A comparison between the permittivity and electric modulus representations of the microwave response of carbon black loaded polymer composites under uniaxial tension

Abstract

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 ɛ 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.