Electric modulus-based analysis of the dielectric relaxation in carbon black loaded polymer composites

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 ( T g − 48 K ) - 319 ( T g + 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.