Эффективная диэлектрическая проницаемость дисперсных систем со случайно расположенными металлическими включениями

Анотація

EFFECTIVE PERMITTIVITI OF DISPERSE SYSTEMS WITH RANDOMLY LOCATEDMETALLIC INCLUSIONS

S. V. Shostak, N. G. Shkoda

Recently, dispersed systems with inclusions of various shapes and nature are of great interest. Such systems, due to a significant difference in the frequencies of surface plasmons, allow one to control the absorption maximums of electromagnetic radiation, depending on the volume fraction of a component. Examples of such systems are matrix-dispersed systems with spherical bimetallic nanoparticles with precious metals such as a silver core - a gold shell, or vice versa - a gold core - a silver shell. The relevance of the study is primarily related to the possibility of using the special properties of various DS for fabricating composite materials on them based on predefined electrodynamic, thermophysical and elastic properties.Calculation of the frequency-dependent effective dielectric function of the composite represents an old, but still unsolved problem. There are many different approximate approaches to its solution, but there is no theory that would ensure complete quantitative agreement with the corresponding experimental data.The aim of the study is to generalize the calculation method for the case of a composite containing spherical metallic inclusions of two different sizesThe mechanisms and regularities of absorption and scattering of electromagnetic radiation by individual metallic spherical particles were used in the work, taking into account the multipole interaction between them.A generalized method for calculating the effective permittivity is proposed for the case of a composite containing spherical metallic inclusions of two different kinds. The effective permittivity is examined for a system of metallic spheres randomly embedded in an uniform dielectric medium. The system is located in an external alternating electric field with a wavelength significantly exceeding the radii of the spheres and the average distances between the particles. The effective dielectric function of such a system at low particle concentrations is represented by the Maxwell-Garnett formula (MG). It is established that when the concentration of particles increases, there is a significant deviation of the results obtained from the MG approximation, because of the interaction between the inclusions. It is noted that with the increase in the volume fraction of particles in the system, the effects of multipole interaction between particles become significant. Taking into account the dipole-dipole interaction between the particles of two varieties, the behavior of the frequency dependence of the imaginary part of the effective permittivity of the system is considered. It is shown that the spectral dependence effective permittivity of the composite is obtained by averaging over all possible positions of pairs of particles in the matrix. It was also noted that in the metal composite with an increase in the volume fraction of particles in the system, the fine structure of the spectrum is observed only when paired dipole-dipole interactions are taken into account.