Multiple threshold percolation in polymer/filler composites

Abstract

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.

Dielectric properties and electric breakdown strength of a subpercolative composite of carbon black in thermoplastic copolymer

“…Actually, since 3D percolation scaling was found above for sample thicknesses of 70 m, it must be concluded that the determined critical thickness is not connected in a simple way to fractal cluster size distribution. 28 The described experiments show that even though the dielectric spectra seem to indicate a well-behaved, insulating composite, a breakdown experiment reveals that the simple subpercolative approach to permittivity enhancements is not useful for general applications that require storage of energy, which is the case for most applications relying on capacitance effects. As already pointed out by Gyure and Beale, 25 this conclusion can be extended to similar systems where conducting particles are mixed with an insulating matrix.…”

Electrically Conductive Metal Polymer Nanocomposites for Electronics Applications

“…McQueen et al 5 recently presented various models for percolation, in which the role of local variations in filler particle concentration and/or shape and orientation in static filler/polymer composites were modeled as distributions of percolation thresholds. The concentration variations were considered to be the result of various processes, such as incomplete mixing, formation of semicrystalline voids during cooling from the melt, shrinkage during polymer curing, and flow during physical compression.…”

Metal–polymer composite with nanostructured filler particles and amplified physical properties

“…1,2 The properties of these composites have been studied since the 1950s and continue to be the focus of theoretical and experimental studies. [3][4][5] The conductivity of these composites can be described, once particle shape or agglomeration is taken into account, by statistical percolation 2 or an effective medium model. 3 The conductivity rises rapidly from a value close to that of the matrix when the filler fraction exceeds the percolation threshold.…”