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

Felderhof, B. U.; Ford, G. W.; Cohen, E. G. D.

doi:10.1007/bf01011874

Cited by 61 publications

(29 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After the pioneering work of Maxwell-Garnett, 8 new effective medium approximations have been formulated in order to incorporate different types of effects which were not considered in this earlier approach. 9 These include, for example, cases of high concentration of the metal particles; 10 the distribution of sizes and shapes of the inclusions at different levels of approximation; [11][12][13][14][15][16][17][18][19] generalization to an anisotropic effective dielectric response for the composite; 20 implication of the significance of multipolar response which is neglected in the standard effective medium approximation; [21][22][23][24][25][26] and generalization to small metallic spheres of two different sizes. 27 In most of the previous effective medium approximations, the dielectric response of the metallic particles is usually limited to include only temporal dispersion with the dielectric function to have only frequency dependence.…”

Section: Introductionmentioning

confidence: 99%

Maxwell-Garnett effective medium theory: Quantum nonlocal effects

Moradi

2015

Physics of Plasmas

View full text Add to dashboard Cite

We develop the Maxwell-Garnett theory for the effective medium approximation of composite materials with metallic nanoparticles by taking into account the quantum spatial dispersion effects in dielectric response of nanoparticles. We derive a quantum nonlocal generalization of the standard Maxwell-Garnett formula, by means the linearized quantum hydrodynamic theory in conjunction with the Poisson equation as well as the appropriate additional quantum boundary conditions. V C 2015 AIP Publishing LLC. [http://dx.

show abstract

Section: Introductionmentioning

confidence: 99%

Maxwell-Garnett effective medium theory: Quantum nonlocal effects

Moradi

2015

Physics of Plasmas

View full text Add to dashboard Cite

show abstract

“…(9) coincides with result Eq. (5.7) of work [7]. Formula (6) also may be represented in the Bergman's form for [9]:…”

Section: Dielectric Function Of Matrix Disperse Systems With Sphericamentioning

confidence: 99%

“…Their expressions are presented in [5] and they are derived from the exact solution of the two-sphere problem in the external field [7]. In the case of the solitary kind of particles it follows from (1):…”

Section: Dielectric Function Of Matrix Disperse Systems With Sphericamentioning

confidence: 99%

<title>Effective dielectric function of metallic particle aggregates</title>

et al. 1997

View full text Add to dashboard Cite

An infrared and visible absorption spectra of aggregates with metallic spherical particles (size of about 10-30 nm) in dielectric matrix are theoretically studied. Calculations of the effective dielectric constant of such systems have been carried out in electrostatical approximation by considering the concentration expansion up to second power off(fis a volume fraction occupied by spheres) with the pair multiple interaction induced by external field been taken into account exactly. We have found that the frequency dependencies of an imaginary part of dielectric function and absorption coefficient in plasma resonance region for a single particle have two peaks that are shifted into longwave and shortwave frequency regions in relation to the known Lorrentzian absorption peak corresponding to the dipolar surface plasma mode of isolated spheres.

show abstract

“…Equation ͑1͒ is a generalization of the relation ͑5.8͒ 12 for the case of a system with inclusions of different kinds. Taking into account only the pair dipole-dipole interaction between particles, we have [14][15][16] where R a is a radius of the particle a. The coefficients X 10 (a) (R ab ) and X 11 (a) (R ab ) can be obtained from the solution of the problem of the electrostatic response for spheres a and b in the field E 0 .…”

mentioning

confidence: 99%

Dielectric function of aggregates of small metallic particles embedded in host insulating matrix

Grechko

Pustovit

Whites

2000

Applied Physics Letters

View full text Add to dashboard Cite

The optical properties of clusters with metallic spherical particles embedded in an insulating matrix are studied. A theoretical approach is proposed for the calculation of the macroscopic dielectric response for a collection of spheres at random positions embedded in a homogeneous medium. While accounting for the dipole-dipole interaction between particles, we have considered the frequency dependence behavior of the imaginary part of the effective dielectric constant in this system with two kinds of particles of different sizes. © 2000 American Institute of Physics. ͓S0003-6951͑00͒05014-2͔The Maxwell-Garnett ͑MG͒ 1-3 approximation and its various updatings have frequently been used 4-13 as the description for the optical properties of composites consisting of a dielectric matrix with embedded metallic inclusions. The main purpose of 4-13 consists of accounting for the multipole interaction between inclusions. We shall consider here the method of cluster expansion developed in works. [8][9][10][11] In this method the effective dielectric constant of the composite is represented as a series where each term consistently takes into account the two-particle, three-particle, and higher interactions between inclusions. The difficulty of this method is that at each stage it is necessary to solve the electrostatic problem for sets of particles ͑two, three, etc.͒ in an external field and to know the appropriate multiparticle distribution functions of inclusions in the matrix.In the present letter, we propose to generalize the method 8 for the case of a composite containing spherical inclusions of various radii. We will take into account only the pair multipole interaction between inclusions ͑first correction in the MG approximation͒. A general expression for and its imaginary part as functions of the composite parameters containing inclusions of two different radii of the same material is considered using this approximation. We shall consider a system that consists of the continuous dielectric matrix with embedded spherical particles of different kinds ͑noted below by indices a,b,c...͒. The dielectric permittivity of the matrix is 0 while the dielectric constants of the particles a , b , c ... . Let the number of spheres of kinds a, b, c, etc. be N a ,N b ,N c ..., respectively. The total number of particles is Nϭ⌺ ␣ N ␣ . The system is located in the external field proportional to e Ϫit with a wavelength ϭ2c/, which is much larger than the sphere radius and mean distance between particles; n a ϭN a /V, n b ϭN b /V,... are the concentrations of particles of the kinds a,b,... .Generalizing the method of cluster expansion [8][9][10][11] in this case, we can develop the following expression for the calculation of the system effective dielectric permittivity:whereis a usual dipole polarizability of the particle of kind a, ⌽ a,b (R ab ) is the two-particle distribution function of particles in the matrix, and R ab ϭ͉r a Ϫr b ͉, where r a and r b are the origins of spheres a and b, respectively. Equation ͑1͒ is a generalizatio...

show abstract

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

Cited by 61 publications

References 12 publications

Maxwell-Garnett effective medium theory: Quantum nonlocal effects

Maxwell-Garnett effective medium theory: Quantum nonlocal effects

<title>Effective dielectric function of metallic particle aggregates</title>

Dielectric function of aggregates of small metallic particles embedded in host insulating matrix

Contact Info

Product

Resources

About