Microstructure-based numerical modeling method for effective permittivity of ceramic/polymer composites

Effective permittivity was modeled and measured for composites that consist of up to 35vol% of titanium dioxide powder dispersed in a continuous epoxy matrix. The study demonstrates a method that enables fast and accurate numerical modeling of the effective permittivity values of ceramic/polymer composites. The model requires electrostatic Monte Carlo simulations, where randomly oriented homogeneous prism-shaped inclusions occupy random positions in the background phase. The computation cost of solving the electrostatic problem by a finite-element code is decreased by the use of an averaging method where the same simulated sample is solved three times with orthogonal field directions. This helps to minimize the artificial anisotropy that results from the pseudorandomness inherent in the limited computational domains. All the required parameters for numerical simulations are calculated from the lattice structure of titanium dioxide. The results show a very good agreement between the measured and numerically calculated effective permittivities. When the prisms are approximated by oblate spheroids with the corresponding axial ratio, a fairly good prediction for the effective permittivity of the mixture can be achieved with the use of an advanced analytical mixing formula.