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Conduction Mechanisms in Graphite Polymer Composites
As mentioned in the previous sections, graphite is characterized by good electrical and thermal conductivity. Since polymers are both electrically and thermally insulating, graphite powders are suitable fillers to improve the conductivity of polymer compounds (see Fig. 5).
Fig. 5 Polymers are intrinsically, electrically, and thermally insulating. Depending on the application, higher conductivity values are required that can be obtained by polymer compounds with appropriate conductive fillers
The mechanism for electrical and thermal conduction is very different. For the electrical conductivity, the percolation models of carbon black (? Chap.19, “Carbon Black for Electrically Conductive Polymer Applications”) are valid also for graphite and other carbon allotropes; electrical resistivity decreases sharply above the percolation threshold by several orders of magnitude. However, the electronic conduction mechanism in the conduction zone is ohmic in nature and consequently based on direct particle contacts once the conductive graphite network is formed at loadings beyond the percolation threshold. This mechanism would apply for carbon black and other carbon particles with diameters below ca. 300 nm only in the compressed dry powder form or in the polymer composite at very high loadings (Hess and Herd 1993).
For the thermal conductivity, on the other hand, the main mechanism is related to thermal vibrations of the atoms (phonons). Thermal transport requires multiple particle-to-particle paths and is a much smoother transition compared to the electrical percolation. The smoother transition is also due to the difference in conductivity between graphite and polymer matrix (typically 3 orders of magnitude for thermal conductivity compared to 20 orders of magnitude for the electrical conductivity). As shown in Fig. 6, two different regimes can be identified: electrically and thermally insulating compound below the percolation threshold and electrically and thermally conductive compound above the percolation threshold.
The thermal conductivity of polymer compounds depends on many factors: loading level, filler type, morphology and particle size distribution, and mixing and processing conditions. Several different models have been developed to predict the thermal conductivity of polymer composites. The two basic models are the “rule of mixture” (or “parallel model”) and the “series model.” In the rule of mixture
Fig. 6 Schematic view of electrical and thermal conductivity as a function of graphite loading in polymer composite. The electrical resistivity decreases sharply at the percolation threshold, whereas the thermal conductivity increases smoothly model, each phase contributes proportionally to its volume fraction to the overall thermal conductivity. This model assumes perfect contact between each particle and generally overestimates the measured thermal conductivity values (upper limit). The series model, on the contrary, assumes no contact between the particles and usually underestimates the real thermal conductivity (lower limit). Most of the experimental results obtained for graphite fillers are between these two models, more likely near the lower limit. More complex models for both isotropic spherical particles and for anisotropic particles (fibers, platelets) have been developed. For example, particle shape and orientation are considered in the Lewis-Nielsen model (Nielsen 1974). In some models, the thermal resistance between particles and matrix is considered (also called Kapitza resistance). The high Kapitza resistance is one of the reasons of the lower thermal conductivity in carbon nanotube polymer composites compared with expectations from the intrinsic thermal conductivity of carbon nanotubes (Hana and Fina 2011). Surface modifications of the filler and addition of compatibilizers during compounding have been suggested in order to improve the interaction to the polymer and to decrease the Kapitza resistance and therefore increase the thermal conductivity of the compound.
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