Application of Bruggeman and Maxwell Garnett homogenization formalisms to random composite materials containing dimers

The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials being coupled to form dimers. The Bruggeman and Maxwell Garnett formalisms were developed to estimate the permittivity dyadic of the homogenized composite material (HCM), under the quasi-electrostatic approximation. Both randomly oriented and identically oriented dimers were accommodated; in the former case the HCM is isotropic, whereas in the latter case the HCM is uniaxial. Representative numerical results for composite materials containing dielectric–dielectric dimers demonstrate close agreement between the estimates delivered by the Bruggeman and Maxwell Garnett formalisms. For composite materials containing metal–dielectric dimers and metal–metal dimers with moderate degrees of dissipation, the estimates of the two formalisms are in broad agreement, provided that the dimer volume fractions are relatively low. In general, the effects of intradimer coupling on the estimates of the HCM’s permittivity are relatively modest but not insignificant, these effects being pronounced by anisotropy when all dimers are identically oriented.     

Gain and loss enhancement in active and passive particulate composite materials

Two active dielectric materials may be blended together to realize a homogenized composite material (HCM) which exhibits more gain than either component material. Likewise, two dissipative dielectric materials may be blended together to realize an HCM which exhibits more loss than either component material. Sufficient conditions for such gain/loss enhancement were established using the Bruggeman homogenization formalism. Gain/loss enhancement arises when (i) the imaginary parts of the relative permittivities of both component materials are similar in magnitude and (ii) the real parts of the relative permittivities of both component materials are dissimilar in magnitude.     

On the Bergman-Milton bounds for the homogenization of dielectric composite materials

The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter regimes for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large.     

A mixing rule for predicting frequency dependence of material parameters in magnetic composites

A number of mixing rules are proposed in the literature to predict the dependence of effective material parameters (permittivity and permeability) of composites on frequency and concentration. However, the existing mixing rules for frequency dependence of permeability in magnetic composites typically do not provide satisfactory agreement with measured data. Herein, a simple mixing rule is proposed. Its derivation is based on the Bergman-Milton spectral theory. Both the Bruggeman effective medium theory and the Maxwell Garnett approximation are included as particular cases of the proposed mixing rule. The derived mixing rule is shown to predict accurately the frequency dependence of permeability in magnetic composites, which contain nearly spherical inclusions.     

Percolation thresholds in the homogenization of spheroidal particles oriented in two directions

We consider percolation thresholds which arise in the homogenization of composite mediums based on three different types of component particles. An extension of the standard Bruggeman homogenization formalism is implemented in order to take account of the sizes, shapes, and orientations of the component particles. The relationships between the geometric attributes of the component particles and the constitutive parameters of the homogenized composite mediums are investigated. In particular, percolation thresholds arising in the homogenization of conducting component particles oriented in two directions and nonconducting component particles are explored via representative numerical examples. Anisotropies in these percolation thresholds are highlighted.     

Linear and nonlinear optical properties of highly concentrated gold nanoparticles

Linear and nonlinear (NL) optical properties of composite materials containing high concentration of gold nanoparticles (NPs) were studied using the Maxwell–Garnett model and the degenerated electron gas model. High values of the linear refraction index of the composite, NL shift of the plasmon resonance peak and reversal sign of the real and imaginary parts of the NL third-order susceptibility were observed. Figures of merit for photonic devices were calculated and fulfilled depending of the filling factor and NPs size.     

Complex permittivity and microwave absorption properties of carbon nanotubes/polymer composite: A numerical study

Based on an equivalent resistance-capacitance (RC) network, we investigate theoretically the complex permittivity and microwave absorption properties of carbon nanotubes (CNTs)/polymer composite in the frequency range of 50 MHz-3 GHz using the logarithmic mixing rule. Both the real and imaginary parts of the permittivities of CNTs and polymer are considered in detail. The simulated results show that the real and imaginary permittivities of the composite increase explicitly with increasing volume fraction of CNTs, and the latter is more sensitive. The calculated complex permittivity spectra of the composite are in good agreement with the available experimental data. In addition, a good linear relationship between microwave absorbance and frequency is found.     

On Tailoring of Nonlinear Spectral Properties of Nanocomposites Having Maxwell Garnett or Bruggeman Structure

Nonlinear spectral properties of two different types of conjugated polymers (polythiophene PT10 and polysilane PDHS) with nanoscale TiO₂ particles forming a Maxwell Garnett or a Bruggeman composite are studied. According to the present simulations, it is possible both to enhance and to tailor the magnitude and the spectral properties, respectively, of the effective degenerate third-order nonlinear susceptibility of the composite. This is done simply by tuning the volume fraction of TiO₂ inclusions and by changing the topology of the composite.     

