Dielectric spectroscopy analysis using viscoelasticity-inspired relaxation theory with finite element modeling

Abstract

We demonstrate the formulation of frequency-dependent dielectric permittivity by superposition of Debye functions inspired by viscoelastic relaxation theory. With multiple relaxation times and permittivity strength, a viscoelastic Prony Series is adapted to construct an expression of dielectric permittivity for polymer dielectric materials, which can be successfully matched with experimental data. We then develop a finite element modeling approach with explicit microstructure dispersion and inclusion of filler-matrix interphase using functionalized silica-epoxy nanocomposite samples as a testbed. The interphase relaxation behavior is expressed using the bulk polymer properties modified by frequency and magnitude shift factors that adjust the shape of the simulated dielectric spectrum to mimic changes in relaxation time due to the polymer/filler interaction. Finally, the influence of interphase thickness and dispersion state is investigated with parametric studies. It is found that total interphase area in the composite has a critical influence over the composite property, and by varying interphase layer and dispersion within a reasonable range, as much as 20% difference can be obtained in the simulated composite property. Our simulation results provide insights into the underlying relaxation mechanism in the interfacial region.