Simulation of polarization, energy storage, and hysteresis in composite dielectrics containing nonlinear inclusions

Finite difference quasi-electrostatic modeling is used to predict the dielectric behavior of composites consisting of spherical inclusions having nonlinear dielectric polarization behavior that are dispersed in a background linear dielectric matrix. The inclusion nonlinearities are parameterized by a hyperbolic tangent model that includes hysteresis. Computations of composite polarization and energy storage versus applied field and inclusion filling fraction are presented for ordered and random geometries. Electric field statistics are investigated with regard to localized intensification in the matrix, which is relevant to breakdown, and with regard to remnant fields in the inclusions, which is associated with hysteresis. Inclusion saturation behavior is found to cause dramatic departures from the predictions of linear theory, resulting in reduced energy storage in the composites and the existence of optimum filling fractions. Considering various competing factors, an energy storage of 10-12 J/cm(3) at applied fields of 300-350 V/mu m could be feasible in a composite composed of a linear matrix with a dielectric constant of 12 containing volumetric filling fraction 0.3-0.4 of inclusions with a low field dielectric constant of 1200 and a saturation polarization of 0.15 Cm(-2). In spite of significant inclusion hysteresis, the composites displayed only minor overall hysteresis behavior, with>94% recoverable energy being typical, provided the filling fraction was below percolation. With sufficiently high inclusion hysteresis, a bimodal distribution in the polarizations and fields within the inclusions appeared during downswing, manifesting itself as spontaneously organized regions of oppositely aligned polarization that resemble domains. [doi:10.1063/1.3633763]