Microwave effective permittivity of carbon black filled polymers: Comparison of mixing law and effective medium equation predictions

Abstract

Carbon black (CB) filled polymers have become the platform to study a number of interesting properties including percolation mechanisms, localization effects, and multiscale modeling of interface and interphase regions surrounding filler particles. A systematic microwave study of the effective complex permittivity of CB filled diglycidylic ether of bisphenol A based epoxy samples, determined by the impedance bridge (35 GHz) and the cavity perturbation (2.4 and 9.5 GHz) techniques, is reported. A series of composite materials was fabricated by mechanical mixing with three types of CB (Monarch and Sterling) particles differing with their average particle size and surface area. On the basis of the limited experimental evidence presented here, our distinctive features are seen in the data: (i) We found no enhancement of the effective permittivity near the dc percolation threshold; (ii) the calculation of the effective permittivity based on Lichteneker and Rother’s mixing law with constant k close to zero reproduces the measured CB volume fraction dependence of the effective permittivity very well for the series of samples containing Monarch particles, (iii) the data are not well fit with the Bruggeman equation for supercolative samples. This is an indication that a mean field model is not strictly applicable because this simple model assumes a given microstructure for the composite material; and (iv) the two exponent phenomenological percolation equation (TEPPE) can yield good predictive values of the imaginary part of the effective complex permittivity over the range of frequencies and CB volume fractions with non-universal values of the percolation exponents. It is concluded that fitting the experimental data with mixing law and effective medium equation predictions has limited applicability because these models assume a given microstructure for the composite material.