Electrical transport measurements of a carbon-black—polymer composite

I have measured simultaneously the resistance and linear expansion of a disordered carbon-black-polymer composite as a function of temperature from 25°C to 180°C. Both the sample resistance and thickness increase monotonically as a function of temperature, with precipitous increases at the polymer melt temperature. The resistance vs. thickness data increase monotonically with no precipitous increases. These results suggest that the electrical conduction mechanism is the same below, during, and above the polymer melt temperature. I have also measured the DC resistivity of these composites as a function of carbon-black concentration at room temperature. The data can be fit to a scaling law, yielding a conductivity critical exponent t = 2.9 ± 0.1. This value agrees well with the theoretical mean-field value t = 3. This result suggests that the electrical transport is governed by mean-field behavior.