Percolation of rigid fractal carbon black aggregates.

We examine network formation and percolation of carbon black by means of Monte Carlo simulations and experiments. In the simulation, we model carbon black by rigid aggregates of impenetrable spheres, which we obtain by diffusion-limited aggregation. To determine the input parameters for the simulation, we experimentally characterize the micro-structure and size distribution of carbon black aggregates. We then simulate suspensions of aggregates and determine the percolation threshold as a function of the aggregate size distribution. We observe a quasi-universal relation between the percolation threshold and a weighted average radius of gyration of the aggregate ensemble. Higher order moments of the size distribution do not have an effect on the percolation threshold. We conclude further that the concentration of large carbon black aggregates has a stronger influence on the percolation threshold than the concentration of small aggregates. In the experiment, we disperse the carbon black in a polymer matrix and measure the conductivity of the composite. We successfully test the hypotheses drawn from simulation by comparing composites prepared with the same type of carbon black before and after ball milling, i.e., on changing only the distribution of aggregate sizes in the composites.