Modelling and prediction of percolation and conductivity properties of CNT-polymer compounds

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A. Wiegmann, O. Iliev
Fraunhofer ITWM, Kaiserslautern, Germany


Abstract 

The use of Carbon nano tubes (CNT) can result in major improvements of manufactured
thermally and electrically conducting plastic parts. Due to their high length-to-diameter (L/D)
ratios, and their high conductivity, very low concentrations of CNT may be employed. This
lowers the price, allows keeping the shape of a part and may even improve on the strength of
a part, while significantly enhancing the conductivity. Enhanced conductivity requries a
connected path of CNT through the part, i.e. that the network of CNT percolates [1].
The GeoDict / FiberGeo model of fiber networks [2] is combined with the GeoDict / Thermo-
Dict [3] solver to predict the effective thermal conductivity and COGraph [4, 5] to predict the
effective electric conductivity and percolation of CNT composites. The contrast of the thermal
conductivity is up to 4 orders of magnitude and the contrast of the electric conductivity is up
to 20 orders of magnitude. While ThermoDict works on 3d virtual tomographic images (vCT)
of the composite, COGraph considers only the network of CNT and neglects the matrix
material. ThermoDict has strenghts for smaller domains and lower contrast. COGraph works
strictly above the percolation threshhold, can handle very large domains (as required by low
CNT concentrations) and extremely high contrast (1e20) very efficiently and robustly.
The predictions for different L/D ratios and varying degrees of anisotropy of the CNT fibers
are compared with analytic models and experimental data for CNT-polymer compounds to
ultimatelyl find optimal volume fractions and L/D ratios of CNT fibers for applicatrons.

References
[1] M. Bierdel (2007). CarboNet: Eigenschaftsvorhersage von CNT-Polymer-Composites
durch Modellierung und Simulation des Perkolationsnetzwerks beim Verarbeitungsprozess. 3.
Wing Konferenz, Berlin, 22-24.10.2007
[2] K. Schladitz, S. Peters, D. Reinel-Bitzer, A. Wiegmann and J. Ohser, O. (2006). Design of
acoustic trim based on geometric modelling and flow simulation for non-woven. Comp. Mat.
Sci. 38, No 1, pp. 56-66.
[3] A. Wiegmann, A. Zemitis. (2006). EJ-HEAT: A Fast Explicit Jump Harmonic Averaging
Solver for the Effective Heat Conductivity of Composite Materials. ITWM Tech. Rep. #94.
[4] O. Iliev, R. Lazarov and J. Willems (2008). A Graph Laplacian Approach for calculating
effective thermal conductivity of complicated fiber geometries. ITWM Tech. Rep. #142.
[5] A. Brandt, O. Iliev and J. Willems (2008). A domain decomposition approach for
calculating the graph corresponding to a fibrous geometry. Proceedings of DD18 Conference
on Domain Decomposition.



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