Rigorous bounds for the complex dielectric constant of a two-component composite

Rigorous bounds are systematically derived for the bulk effective dielectric constant of a two-phase composite material ε_e under various assumptions about the available information. The bounds are drawn for some special cases in the complex ε_e-plane. The question of optimality of the bounds and their connection to solvable microgeometries is discussed. It is shown how linear programming theory can be used to aid in the derivation of these bounds.     

Variational treatment of the elastic constants of disordered materials

Using the method of Hill a variational principle is derived to obtain upper and lower bounds for the effective elastic constants of disordered materials, such as polycrystals or multiphase materials. All bounds previously known are rederived and especially new bounds are given being closer than the ones of Hashin and Shtrikman. In detail the elastic constants of polycrystals built of cubic single crystals and of multiphase materials are considered. The analogous bounds for the dielectric constant of polycrystals are also given.     

Bounds for effective parameters of multicomponent media by analytic continuation

Recently D. Bergman introduced a method for obtaining bounds for the effective dielectric constant (or conductivity) of a two-component medium. This method does not rely on a variational principle but instead exploits the properties of the effective parameter as an analytic function of the ratio of the component parameters. We extend the method to multicomponent media using techniques of several complex variables.     

Cluster expansion for the dielectric constant of a polarizable suspension

We derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background. This also leads to a cluster expansion for the effective dielectric constant. It is shown that the cluster integrals of any order are absolutely convergent, so that the dielectric constant is well defined and independent of the shape of the sample in the limit of a large system. We compare with virial expansions derived earlier in statistical mechanics for the dielectric constant of a nonpolar gas. In these expansions the virial coefficients are given by integrals which are only conditionally convergent.     

Phase retrieval of reflectance for nanoparticle optical identification

We present a method for optical identification of dielectric and metal nanoparticles in a liquid matrix using phase retrieval of reflectance with TE- and TM-polarized light. A formula is derived for extracting the effective complex dielectric function of a nanoparticle colloid based on different complex reflectance components. The phase retrieval is performed using the maximum entropy method. We observe excellent accuracy both for dielectric and metallic nanoparticles with volume fractions up to 10%.     

Two-particle cluster integral in the expansion of the dielectric constant

We study in detail the two-particle cluster integral in the cluster expansion for the effective dielectric constant of a suspension of spherically symmetric polarizable inclusions embedded in a uniform medium. Although our form for the integrand differs from that derived earlier by Finkel'berg and by Jeffrey, we show that the integral is equivalent. The two-body dielectric problem for particles with an arbitrary radial dependence of the dielectric constant is solved by an expansion in spherical harmonics. Numerical results for some special models illustrate the importance of multipole contributions to the effective dielectric constant.     

弱非线性复合体中的高阶非线性响应

利用谱表示理论和微扰展开法，从理论上给出了适合于一般微结构复合体系的有效非线性响 应的一般表示式，并结合有效媒质近似（EMA），在弱非线性条件下研究了由三阶非线性组 分（体积分数为p）和线性组分构成的非线性复合体系的有效非线性响应，讨论了复合 体系的有效介电常数ε～e=εe+χe|E0|2+ηe|E0| 4中的有效三次非线性响应χe和有效高次非线性响应ηe与体积分数p和 退极化因子L之间的关系，分析了非线性组分的介电常数为复数情形时体系的有效高阶非线 性响应，从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响.  关键词： 非线性复合介质 有效非线性响应 谱表示理论     

Dielectric and thermodynamic properties of CHF3 near the critical temperature

We report here some measurements of the complex dielectric constant of CHF₃ near the critical temperature from the low pressure gas densities up to the compressed liquid ones. The behaviour of the complex dielectric constant, measured at about 10 GHz, is compared with the provisions of some recent theories. The dielectric relaxation time is derived and an interpretation of the relaxation mechanisms in the whole explored density range is proposed. The pressure second virial coefficient is also obtained.     

Ab-initio calculation of optical properties of AA-stacked bilayer graphene with tunable layer separation

Density functional theory based calculations revealed that optical properties of AA-stacked bilayer graphene are anisotropic and highly sensitive to the interlayer separation. In the long wave length limit of electromagnetic radiation, the frequency dependent response of complex dielectric function becomes vanishingly small beyond the optical frequency of 25.0 eV. Besides, static dielectric constant shows a saturation behaviour for parallel polarization of electric field vector when interlayer spacing is greater than 2.75 Å. As a consequence, an appropriate modification of effective fine structure constant is observed as a function of layer separation. Moreover, the bilayer systems are highly transparent in the optical frequency range of 7.0–10.0 eV. The electron energy loss function exhibits two different in-plane collective (plasmon) excitations and a single out of plane plasmon excitation. The spectral nature of different frequency dependent optical properties is observed to be very similar to that of the monolayer pristine graphene apart from their exact numerical values.     

