Application of Bruggeman and Maxwell Garnett homogenization formalisms to random composite materials containing dimers (original) (raw)
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On the application of homogenization formalisms to active dielectric composite materials
Optics Communications, 2009
The Maxwell Garnett and Bruggeman formalisms were applied to estimate the effective permittivity dyadic of active dielectric composite materials. The active nature of the homogenized composite materials (HCMs) arises from one of the component materials which takes the form of InAs/GaAs quantum dots. Provided that the real parts of the permittivities of the component materials have the same sign, the Maxwell Garnett and Bruggeman formalisms give physically plausible estimates of the HCM permittivity dyadic that are in close agreement. However, if the real parts of the permittivities of the component materials have different signs then there are substantial differences between the Bruggeman and Maxwell Garnett estimates. Furthermore, these differences becomes enormous -with the Bruggeman estimate being physically implausible -as the imaginary parts of the permittivities of the component materials tend to zero. 3 These formalisms are readily extended to estimate the relative permittivity of HCMs arising from a mixture of three or more component materials .
Effective dielectric constant of random composite materials
Journal of Applied Physics, 1997
The randomness in the structure of two-component dense composite materials influences the scalar effective dielectric constant, in the quasistatic limit. A numerical analysis of this property is developed in this paper. The computer-simulation models used are based on both the finite element method and the boundary integral equation method for two-and three-dimensional structures, respectively. Owing to possible anisotropy the orientation of spatially fixed inhomogeneities of permittivity 1 , embedded in a matrix of permittivity 2 , affects the effective permittivity of the composite material sample. The primary goal of this paper is to analyze this orientation dependence. Second, the effect of the components geometry on the dielectric properties of the medium is studied. Third the effect of inhomogeneities randomly distributed within a matrix is investigated. Changing these three parameters provides a diverse array of behaviors useful to understand the dielectric properties of random composite materials. Finally, the data obtained from this numerical simulation are compared to the results of previous analytical work.
Physical Review B, 2001
We have carried out numerical simulations on the effective transport properties of composites consisting of well separated conductive spherical inclusions in an insulating matrix. The simulations show that the effective permittivity depends markedly on the size distribution of the inclusions. Results are presented in a broad range of filling factors and degrees of polydispersity. For a simple cubic lattice of identical spheres the calculated values agree exactly with the analytical solution. The Maxwell-Garnett model has shown to describe well the case of randomly distributed uniformly sized inclusions independently of the concentration, even at filling factors up to 30%. With increasing degree of polydispersity the permittivity rises towards a limiting value close to the Bruggeman result.
Size-dependent Bruggeman approach for dielectric–magnetic composite materials
AEU - International Journal of Electronics and Communications, 2005
Expressions arising from the Bruggeman approach for the homogenization of dielectric-magnetic composite materials, without ignoring the sizes of the spherical particles, are presented. These expressions exhibit the proper limit behavior. The incorporation of size dependence is directly responsible for the emergence of dielectric-magnetic coupling in the estimated relative permittivity and permeability of the homogenized composite material.
Recent Advances in the Characterization of Composite Dielectric Structures
The central problem in predicting the dielectric behavior of heterogeneous materials (like, e.g., composite or nanostructured systems, powders or mixtures) consists in the evaluation of their effective macroscopic properties, still taking into account the actual microscale material features. This leads to the concept of homogenization, a coarse graining approach addressed to determine the relationship between the microstructure and the effective behavior: the prediction of the effective electromagnetic properties of a composite material from those of its constituent material phases is the major objective of various homogenization models. The resulting effective properties can be observed at the macroscale, where the refined effects of the morphology cannot be directly measured. Dispersions of particles (inclusions with a given shape and a given volume) in a host homogeneous matrix are the most studied heterogeneous structures. From the historical point of view, early mixture theories generally work well when the volumetric proportion of the inclusion phase is small and when the contrast between the electromagnetic properties of the two material phases is not large. More recently, refined and improved models have been developed in order to yield better predictions, also in these critical situations. Recent increases in activity in the field are, at least, partially caused by the interest in selective absorbers of solar and infrared radiation, by an increasing number of applications in astronomy and atmospheric physics, by several applications in the design of novel materials in optics and in material science, and by the indications that the electromagnetic behavior of the composite system may be very different from the behavior of individual components.
IEEE Transactions on Electromagnetic Compatibility, 2000
A mixing rule in the theory of composites is intended to describe an inhomogeneous composite medium containing inclusions of one or several types in a host matrix as an equivalent homogeneous medium. The Maxwell Garnett mixing rule is widely used to describe effective electromagnetic properties (permittivity and permeability) of composites, in particular, biphasic materials, containing inclusions of canonical shapes (spherical, cylindrical, or ellipsoidal). This paper presents a procedure for deriving an equivalent Debye model that approximates the geometry-based Maxwell Garnett model for randomly distributed cylindrical inclusions. The derived Debye model makes the equivalent dielectric material suitable for any time-domain electromagnetic simulations.
Effective permittivity of random composite media: A comparative study
Physica B: Condensed Matter, 2007
In the present study, experimental data for effective permittivity of amorphous, polycrystalline thick films, and ceramic form of samples, taken from the literature, have been chosen for their comparison with those yielded by different mixture equations. In order to test the acceptability of dielectric mixture equations for high volume fractions of the inclusion material in the mixture, eleven such equations have been chosen. It is found that equations given by Cuming, Maxwell-Wagner, Webmann, Skipetrov and modified Cule-Torquato show their coherence and minimal deviation from the experimental results of permittivity for all the chosen test materials almost over the entire measurement range of volume fractions. It is further found that Maxwell-Wagner, Webmann, and Skipetrov equations yielded equivalent results and consequently they have been combined together and reckoned as a single equation named MWWS. The study revealed that the Cuming equation had the highest degree of acceptability (errors o71-5%) in all the cases. r
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.
Effective permittivity of mixtures of anisotropic particles
Journal of Physics D: Applied Physics, 2009
We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotropic multicomponent mixtures of anisotropic inhomogeneous dielectric particles. Two factors of anisotropy are taken into account, the shape of the particles and anisotropy of the dielectric parameters of the particles' substances. Our approach is based upon the notion of macroscopic compact groups of particles and the procedure of averaging of the fields over volumes much greater than the typical scales of these groups. It enables us to effectively sum up the contributions from multiple interparticle reemission and short-range correlation effects, represented by all terms in the infinite iterative series for the electric field strength and induction. The expression for the effective permittivity can be given the form of the Lorentz-Lorenz type, which allows us to determine the effective polarizabilities of the particles in the mixture. These polarizabilities are found as integrals over the regions occupied by the particles and taken of explicit functions of the principal components of the permittivity tensors of the particles' substances and the permittivity of the host medium. The case of a mixture of particles of the ellipsoidal shape is considered in detail to exemplify the use of general formulas. As another example, Bruggeman-type formulas are derived under pertinent model assumptions. The ranges of validity of the results obtained are discussed as well.
On micro-structural effects in dielectric mixtures
Journal of Physics D, 2004
The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an important role in the electrical properties of the composite, are introduced both for designing and analyzing material mixtures. Later, influence of structural differences and intrinsic electrical properties of constituents on the composite’s over all electrical properties are investigated. The structural differences are resolved by the spectral density representation approach. At low concentrations of inclusions (concentrations lower than the percolation threshold), the spectral density functions are delta-sequences, which corresponds to the predictions of the general MaxwellGarnett mixture formula. At high concentrations of inclusions (close to the percolation threshold) systems exhibit non-Debye type dielectric dispersions, and the spectral density fun...