Measurement and interpretation of nonuniversal critical exponents in disordered conductor–insulator composites

Abstract

The dc resistivity of carbon-black–polymer composites as a function of carbon-black concentration has been measured and fit to a power law, yielding a conductivity critical exponent t=2.9±0.1. This value is in excellent agreement with the mean-field value t=3. The sample-to-sample variations in resistivity at each concentration also show power-law behavior. If interpreted as due to correlation length fluctuations, these data yield a correlation-length critical exponent ν=0.51±0.02. This value is in excellent agreement with the mean-field value ν=1/2. These results suggest that nonuniversal (t≠2) transport behavior in this and similar composites is caused by the composite being outside the universal scaling regime and in the mean-field regime.