Dielectric constant of porous ultra low-k dielectrics by fractal-Monte Carlo simulations

The effective dielectric constant of porous ultra low-k dielectrics is simulated by applying the fractal geometry and Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for effective dielectric constant are derived. The proposed model for the effective dielectric constant is expressed as a function of the dielectric coefficient of base medium and the volume fractions of pores and base medium, fractal dimension for pores, the pore size, as well as random number. The Monte Carlo simulations combined with the fractal geometry are performed. The predictions by the present simulations are shown in good accord with the available experimental data. The proposed technique may have the potential in analyzing other properties such as electrical conductivity and thermal conductivity in porous ultra low-k dielectrics.     

Scattering from an eccentric system,including a dielectric rod placed in a thin annular magnetized relativistic rotating electron beam (TAMRREB)

The electromagnetic wave scattering from a dielectric rod placed in a non-coaxial thin annular magnetized relativistic rotating electron beam is simulated. The resonance frequency shift and the effective factors on it are investigated. In addition, the dependencies of pattern of scattering to the plasma frequency, the rotating frequency, geometrical dimensions and dielectric constant of dielectric rod have been investigated. The eccentricity effect on the resonance frequencies is studied.     

Dielectric relaxation study of aqueous 2-ethoxyethanol using time domain reflectometry technique

The complex permittivity spectra of 2-ethoxyethanol in water solutions have been studied at different concentrations and temperatures using a picosecond time domain reflectometry technique. The complex dielectric permittivity spectrum of 2-ethoxyethanol shows Cole-Davidson type behavior. Increase in dielectric relaxation time may be due to increase in hetero molecular interaction strength. Minimum in Excess dielectric constant values provides the information about stable complex adduct. The Kirkwood correlation factor, thermodynamic properties and Bruggeman factor have also been determined and the results are interpreted in terms of hydrogen bonding and interactions among the solute — solvent molecules.     

Dielectric properties of paper as a function of of moisture content at 9 GHz

This letter gives values of the complex dielectric constant of a good quality paper as a function of the moisture content at 9 GHz. The experimental results are interpreted using Weiner's theory for dielectric mixtures.     

A simple design method of negative refractive index metamaterials

We propose a very simple design method of negative refractive index (NRI) materials that can overcome some drawbacks of conventional resonant-type NRI materials. The proposed NRI materials consist of single or double metallic patterns printed on a dielectric substrate. Our metamaterials (MTMs) show two properties that are different from other types of MTMs in obtaining effective negative values of permittivity (ε) and permeability (μ) simultaneously; the geometrical outlines of the metallic patterns are not confined within any specific shape, and the metallic patterns are printed on only one side of the dielectric substrate. Therefore, they are very easy to design and fabricate using common printed circuit board (PCB) technology according to the appropriate application. Excellent agreement between the experiment and prediction data ensures the validity of our design approach.     

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.     

Dielectric losses in heterogeneous systems

Analytic formulas are derived for the effective complex dielectric constant of a matrix system with Maxwell-Wagner losses. An approximate solution is given for a system of dielectrics with a single relaxation time. It is shown that this approximation is applicable to systems containing a semiconductor with blocking electrodes. The effect of spread in the dimensions of the semiconductor component on the frequency dependence of losses in a matrix system is discussed.     

Characterization of heterogeneous interaction in binary mixtures of ethylene glycol oligomer with water, ethyl alcohol and dioxane by dielectric analysis

