The electrical property of polymer matrix composites with added carbon powder is studied based on the temperature dependency of the conduction mechanism. The temperature coefficient of the resistance of the polymer matrix composites below the percolation threshold (x) changed from negative to positive at 0.20 < x < 0.21; this trend decreased with increasing of the percolation threshold. The temperature dependence of the electrical property(resistivity) of the polymer matrix composites below the percolation threshold can be explained by using a tunneling conduction model that incorporates the effect of the thermal expansion of the polymer matrix composites into the tunneling gap. The temperature coefficient of the resistance of the polymer matrix composites above the percolation threshold has a positive value; its absolute value increased with increasing volume fraction of carbon powder. By assuming that the electrical conduction through the percolating paths is a thermally activated process and by incorporating the effect of thermal expansion into the volume fraction of the carbon power, the temperature dependency of the resistivity above the percolation threshold can be well explained without violating the universal law of conductivity.

This paper investigates the change of the percolation threshold in the carbon powder-filled polystyrene matrix composites based on the experimental results of changes in the resistivity and relative permittivity of the carbon powder filling, the electric field dependence of the current, and the critical exponent of conductivity. In this research, the percolation behavior, the critical exponent of resistivity, and electrical conduction mechanism of the carbon powder-filled polystyrene matrix composites are discussed based on a study of the overall change in the resistivity. It was found that the formation of infinite clusters is interrupted by a tunneling gap in the volume fraction of the carbon powder filling, where the change in the resistivity is extremely large. In addition, it was found that the critical exponent of conductivity for the universal law of conductivity is satisfied if the percolation threshold is estimated at the volume fraction of carbon powder where non-ohmic current behavior becomes ohmic. It was considered that the mechanism for changing the gaps between the carbon powder aggregates into ohmic contacts is identical to that of the connecting conducting phases above the percolation threshold in a random resister network system. The electric field dependence is discussed with a tunneling mechanism. It is concluded that the percolation threshold should be defined at this volume fraction (the second transition of resistivity for the carbon powder-filled polystyrene matrix composites) of carbon powder.

Conductive polymer composites (CPCs) consist of a polymeric matrix and a conductive fil-er, for example, carbon black, carbon fibers,graphite or carbon nanotubes (CNTs). The criti-cal amount of the electrically conductive fillernecessary to build up a continuous conductive network, and accordingly, to make the material conductive; is referred to as the percolation threshold. From technical and economical viewpoints, it is desirable to decrease the conduc-tive-fillerpercolation-threshold as much as possible. In this study, we investigated the effect of polymer/conductive-fillerinteractions, as well as the processing and morphological devel-opment of low-percolation-threshold (Φc) conductive-polymer composites. The aim of the study was to produce conductive composites containing less multi-walled CNTs (MWCNTs) than required for pure polypropylene (PP) through two approaches: one using various mix-ing methods and the other using immiscible polymer blends. Variants of the conductive PP composite filledwith MWCNT was prepared by dry mixing, melt mixing, mechanofusion, and compression molding. The percolation threshold (Φc) of the MWCNT-PP composites was most successfully lowered using the mechanofusion process than with any other mixing method (2-5 wt%). The mechanofusion process was found to enhance formation of a perco-lation network structure, and to ensure a more uniform state of dispersion in the CPCs. The immiscible-polymer blends were prepared by melt mixing (internal mixer) poly(vinylidene fluoride) (PVD, PP/PVDF, volume ratio 1:1) filled with MWCN.

Composites of insulating polyethylene and carbon black are widely used in switching elements, conductive paint, and other applications due to the large gap of resistance value. This research addresses the critical exponent of dielectric breakdown strength of polymer matrix composites (PMC) made with carbon black and polyethylene below the percolation threshold (Pt) for the first time. Here, Pt means the volume fraction of carbon black of which the resistance of the PMC is transferred from its sharp decrease to gradual decrease in accordance with the increase of carbon-black-filled content. First, the Pt is determined based on the critical exponents of resistivity and relative permittivity. Although huge cohesive bodies of carbon black are formed in case of being less than the Pt, a percolation path connecting the conducting phases is not formed. The dielectric breakdown strength (Dbs) of the PMC below Pt is measured by using an impulse voltage in the range from 10 kV to 40 kV to avoid the effect of joule heating. Although the observed Dbs data seems to be well fitted to a straight line with a slope of 0.9 on a double logarithm of (Pt-VCB) and Dbs, the least squares method gives a slope of 0.97 for the PMC. It has been found that finite carbon-black clusters play an important role in dielectric breakdown.

It is known that the relative dielectric constant of insulating polyethylene matrix composites with conducting materials (such as carbon black and metal powder) increases as the conducting material content increases below the percolation threshold. Below the percolation threshold, dielectric properties show an ohmic behavior and their value is almost the same as that of the matrix. The change is very small, but its origin is not clear. In this paper, the dielectric properties of carbon black-filled polyethylene matrix composites are studied based on the effect medium approximation theory. Although there is a significant amount of literature on the calculation based on the theory of changing the parameters, an overall discussion taking into account the theory is required in order to explain the dielectric properties of the composites. Changes of dielectric properties and the temperature dependence of dielectric properties of the composites made of carbon particle and polyethylene below the percolation threshold for the volume fraction of carbon black have been discussed based on the theory. Above the percolation threshold, the composites are satisfied with the universal law of conductivity, whereas below the percolation threshold, they give the critical exponent of s = 1 for dielectric constant. The rate at which the percentages of both the dielectric constant and the dielectric loss factor for temperature increases with more volume fraction below the percolation threshold.

In this paper two aspects of the percolation and conductivity of carbon black-filled polyethylene matrix composites will be discussed. Firstly, the percolation behavior, the critical exponent of conductivity of these composites, are discussed based on studying the whole change of resistivity, the relationship between frequency and relative permittivity or ac conductivity. There are two transitions of resistivity for carbon black filling. Below the first transition, resistivity shows an ohmic behavior and its value is almost the same as that of the matrix. Between the first and second transition, the change in resistivity is very sharp, and a non-ohmic electric field dependence of current has been observed. Secondly, the electrical conduction property of the carbon black-filled polyethylene matrix composites below the percolation threshold is discussed with the hopping conduction model. This study investigates the electrical conduction property of the composites below the percolation threshold based on the frequency dependence of conductivity in the range of 20 Hz to 1 MHz. There are two components for the observed ac loss current. One is independent of frequency that becomes prevalent in low frequencies just below the percolation threshold and under a high electrical field. The other is proportional to the frequency of the applied ac voltage in high frequencies and its origin is not clear. These results support the conclusion that the electrical conduction mechanism below the percolation threshold is tunneling.

Temperature dependency of resistivity of the carbon black-polyethylene composites below and above percolation threshold is studied based on the electrical conduction mechanism. Temperature coefficient of resistance of the composites below percolation threshold changed from minus to plus, increasing volume fraction of carbon black; this trend decreased with increasing volume fraction of carbon black. The temperature dependence of resistivity of the composites below percolation threshold can be explained with a tunneling conduction model by incorporating the effect of thermal expansion of the composites into a tunneling gap. Temperature coefficient of resistance of the composites above percolation threshold was positive and its absolute value increased with increasing volume fraction of carbon black. By assuming that the electrical conduction through percolating paths is a thermally activated process and by incorporating the effect of thermal expansion into the volume fraction of carbon black, the temperature dependency of the resistivity above percolation threshold has been well explained without violating the universal law of conductivity. The apparent activation energy is estimated to be 0.14 eV.