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In this work, the relaxation dynamics (RD) in carbon black (CB)-polymer composites under stress is investigated by two complementary approaches: effective permittivity and electric modulus formally defined as the reciprocal of the complex relative permittivity. Experimental measurements of the microwave data over the of CB volume fractions below the percolation threshold and microwave frequencies studied agree well with the predictions of the Cole-Cole (CC) phenomenological model of RD. Similar conclusions about the RD of subpercolative samples could be reached by viewing the data in terms of their &eh; and M representations. For subpercolative systems, the CB aggregates show nearly no influence on the dielectric relaxation through the matrix. However, we show that the relaxation time scale is increased by two orders of magnitude when CB volume fraction is increased from below to above the percolation threshold at about 8.5 vol%. Extraction of the RD information from CC modeling shows that when the system is subpercolative the dielectric relaxation kinetics is proportional to λ-1/λ2, which is consistent with the Gaussian molecular network (affine network) model in the low-strain case. [ABSTRACT FROM AUTHOR]

A thorough investigation of the ac electrical properties of carbon black (CB) mixed into ethylene butylacrylate copolymer has been conducted using ac impedance spectroscopy in the frequency range 10 Hz–100 kHz and over the temperature range of 150 (Tg-48 K)–319 (Tg+121 K) K. For this investigation, a series of eight samples were prepared with various filler contents above the percolation threshold. Using the electric modulus formalism it has been found that the Cole–Cole equation of dielectric relaxation expressed in the electric modulus form is capable of quantitatively describing the experimental data from which we extract the relaxation time and a parameter α which gauges the broadening of the loss spectrum. The small values of α ranging from 0.06 to 0.10 suggest a behavior close to the state of a single relaxation time. Furthermore, the relaxation time as a function of temperature is characterized by an Arrhenius behavior. While the effective activation energy is on the order of 60 meV and is insensitive to CB volume fraction, the Arrhenius prefactor is found to strongly depend on this volume fraction. The observed relaxation mechanism does not result simply from thermally activated dipolar interactions but is a collective cooperative effect of the CB mesostructure. [ABSTRACT FROM AUTHOR]