Relationship between the positive temperature coefficient of resistivity and dynamic rheological behavior for carbon black‐filled high‐density polyethylene

Abstract Studies on the relationship between resistivity and dynamic rheological properties of carbon black‐filled high‐density polyethylene (CB/HDPE) composites were carried out. Change of resistivity ρ is associated with the dynamic modulus before the positive temperature coefficient/negative temperature coefficient (PTC/NTC) transition temperature. When the temperature approaches the melting point of HDPE, ρ increases rapidly with a decreasing modulus, corresponding to PTC transition. The resistivity‐dynamic viscoelasticity relationship in the PTC region can be divided into two parts in which the changes of ρ with storage modulus G ′ and loss modulus G ″ can be described by the scaling laws given by the critical storage modulus and loss modulus G ′ c and G ″ c ; adjustable parameters ρ′ 1c , ρ′ 2c , ρ″ 1c and ρ″ 2c ; and nonlinear exponents n and m , respectively. The accordance between the experimental data and the scaling functions of the dimensionless quantities ( G ′/ G ′ c − 1) and ( G ″/ G ″ c − 1) in the PTC transition region suggests that the ρ jump may be the result of a modulus‐induced percolation. G ′ c and G ″ c increase, but the four scaling resistivitis, ρ′ 1c , ρ′ 2c , ρ″ 1c , and ρ″ 2c , decrease with increasing CB concentration, implying that the microstructure change of the composites is the determinant factor for the PTC behavior and the resistivity‐dynamic modulus relationship. However, ρ′ 2c and ρ″ 2c exhibit no scaling dependence. It is suggested that a threshold concentration exists for the modulus of the composites on the basis of examining the plot of both G ′ c and G ″ c against CB concentration. The scaling laws G ′ ∼ Φ x and G ″ ∼ Φ y hold for the concentration dependence of the critical modulus when Φ > Φ c and the estimated values of x and y are 1.10 ± 0.10 and 0.89 ± 0.29, respectively. The resistivity‐dynamic modulus can shift to form a master curve. The horizontal factors a G ′ and a G ″ and the vertical factors a ′ and a ″ are relevant to the concentration dependence of the dynamic modulus or PTC behavior. It is believed that the former would be involved in changing the mechanical microstructure formed by the complicated interaction of CB particle and polymer segments, and the latter would be involved in the overall changes of conducting a network during the PTC transition region. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 983–992, 2003