Structural Model for the Estimation of the Equivalent Permittivity of Nanodielectrics Based on Polyethylene and Epoxy Resins

A structural model for the calculation of the equivalent permittivity of nanocomposites based on low-density polyethylene (LDPE) and epoxy resins (ERs) with inorganic fillers was developed. It was assumed that each nanoparticle was centered in an interfacial region composed of three layers in the case of LDPE-based nanocomposites, and of two layers in the case of ER-based nanocomposites. The model for the estimation of the permittivity was designed for flat samples of the height
$g$
, divided into cubes with the side-length
$l$
. Each of these cubes contains eight nanoparticles, which are separated from the polymer matrix by two or three layers. Based on the types and concentrations of dipoles present in the layers, the relative permittivity of each layer of the interface can be calculated. By the employment of a 3D numerical model in COMSOL, implemented by the finite element method associated with a cube, the distribution of the electric field inside a cube can be determined, which yields the values of the equivalent permittivity of the nanocomposites. In order to verify the numerical results, the permittivity of the nanocomposites based on LDPE and ERs with inorganic nanofillers (SiO
₂
or Al
₂
O
₃
) was determined in laboratory experiments. The results reveal congruent correlation between the computed and the experimentally determined values of the equivalent permittivity of the nanodielectrics.