Compact group method in the theory of permittivity of heterogeneous systems

The static permittivity of macroscopically homogeneous and isotropic heterogeneous systems is analyzed using the concepts of compact groups of inhomogeneities. The method makes it possible to avoid excessive specification of mutual polarization processes in the system, which ensures effective application of this method for concentrated systems with arbitrary relations between the permittivities of system components. By way of example, the Maxwell-Garnett and Bruggeman formulas for the effective permittivity of heterogeneous matrix systems are reconstructed and their interrelation is analyzed. It is shown that the Bruggeman formula is more limited in the sense that it is based on additional model assumptions concerning the properties of the system and the type of averaging of fields over the volume of the system. Generalizations of these formulas are obtained for multicomponent heterogeneous systems consisting of inhomogeneous nonspherical particles or parts.     

高浓度纤维增强材料介电特性计算方法

针对复合材料的微观结构非均匀和各向异性特点带来的数值方法计算慢、内存消耗大的问题,利用均匀化方法计算纤维增强复合材料的等效电磁参数.采用了纤维低体积添加比至高体积添加比的迭代方法,同时提出了一个描述材料微观结构的修正的特征长度,将现有的均匀化方法推广至非准静态(微波频段)条件下高纤维浓度情况.提出的修正的均匀化模型可直接用于反射系数、屏蔽效能等计算,其屏蔽效能与实际微观结构复合材料的数值仿真结果进行了对比,验证了提出的等效电磁参数计算公式的有效性和频率适用范围.     

Tailoring the microwave permittivity and permeability of composite materials

The microwave permittivity (ɛ_r) and permeability (μ_r) of composite materials are tailored by adding various loading agents to a host plastic and are subsequently modeled using the Maxwell Garnett theory and second order polynomials. With the addition of manganese zinc ferrite, strontium ferrite, nickel zinc ferrite, barium tetratitanate and graphite powders, materials with values of ɛ′, e″, μ′, μ″ as high as 22, 5, 2.5 and 1.7 have been obtained. Permittivity and permeability data are calculated at 2.0245 GHz from reflection and transmission measurements performed in a 7 mm coaxial test line. The Maxwell Garnett (MG) theory successfully models ɛ_r if the filling factor is less than 0.30 and ratio |ɛ₁| (host)/ |ɛ₂| (powder) is greater than 0.04. As this ratio decreases, the MG theory is shown to be independent of ɛ₂ and second order polynomials are used to effectively model the dielectric constant. Polynomials are also used for the ferrite composites because it was determined that the MG theory was unable to model μ_r. This deficiency is attributed to the difference of domain structures that exist in powdered and sintered ferrites.     

Modeling of ferrite-based materials for shielding enclosures

An analytical model for a magneto-dielectric composite material is presented based on the Maxwell Garnett rule for a dielectric mixture, and on Bruggeman's effective medium theory for permeability of a ferrite powder embedded in a dielectric. In order to simultaneously treat frequency-dispersive permittivity and permeability of a composite in a full-wave FDTD code, a new algorithm based on discretized auxiliary differential equations has been implemented. In this paper, numerical examples of modeling structures containing different magneto-dielectric mixtures are presented.     

On chemiluminescent emission from an infiltrated chiral sculptured thin film

The theory describing the far-field emission from a dipole source embedded inside a chiral sculptured thin film (CSTF), based on a spectral Green function formalism, was further developed to allow for infiltration of the void regions of the CSTF by a fluid. In doing so, the extended Bruggeman homogenization formalism — which accommodates constituent particles that are small compared to wavelength but not vanishingly small — was used to estimate the relative permittivity parameters of the infiltrated CSTF. For a numerical example, we found that left circularly polarized (LCP) light was preferentially emitted through one face of the CSTF while right circularly polarized (RCP) light was preferentially emitted through the opposite face, at wavelengths within the Bragg regime. The centre wavelength for the preferential emission of LCP/RCP light was red shifted as the refractive index of the infiltrating fluid increased from unity, and this red shift was accentuated when the size of the constituent particles in our homogenization model was increased. Also, the bandwidth of the preferential LCP/RCP emission regime decreased as the refractive index of the infiltrating fluid increased from unity.     

Effective permittivity of periodic composite materials: Numerical modeling by the finite element method

The effective properties of composite materials are closely related to the composition and arrangement of its constituents. Many studies and articles are actively studying the dielectric properties of heterogeneous structures with random and periodic arrangement. In the quasistatic limit, we use the finite element method as a numerical tool to evaluate the effective permittivity of two and three component composites. Two heterostructures are investigated; the first is formed by crossed dielectric cylinders in permanent contact and arranged in three layers. The cylinders are immersed in a dielectric host medium. The second structure is similar to the first except that the tubes are covered by an interphase layer. The numerical tool used to extract the exact value of the effective permittivity takes into account all internal multipolar interactions which contribute to the polarization of the material medium. The impacts of the relative permittivity and volume fraction of cylinders, the thickness of interphase and its dielectric constant are reported. The Maxwell–Garnett theory fails to predict the effective permittivity of the studied structures for high volume fraction and permittivity contrast. To overcome this problem, an amendment was made to the McLachlan equation McQ also termed the Two Exponent Single Percolation Equation TESPE. The first exponent t is held equal to 1 and the other exponent s is depending on the volume fraction. s is calculated so that the whole values of the effective permittivity obtained by the McQ rule are exactly the same values obtained by the simulations. Finally, we obtained a chart and a model to find the values of s, a fast way that is very useful for practitioners and design engineers of composite materials.     