The associating behaviour of the binary mixtures of ethylene glycol oligomer (EGO), i.e. ethylene glycol (EG), diethylene glycol (DEG) and poly(ethylene glycol)s (PEG200, PEG300, PEG400 and PEG600) with water (W), ethyl alcohol (EA) and 1,4-dioxane (DX) over the entire concentration range at 25 °C have been investigated through their accurately measured values of dielectric constant. The static dielectric constant ε_o, high frequency limiting dielectric constant ε_∞, dielectric relaxation strength Δε, excess dielectric parameters ε^E₀ and ε^E_∞, effective Kirkwood correlation factor g^eff and corrective correlation factor g_f of EGO–W, EGO–EA and EGO–DX mixtures were determined to obtain qualitative and quantitative information about the complex formation through H-bond in these systems. Most of the evaluated dielectric parameters of EG and DEG in different ‘cosolvents’ have different characteristics as compared to the PEG–cosolvent mixture. The observed linear and non-linear behaviour of Δε against EGO monomer unit mole fraction X confirms the variation in the homogeneous structures in their binary mixtures with concentration variation. Appearance of the maximum in ε^E₀ against X plots indicates that a complex stable adduct is formed in the EGO–W mixtures at stoichiometric ratio 1:1.7 for lower oligomers but this ratio seems to be 1.7:1 for higher EGO molecules, which confirms that the EGO size and chain flexibility affects the complex formation between EGO and W. In case of EG–EA mixture 1:1 stoichiometric ratio form stable adduct whereas for higher EGO–EA, it is 3:1, at EGO monomer unit level. The complex formation behaviour of DEG–EA has entirely different characteristics when compared to the other studied EGO–EA mixtures. Although, 1,4-dioxane has weak polar behaviour dielectric properties of EG–DX and DEG–DX confirm the formation of stable adducts at the stoichiometric ratio 2:1 of EGO monomer unit mole fraction to the DX. For the higher EGO–DX mixtures, stable adduct forms at the stoichiometric ratio 9:1. Except DEG–EA mixtures, the EGO–W and EGO–EA form the complex with reduction in the effective number of dipoles. In EG–DX mixtures, the heterogeneous species form with a large reduction in the effective number of dipoles, which changes as the effective number of dipoles increases with the increase in monomer repeat units of EGO. Further the net electronic polarization in these binary mixtures increases due to heterogeneous interaction over the entire mixing concentration range.     

Study on dielectric properties of oil/water random composites

Considering the electric double layers between oil and water, a new “complex model” of dielectric constant of oil/water composites was built up. Starting from the Maxwell–Garnett theory and Bruggeman theory, the effective dielectric constant of oil/water random composites is presented. The nonlinearity of the theory is obvious. The model is especially suited to study the dielectric properties of oil/water composites of different nature. The model is also suited to study the dielectric properties of two-phase random composites with an interfacial shell. The theoretical results on dielectric properties of different kinds of oil/water composites are in good agreement with experimental data.     

Static van der Waals interactions in electrolytes

Using a field-theoretic formalism, we calculate the static contribution to the van der Waals interaction between two dielectric semi-infinite half-spaces in the presence of mobile salt ions. The ions can be located in the slab, in one, or in both half-spaces. We include an excess polarizability of the salt ions, i.e., each (spherical) ion has a dielectric constant which in general is different from the surrounding medium. This leads to a modification of the effective dielectric constant of the medium hosting the ions. This shift can be large for high salt concentrations and therefore influences the Hamaker constant decisively. Salt ions in the slab screen the static van der Waals interaction, as was shown by Davies and Ninham. The salt-modified van der Waals interaction also contains salt-confinement and salt-correlation effects. This is clearly demonstrated by the fact that the interaction is non-zero even in the case when the dielectric constant is homogeneous throughout the system, in which case salt correlations are solely responsible for the interaction. If the salt ions are in one or both of the two half-spaces (and no ions in the slab), the van der Waals interaction is not screened but the effective Hamaker constant approaches a universal value for large slab thickness which is different from the value in the absence of salt ions and which is independent of the salt concentration and of the effective electrolyte dielectric constant. If both half-spaces contain salt, the asymptotic value of the Hamaker constant for large separation between the half-spaces is the one obtained for the interaction between two metallic half-spaces through an arbitrary dielectric medium, which is given by A≃ - 1.20. As is explicitly demonstrated, ion enrichment or depletion at the interfaces due to image-charge effects is already included on the one-loop level and therefore does not lead to a change of the screened van der Waals interaction as given by Davies and Ninham. For positive and negative ions with different valencies or different excess polarizabilities, we obtain different adsorbed surface excesses of positive and negative ions, leading to a non-vanishing surface potential, which is computed explicitly. All of these results are obtained on the linear one-loop level. For a special case we extend the calculation of the dispersion interaction to the two-loop level. We find the corrections to the one-loop results to be quite large for high salt concentrations or multivalent ions. Received 17 February 2000