In this study we present measurements and data analysis of the dielectric relaxation in carbon black (CB) loaded epoxy composites over a wide range of CB concentration (below and above the percolation threshold) and a broad range of frequency (180–1.5×107 Hz). We show that our data are in conflict with the expectation that the fit parameters of the much-discussed two exponent phenomenological percolation equation (TEPPE) represent the critical exponents of the standard percolation theory. This result therefore gives new insight to the problem of why the TEPPE has a limited applicability in representing the effective permittivity versus CB volume fraction functional relationship. We believe that the reason for this discrepancy is that the true dependence of the internal length scales of the mesostructure and the elasticity network is too complicated to fulfill a simple unified functional equation.

Articles you may be interested inA comparison between the permittivity and electric modulus representations of the microwave response of carbon black loaded polymer composites under uniaxial tension J. Appl. Phys. 110, 054101 (2011); 10.1063/1.3630023Uncovering the intrinsic permittivity of the carbonaceous phase in carbon black filled polymers from broadband dielectric relaxation A comparison between physical properties of carbon black-polymer and carbon nanotubes-polymer composites 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.

An outstanding experimental issue in the physics of composites concerns the reliable extraction of the intrinsic dielectric characteristics from effective permittivity measurements of heterostructures. Though recent analytical and numerical models have made progress in tackling this question, their applicability is typically limited by the lack of information about the structural organization of the filler phase. As a follow-up of our earlier work [S. El Bouazzaoui et al. J. Appl. Phys. 106, 104 (2009), we report in this paper a systematic study of the intrinsic permittivity ɛ2 of the carbonaceous phase in carbon black (CB) loaded polymers. A variety of authors has suggested very early that ɛ2 can be modeled with a simple free-electron (Drude) metal model with static disorder. Despite the interest in the physics of carbonaceous materials, there have been few experimental tests of this assumption, in part, due to the experimental challenge of measuring ɛ2. Here, this interpretation is questioned by an analysis of the frequency-dependent complex effective permittivity of these lossy conductor-insulator composites using the Hashin-Shtrikman bounds of the effective medium approximation. For the materials investigated over the range of frequencies explored (10–104 kHz) it is found that ɛ2 can be written as ɛ2=ɛ2'-iɛ2′′ with ɛ2''>>|ɛ2'|. We critically evaluate the possibility that the estimates of ɛ2 are related to Drude model. We found that the intrinsic permittivity of the carbonaceous phase dispersed in the composite materials investigated is consistent with the dielectric response described by the Drude metal model in a percolative morphology. The sensitivity of this method is fundamentally related to the complexity of the morphological changes which occur during mechanical mixing, i.e., interphase formation, CB particles aggregation. Such knowledge can be used to determine the role of the conducting states at the interface between insulating polymer chains and carbonaceous phase.

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