A comparative study of the effective dielectric constant of a medium containing randomly distributed dielectric spheres embedded in a homogeneous background medium

Abstract

The effective dielectric constant ∈_eff of a medium containing randomly distributed dielectric particles has been analysed by conventional methods: Foldy's approximation, the quasi-crystalline approximation (QCA) and the QCA with coherent potential. These conventional methods, however, have been indicated to become invalid for particles with a high dielectric constant; we have thus presented a new method that is valid for them. This paper compares ∈_eff of our method with those of the conventional methods by changing the volume fraction and the dielectric constant of spheres. As a result, our method is shown to be more powerful for the analysis of ∈_eff than the conventional methods.     

The effective dielectric constant of a dispersion of clustering spheres

If one measures the dielectric constant of a water in oil microemulsion the large increase of this dielectric constant both as function of the temperature as well as a function of the volume fraction of water suggests that the water droplets will bind together in clusters. In order to analyse this suggestion in more detail we derive a systematic expansion of the Clausius-Mossotti function in terms of integrals over products of excess cluster polarizabilities and correlation functions. It is found that the excess polarizability of a cluster of spherical droplets is zero except when the spheres almost touch each other. Crucial for this property is the fact that the water spheres are conducting or if they are not conducting have a dielectric constant much larger than the dielectric constant of oil. The large increase of the dielectric constant is a consequence of the increase of the number of bound clusters. An explicit formula is given for the resulting temperature and volume fraction dependence of the dielectric constant.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Contribution of multiple scattering to the dielectric constant of a randomly inhomogeneous medium

Within the statistical theory of multiple scattering of light in random media, the dielectric constant of a suspension is represented as a diagram series in scattering orders and concentration of particles. The contributions of double and triple scattering events are determined. The extinction length and the transport mean free path in highly concentrated suspensions calculated with the use of the optical theorem are in good agreement with the available data. It is shown that the two-particle Born approximation, combined with the Mie form factor and the Percus-Yevick structure factor, is not adequate for systems with a high concentration of scatterers. A contribution to the optical parameters is found that is missing in the above approximation.     

Multipole contributions to the effective dielectric constant of suspensions of spheres

We study multipole contributions to the effective dielectric constant of dilute suspensions of uniform spheres. It is shown that for frequencies near the plasma resoance multipole contributions are negligible in comparison with the dipole contributions. Outside resoance multipolar corrections to the Clausius-Mossotti formula are of the same order of magnitude as the dipolar ones. We argue that in resonance the dipole approximation should be valid also for more complicated sphere models.     

Multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres

We study multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres with identical uniform dielectric constant embedded in a uniform background. The first few moments of the spectral density occurring in the Bergman representation are evaluated exactly to second order in the volume fraction. We present numerical results for a log-normal distribution of sphere radii.     

Fluctuations of dielectric constant in a system of hard spheres

The correlation function for fluctuations of a dielectric constant in a latex-like suspension of spherical particles was calculated. An exact analytical expression was derived for the correlation function using the Percus-Yewick approximation for a system of hard spheres. The obtained results made it possible to calculate the indicatrix of single scattering, the extinction coefficient, and the transport mean path. It is shown that, starting with a volume content of about ten percent, the “gas” approximation becomes invalid, and optical parameters begin to depend on concentration in quite a complicated manner. In particular, the extinction length and the mean transport path, which are the basic parameters in describing the coherent effects in multiple scattering, vary nonmonotonically with concentration. It is found that there exists a range of sizes and concentrations of scattering particles in which an effect similar to the emergence of blue phase in liquid crystals can be observed.     

A Monte Carlo study of dipolar hard spheres The pair distribution function and the dielectric constant

This paper is a systematic investigation of the effects of boundary conditions upon Monte Carlo calculations for dipolar fluids. Results are reported for the minimum image (MI), spherical cut-off (SC) and uniform reaction field methods. All three approximations are shown to give different pair distribution functions, g(12), and none yields the infinite system result. It is concluded that theories giving g(12) for an infinite system should not be evaluated by direct comparison with Monte Carlo results. Two alternative methods by which meaningful comparisons can be made are described in the text. The dependence of the thermodynamic properties upon boundary conditions is important only at large values of the dipole moment. For small to moderate dipoles both MI and SC are found to give reasonable estimates of the dielectric constant.     

Thermal conductivity of NaCl embedded in randomly distributed porous-glass channels

Our earlier experimental data on the thermal conductivity of porous glass and of the porous glass + NaCl composite in the temperature interval 25–300 K are analyzed from a different standpoint. It is shown that the thermal conductivity of sodium chloride filling randomly arranged nanochannels in porous glass behaves exactly like that of a strongly disordered crystalline system and can be described in terms of Einstein’s model of the thermal conductivity of solids.     

