Multiple threshold percolation in polymer/filler composites

Local variations in filler particle concentration and/or shape and orientation in static filler/polymer composites are modelled as distributions of percolation thresholds. The concentration variations can be due to insufficient mixing, formation of semicrystalline voids during cooling from the melt, shrinkage during polymer curing, flow during physical compression or the like. Irregular filler shapes, especially elongated shapes, reduce the percolation threshold; thus, natural variations in the shapes and orientations of filler particle aggregates lead to locally varying percolation thresholds. A distribution of percolation thresholds leads to an apparent average percolation threshold based on the conductivity below the mean percolation threshold. For filler concentrations above the apparent percolation threshold, the dielectric constant continues to increase before reaching a lowered peak value at the mean percolation threshold and then decreasing. This can explain some 'anomalous' published experimental results concerning the dielectric constant just above the percolation threshold. In the frequency plane, the percolation threshold distribution can lead to a slight reduction of the apparent critical exponents x and y of the frequency dependencies of the conductivity and relative dielectric constant, respectively. Our experimental results on ethylene butylacrylate copolymer/carbon black composites support the theory.