Uncovering the intrinsic permittivity of the carbonaceous phase in carbon black filled polymers from broadband dielectric relaxation

Abstract

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.