practical design tasks for dielectric mixtures and allow us to understand their physical phenomena and electromagnetic behaviours.
Progress In Electromagnetics Research, 2009
An analytical model of an effective permittivity of a composite taking into account statistically distributed orientations of inclusions in the form of prolate spheroids will be presented. In particular, this paper considers the normal Gaussian distribution for either zenith angle, or azimuth angle, or for both angles describing the orientation of inclusions. The model is an extension of the Maxwell Garnett (MG) mixing rule for multiphase mixtures. The resulting complex permittivity is a tensor in the general case. The formulation presented shows that the parameters of the distribution law for orientation of inclusions affect the frequency characteristics of the composites, and that it is possible to engineer the desirable frequency characteristics, if the distribution law is controlled.
How strict are theoretical bounds for dielectric properties of mixtures?
IEEE Transactions on Geoscience and Remote Sensing, 2002
This report discusses bounds for mixing rules. Several theoretical bounds and limits for the effective permittivity of heterogeneous media have been derived. However, it may happen that the bounds are trespassed in the real-life applications. Examples of such behavior are given for snow, random media simulations, lossy heterogeneous materials, and magnetic and magnetoelectric materials. Reasons for the bound-violation phenomenon are discussed.
Dielectric mixtures: electrical properties and modeling
IEEE Transactions on Dielectrics and Electrical Insulation, 2002
A review of current state of understanding of dielectric mixture properties and approaches to use numerical calculations for their modeling are presented. It is shown that interfacial polarization can yield different non-Debye dielectric responses depending on the properties of the constituents, their concentrations and geometrical arrangements. Future challenges on the subject are also discussed.
Effective dielectric properties of packed mixtures of insulator particles
Physical Review B, 1994
We present an expression, obtained by following the principles of the effective medium theory (EMT), to compute average dielectric properties of mixtures of random ellipsoids. We show that our formulation is quite general and includes former expressions, valid only for dilute mixtures, as particular cases; moreover it gives accurate predictions when compared with experimental measurements in the whale range of filling factors. The expression can be extended to mixtures of irregularly shaped particles with very little loss of accuracy. Also, our equation is suitable to be used with anisotropic samples. The equation requires an additional parameter, which amounts to a percolation threshold, to the parameters usually employed to describe a binary mixture in EMT, namely, the dielectrical functions of the components and the filling factor. This parameter contains information about the geometry of the particle packing, and approximate values have been found by numerical simulation of di8'erent arrangements of spheres in a matrix. Reflectance IR spectra have been measured on pressed pellets of particles of LiF, MgO, a-Fe203, and MgA1204 and compared with the spectra predicted by the expression presented in this paper, and other previous formulations.
A formula for dielectric mixtures
Philosophical Magazine Letters, 2005
Dielectric properties of material mixtures are of importance in diagnostics, characterization and design of systems in various engineering fields. In this Letter, we propose a peculiar dielectric mixture expression, which is based on the dielectric relaxation phenomena and the spectral density representation [E. Tuncer J. Phys. Condens. Matter 17(12) L125 (2005)]. The expression is tested on several composite systems. Results illustrate that the proposed expression can be used to obtain valuable structural informations in composites, even for highly filled, bi-percolating, systems. Lastly, the proposed expression is an alternative to other existing homogenization formulas in the literature.
Mixing Rules with Complex Dielectric Coefficients
2000
This article discusses the determination of effective dielectric properties of hetereogeneous materials, in particular media with lossy constituents that have complex permittivity parameters. Several different accepted mixing rules are presented and the effects of the structure and internal geometry of the mixture on the effective permittivity are illustrated. Special attention is paid to phenomena that the mixing process causes in the character of the macroscopic dielectric response of the mixture when the losses of one or several of the components are high or when there is a strong dielectric contrast between the component permittivities.
Numerical analysis of complex dielectric mixture formulae
Colloid and Polymer Science, 1988
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.