Percolation conductivity of polymer composites filled with dispersed conductive filler

Abstract

This paper deals with the conductivity of binary polymer composites filled with an electronically conductive material. A “dynamic cluster model” is offered to describe the conductivity of such polymer composites in the highly filled region, i.e. above the percolation threshold. The model is based on the following assumptions: a modification of the basic statistical percolation equation, i.e. σ (φ−φc)t, where t = 1.6 to 1.9, should be applied for all systems in the highly filled region, although application is limited to the range φ = φc + Δφ, Δφ ⟹ 0 in the strict statistical percolation approach; the most important modifications with respect to the basic equation of the statistical percolation theory are (a) the use of a constant teff, including a constant part t1 (resembling “t” in the basic statistical percolation approach) and a variable part t2 (depending on the filler concentration φ of the specific mixture) and (b) the definition of φc as the filler concentration where a perfect three‐dimensional network of the conductive phase has been established. This idea has been adopted from the bond‐percolation approach of Aharoni; the resulting equation should include parameters of specific polymer composites. The generalized equation σ = f(φ) is used to calculate the maximum possible conductivity of a certain mixture as well as the dependence of σ on the filler content.

Electrical Conductivity Modeling of Polypropylene Composites Filled with Carbon Black and Acetylene Black

“…It takes into account the parameters previously neglected by other researchers. It gives a good agreement in the case of polymer composites filled with carbon black beyond the percolation threshold [14,15,[17][18][19][20][21][22]. Mamunya model cannot be used for filler concentrations lower than those of the percolation threshold and the term ((x − 2, 61)/27, 39) becomes negative in this area.…”

“…But at the onset of the percolation threshold the conductivity increases drastically as illustrated in Figure 2 on a semilogarithmic scale. Beyond a certain critical concentration this increase seems to be evolving more moderately [21][22][23][24].…”

“…This is explained by the fact that Mamunya model was designed primarily to predict the behavior of polymers filled with carbon black beyond the percolation threshold [14,15,[17][18][19][20][21][22].…”

Material property models for polyethylene-based conductive blends suitable for PEM fuel cell bipolar plates

“…One thermodynamic model by Mamunya 15 exists which takes into account the interactions between the polymer and filler using interfacial tension and surface energies in addition to the size and quantity of material where a packing factor of the filler takes into account filler morphology. However, the model predicts the rapid increase in conductivity (i.e.…”

“…Two hot presses were used, one for heating and one for cooling. For carbon black and graphite composites, the heated press was initially set to 170 C for the lowest composite filler content and then increased by 15 C for every 10 wt% increase to allow the material to flow sufficiently. The pure polymer samples were formed at 160 C and the magnetite filled composites flowed sufficiently at a constant 170 C for all composite grades as the filler volume fraction was low due to magnetite's higher density of 5.02 g cm À3 compared to 1.82 g cm À3 and 2.24 g cm À3 for carbon black and graphite, respectively.…”