2018/11/04 by M. Ya. Sushko, Sushko, M. Ya., A. V. Dorosh +1
Chemistry · Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Electromagnetic Scattering and Analysis #Electrostatics and Colloid Interactions #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.1811.01414
openalex publication_date 2018/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A many-particle theory is presented for the effective quasistatic permittivity of macroscopically homogeneous and isotropic systems of inhomogeneous dielectric particles with different degrees of penetrability. The theory is based upon our original compact-group approach, complemented by the Hashin-Shtrikman variational principle. The governing equation is obtained by summing up the statistical moments for the deviations of the local permittivity in the system from the desired effective permittivity. The latter is, in principle, recoverable from the governing equation as a functional of the constituents' volume concentrations (expressed through statistical averages of certain products of the particles' characteristic functions) and permittivity profiles. Under the suggestion that the local permittivity is determined by the shortest distance from the point of interest to the nearest sphere, a complete analysis is carried out for hard and fully penetrable spheres with piecewise-continuous radial permittivities. The results are contrasted with other authors' analytical theories and simulation data. This comparison validates our theory and also sheds light on possible computational errors caused by the use of rectangular lattices to simulate dispersions of spherical particles.