Hard-core–penetrable-shell model for effective electric parameters of random particulate systems

Research fellow Andrii Semenov (Ukraine)

Video was recorded during the 7th International research and practice Conference "Nanotechnolgy and Nanomaterials" (NANO-2019)

We present the basic ideas and further developments of a new many-particle homogenization theory [1] for the electrical parameters (quasistatic conductivity, dielectric permittivity, and dielectric loss coefficient) of statistically homogeneous and isotropic particulate systems. The system’s microstructure is formulated in terms of the model of hard-core–penetrable-shell spheres. The cores are associated with particles. The shells account for different types of interfacial and matrix effects and are in general inhomogeneous. The desired parameters are calculated using the compact groups approach (CGA) [2] and internally-closed homogenization procedure. The former allows one to efficiently estimate many-particle polarization and correlation contributions without explicit detailing of the processes involved. The latter follows immediately from the requirement that the CGA and the boundary conditions for the complex electric field be consistent.

The theory has been used to process experimental data [3] for paraffin-based dispersed systems with embedded semiconductor (Fe2O3, CuO) or conductor (thermographite, Fe, Al) filler particles. It proves to describe the experiment surprisingly well in the entire range of filler particle concentrations. The physical nature of the effects incorporated by the shells is discussed. These may include: irregularities of particles’ shapes; contact resistance; formation and destruction of oxide layers; impurification of the host in the course of sample preparation; and others.


  1. Sushko M. Ya., Semenov A. K. Rigorously solvable model for the electrical conductivity of dispersions of hard-core–penetrable-shell particles and its applications // arXiv:1811.10591-P. 1-16.

  2. Sushko M. Ya., Effective dielectric response of dispersions of graded particles // Phys Rev E.-2017.-96, N. 6.- P. 062121-1-6.

  3. Sotskov V. A., Electrical characteristics of insulator–conductor and insulator–semiconductor macrosystems // Semiconductors.-2005.- 39,N. 2.-P. 254-260.