Microwave radiative transfer in scattering atmosphere: Effects of complex permittivity of ice spherical crystals

This paper presents the effects of ice particle's complex permittivity uncertainties on the scattering properties and upwelling brightness temperatures of cloudy atmospheres at the Advanced Microwave Sounding Unit-B (AMSU-B) channel frequencies of 89, 150 and 183 GHz. We investigated the mean deviations of ice particle's optical efficiencies and asymmetry parameters due to the uncertainties in the real and imaginary parts of its complex permittivities. We assumed that the true values of ice particle's permittivity are, respectively, within ±20% for the imaginary part and ±5% for the real part of the permittivity values given by the model of Hufford. Microwave radiative transfer calculations were performed to estimate the absolute errors of brightness temperatures due to uncertainties in ice particle's permittivities. Ice particles were taken to be spherical and their diameters were chosen in the range of 40-4000 μm. Gamma-size distribution was employed in computing volume scattering properties and the effective diameters were 70, 100 and 150 μm with an effective variance being 0.25. We found that ±20% uncertainty in the imaginary part of ice particle's permittivity resulted in only about 10% mean deviations in the absorption efficiencies at the three AMSU-B channel frequencies. However, an uncertainty of ±5% in the real part resulted in more than 15% mean deviations in both scattering and extinction efficiencies, especially significant at the frequency of 183 GHz. The absolute variations of the emerging brightness temperature from the cloudy atmosphere due to uncertainties in the permittivity were found to be more than 1 K, which is already significant compared with the sensitivities achieved with today's technology for millimeter wave radiometers.     

Study of the relationship between porous ratio and effective index in nanoporous film

In this paper, a theory model called 'composite media in parallel' is proposed to explain the connection between the porous ratio and effective index of the nanoporous film. This model comes from theory of composite media's effective dielectric constant in solid material field. From this model, a function relationship between the porous ratio and effective index of the nanoporous film is obtained. And the Finite Difference Time Domain (FDTD) method is used to construct the model of nanoporous film, simulate the propagation of lightwave in the film and calculate some effective indices according to different ratios of pore. Compared with Maxwell Garnett theory model and Bruggeman theory model, it is found that the function curve based on the composite media in parallel model is most consistent with the results simulated by FDTD method.     

Modeling columnar thin films as platforms for surface–plasmonic–polaritonic optical sensing

Via exploitation of surface plasmon polaritons (SPPs), columnar thin films (CTFs) are attractive potential platforms for optical sensing as their relative permittivity dyadic and porosity can be tailored to order. Nanoscale model parameters of a CTF were determined from its measured relative permittivity dyadic, after inverting the Bruggeman homogenization formalism. These model parameters were then used to determine the relative permittivity dyadic of a fluid-infiltrated CTF. Two boundary-value problems were next solved: the first relating to SPP-wave propagation guided by the planar interface of a semi-infinitely thick metal and a semi-infinitely thick CTF, and the second to the plane-wave response of the planar interface of a finitely thick metallic layer and a CTF in a modified Kretschmann configuration. Numerical studies revealed that SPP waves propagate at a lower phase speed and with a shorter propagation length, if the fluid has a larger refractive index. Furthermore, the angle of incidence required to excite an SPP wave in a modified Kretschmann configuration increases as the refractive index of the fluid increases.     

Modification of laser gain properties through local-field effects and nanostructuring

We have recently developed a simple phenomenological model that allows one to account for the modifications of the gain characteristics of nanocomposite optical materials with specific geometries. Here we give a generalized formulation of our model to show that it can be applied to a broad variety of composite geometries. We demonstrate the application of our model using the Maxwell Garnett composite geometry with the resonant molecules in its host, which represent a practically important case that has not been treated earlier. We also give numerical examples for the Maxwell Garnett composite geometry with the resonances in either host or inclusions, and find the conditions under which it is possible to achieve an enhancement or suppression of the small-signal gain coefficient compared to its value in a bulk material. Using our simple model, one can identify the set of parameters, exhibiting the desired changes to the gain characteristics, prior to or instead of performing a more precise computationally intensive analysis.     

Contribution a L'etude de melanges susceptibles de former des microemulsions selon leurs compositions,par la definition de leurs comportements dielectriques a 9,455 GHz

The dielectric studies of four components mixtures are rarely made on a great deal of concentrations. The authors propose a dielectric behavior study of mixtures made with toluene-water-butanol-SDS, from specific mappings of permittivities which are plotted on pseudo ternary diagrams at 9.455 GHz. They draw different conclusions to know how at 9.455 GHz the variations of real and imaginary parts of permittivity involve the concentration of each component and the structure of the mixture.These conclusions will be perfected by studies made at other frequencies and by spectral analysis of each mixture.