Carbon percolation networks

Martin CA, Sandler JKW, Shaffer MSP, Schwarz M-K, Bauhofer W, Schulte K, et al. Formation of percolating networks in multi-wall carbon-nanotube-epoxy composites. Composites Science and Technology. 2004 Nov 64(15) 2309-16. 

In addition to the amount of filler content, the shape, size and size distribution, surface wettability, interface bonding, and compatibility with the matrix resin of the filler can all influence electrical conductivity, mechanical properties, and other performance characteristics of the composite plates. As mentioned previously, to achieve higher electrical conductivity, the conductive graphite or carbon fillers must form an interconnected or percolated network in the dielectrical matrix like that in GrafTech plates. The interface bonding and compatibility between... 

This behavior can be understood if a superimposed kinetic aggregation process of primary carbon black aggregates in the rubber matrix is considered that alters the local structure of the percolation network. A corresponding model for the percolation behavior of carbon black filled rubbers that includes kinetic aggregation effects is developed in [22], where the filler concentrations and c are replaced by effective concentrations. In a simplified approach, not considering dispersion effects, the effective filler concentration is given by ... 

Fig. 30a behaves similarly to that of the NBR/N220-samples shown in Fig. 29, i.e., above a critical frequency it increases according to a power law with an exponent n significantly smaller than one. In particular, just below the percolation threshold for 0=0.15 the slope of the regression line in Fig. 30a equals 0.98, while above the percolation threshold for 0=0.2 it yields n= 0.65. This transition of the scaling behavior of the a.c.-conductivity at the percolation threshold results from the formation of a conducting carbon black network with a self-similar structure on mesoscopic length scales. 

Admixing of 3-25% carbon black, thus generating a percolating network of electronically conducting inert material (cf. [477]). 

Martin, C. A., Sandler, J. K. W., Shaffer, M. S. P, Schwarz, M. K., Bauhofer, W., Schulte, K., and Windle, A. H., Formation of percolating networks in multi-wall carbon-nanotube-epoxy... 

Percolation theory can be applied to carbon nanotube networks.(S7-S3) As mentioned earlier, one third of carbon nanotubes or metallic and two thirds or semiconductive. If one has a random arrangement of SWNTs on a nonconducting smface at very low density, there are no electrical pathways. However, as the number of SWNTs increases, one will first reach the percolation threshold for the semiconductive carbon nanotubes. At this point, there is the possibility of having fully semiconductive pathways throughout the thin-film. However metallic pathways are not yet favored as metallic carbon nanotubes compose only l/S of the sample (Figure 2). 

Khalkhal and Carreau (2011) examined the linear viscoelastic properties as well as the evolution of the stmcture in multiwall carbon nanotube-epoxy suspensions at different concentration under the influence of flow history and temperature. Initially, based on the frequency sweep measurements, the critical concentration in which the storage and loss moduli shows a transition from liquid-like to solid-like behavior at low angular frequencies was found to be about 2 wt%. This transition indicates the formation of a percolated carbon nanotube network. Consequently, 2 wt% was considered as the rheological percolation threshold. The appearance of an apparent yield stress, at about 2 wt% and higher concentration in the steady shear measurements performed from the low shear of 0.01 s to high shear of 100 s confirmed the formation of a percolated network (Fig. 7.9). The authors used the Herschel-Bulkley model to estimate the apparent yield stress. As a result they showed that the apparent yield stress scales with concentration as Xy (Khalkhal and Carreau 2011). 

It has been possible to directly image the percolation network at the surface of a CB-polymer composite. An early report is that of Viswanathan and Heaney [24] on CB in HOPE in which it was shown that there are three regions of conductivity as a function of the length L, used as a metric for the image analysis. Below I = 0.6pm, the fractal dimension D of the CB aggregates is 1.9 0.1. Between 0.8 and 2 pm, the data exhibit D = 2.6 0.1 while above 3 pm, D = 3 corresponding to homogeneous behavior. Theory predicts D = 2.53. It is not obvious that the carbon black-polymer system should be explainable in terms of standard percolation theory, or that it should be in the same universality class as three-dimensional lattice percolation problems [24]. Subsequent experiments of this kind were made by Carmona [25, 26]. 

Gao L, Chou TW, Thostenson ET, Zhang Z, Coulaud M. Carbon. Vol 49, Iss 10, Aug 2011, 3382-3385. In situ sensing of impact damage in epoxy/glass fiber composites using percolating carbon nanotube networks. 

Concentrations that are too low will not form percolation networks. The Jansen equation (51) predicts that the critical concentration occurs when volume of polymer equals four times the volume of the CDBP value. The compounds are continuous when the amount of polymer is the CDBP value or greater and contain continuous carbon networks when the volume of polymer is between the CDBP value and four times that amount. 

In some conductive pol5uner composites, the NTC effect follows, for example, the resistivity decreases as the temperature increases further after PTC transition. The NTC effect is probably due to the reorientation, reaggregation, or reassembling of carbon black. Initially dispersed particles may become mobile in the temperature range of poljuner melting to repair the broken percolation network. The measurement of resistance versus the temperature behavior of the conductive... 

Hu, L., Hecht, D., Griiner, G., 2004. Percolation in transparent and conducting carbon nanotube networks. Nano Letters 4, 2513—2517. 

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