Dynamic percolation of carbon nanotube agglomerates in a polymer matrix: comparison of different model approaches

A series of samples with different content of multi-walled carbon nanotubes (0.5-7.5 wt%) in polycarbonate was investigated by electrical conductivity measurements. During isothermal annealing of the as-produced samples in the melt state an increase of the conductivity with time was observed. A similar conductivity recovery was found after a short shear deformation of the melt. The time-dependent transition from insulating to conductive state is explained by dynamic formation of a conductive network of interconnected carbon nanotube agglomerates. The conductive networks were found to be stable after cooling the samples below their glass transition temperature. Comparison of the room temperature conductivity plotted vs. nanotube content for as-produced and annealed samples shows a tremendous shift of the insulator-conductor transition from above 5 wt% to about 0.75 wt%, respectively. For the description of the insulator-conductor transition three different approaches were tested; classical percolation, general effective medium model (GEM), and Fournier equation. All three models fit the data satisfactory. Dynamic percolation was described by the GEM model coupled to kinetic equation for CNT agglomeration. (C) 2008 WILEY-VCH Verlaq GmbH & Co. KGaA, Weinheim