Calculation of the effective permeability of a randomly inhomogeneous porous medium

The effective permeability of a porous medium is calculated nonperturbatively. An exact expression for the permeability in terms of a double path integral is derived on the assumption that the permeability obeys a log-normal distribution function. Path integration is carried out in general form in the large-scale limit. The result confirms the well-known conjecture that the effective permeability is independent of the structure of the correlation function, but it disagrees with the hypothesis that the effective permeability depends exponentially on the variance. Zh. éksp. Teor. Fiz. 112, 313–324 (July 1997)     

A parameterization of the effective dielectric function of a two-phase composite medium

The effective dielectric function of a heterogeneous medium can be calculated according to the Bergman-representation. It is a general approach to calculate the effective material properties of a two-phase composite. In this article a parameterization of the effective dielectric function on the basis of the Bergman representation is suggested and fits to measured data are presented.     

High-frequency dielectric constant of a two-dimensionally disordered model medium

An exact solution is derived for the two-dimensional two-phase model of a disordered medium proposed by Morozovskii and Snarskii [Ukr. Fiz. Zh. (Russ. Ed.) 28, 1230 (1983)] that arises because of hierarchical mixing of phases with different dielectric constants. The problem reduces to a nonlinear recurrence relation for the dielectric constants. It is found that the expressions for the dielectric constants at the nth stage of the iteration process can be expressed in terms of elementary functions. It is also found that in the absence of absorption the high-frequency dielectric constant of a composite material with different signs of the initial dielectric constants ε does not converge to a limit and is an oscillatory function of the frequency and n. Finally, for massive and thin-film samples, the local plasmon frequencies in the medium are established. Zh. éksp. Teor. Fiz. 114, 669–675 (August 1998)     

A dense collection of two-level atoms embedded in a dielectric medium in a ring cavity

The hysteresis behavior of a dense collection of two-level atoms embedded in a linear dielectric medium in an optical cavity is investigated theoretically in terms of a parametric formulation method under the thin-sample approximation. The relation of the output intensity to the input intensity is obtained in an explicit formula. The numerical results show that the hysteresis behavior and the cavity transmission are different from those in vacuum because of the local-field enhancement and the local cooperative decay effect. Received: 27 June 2000 / Revised version: 11 September 2000 / Published online: 10 January 2001     

Equivalent volume-averaged light scattering behavior of randomly inhomogeneous dielectric spheres in the resonant range

Finite-difference time-domain numerical experiments and supporting analyses demonstrate that the spectral dependence of the total scattering cross sections of randomly inhomogeneous dielectric spheres of sizes in the resonant range closely resemble those of their homogeneous counterparts that have a volume-averaged refractive index. This result holds even for the extreme case in which the refractive index within an inhomogeneous sphere varies randomly over the range 1.0-2.0.     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

Analytic properties of the effective dielectric constant of a two-dimensional Rayleigh model

Analytic properties of the dimensionless static effective dielectric constant f(p, h) of a two-dimensional Rayleigh model (p is the concentration and h is the ratio of the dielectric constants of components) are considered as a function of the complex variable h. It is shown that the only singularities of the function f(p, h) are first-order poles for real h = h _n < 0 (n = 1, 2, ...) with the condensation point h = ?1, which form an infinite discrete (countable) set. The positions of the first ten poles of the function f(p, h) and the residues at these points are calculated and represented graphically versus the concentration. Based on the results obtained, a pole-type approximate formula is proposed that describes the behavior of the function f(p, h) over a wide range of p and complex h.     

随机分布烟尘团簇粒子辐射特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的烟尘团簇粒子结构进行了仿真模拟,利用离散偶极子近似(discrete dipole approximation, DDA)方法研究了随机分布的烟尘团簇粒子的辐射特性,分析讨论了分形维数、原始微粒粒径和数量以及复折射率对随机分布烟尘团簇粒子辐射特性的影响.研究表明,在给定分形维数的情况下,烟尘团簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率;原始微粒较小的团簇粒子,当分形维数较小时,吸收截面变化不明显,但当分形维数大于2时,吸收截面骤然增大,然而,对于具有比较大的原始微粒粒径、数量及复折射率的烟尘团簇粒子,吸收截面随着分形维数的增大而单调递减;随着分形维数的增大,团簇粒子的散射截面、消光截面及单次散射反照率均单调递增;从整体上来讲,团簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别,并且这种差别随着分形维数的增大而减小.该工作对研究气溶胶粒子的辐射及气候效应具有重要的科学价值. 关键词： 烟尘团簇粒子 辐射特性 离散偶极子近似方法