Carbon percolation thresholds

In pressing, the threshold concentration of the filler amounts to about 0.5% of volume. The resulting distribution of the filler corresponds, apparently, to the model of mixing of spherical particles of the polymer (with radius Rp) and filler (with radius Rm) for Rp > Rm as the size of carbon black particles is usually about 1000 A [19]. During this mixing, the filler, because of electrostatical interaction, is distributed mainly on the surface of polymer particles which facilitates the forming of conducting chains and entails low values of the percolation threshold. 

For the second method the threshold concentration of the filler in a composite material amounts to about 5 volume %, i.e. below the percolation threshold for statistical mixtures. It is bound up with the fact that carbon black particles are capable (in terms of energy) of being used to form conducting chain structures, because of the availability of functional groups on their surfaces. This relatively sparing method of composite material manufacture like film moulding by solvent evaporation facilitates the forming of chain structures. 

Above a critical hller concentration, the percolation threshold, the properties of the reinforced rubber material change drastically, because a hller-hUer network is estabhshed. This results, for example, in an overproportional increase of electrical conductivity of a carbon black-hUed compound. The continuous disruption and restorahon of this hller network upon deformation is well visible in the so-called Payne effect [20,21], as represented in Figure 29.5. It illustrates the strain-dependence of the modulus and the strain-independent contributions to the complex shear or tensUe moduli for carbon black-hlled compounds and sUica-hUed compounds. 

Fillers with extremely high aspect ratios (1000-10,000) such as carbon nanotubes (Figure 32.5) have a much lower percolation threshold (lower amount is required for equivalent reinforcement). 

Carbon structure Percolation threshold Electrical conductivity (S/cm) References... 

Where a is the composite conductivity, a0 a proportionally coefficient, Vfc the percolation threshold and t an exponent that depends on the dimensionality of the system. For high aspect ratio nanofillers the percolation threshold is several orders of magnitude lower than for traditional fillers such as carbon black, and is in fact often lower than predictions using statistical percolation theory, this anomaly being usually attributed to flocculation [24] (Fig. 8.3). 

Logakis E, Pissis P, Pospiech D, Korwitz A, Krause B, Reuter U, et al. Low electrical percolation threshold in polyethylene terephthalate)/multi-walled carbon nanotube nanocomposites. European Polymer Journal. 2010 May 46(5) 928-36. 

Sandler JKW, Kirk JE, Kinloch IA, Shaffer MSP, Windle AH. Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites. Polymer. 2003 Sep 44(19) 5893-9. 

Well-established anode materials are Ni cermets such as Ni/YSZ composites. The presence of the second phase increases the contact area and prevents the catalytically active Ni particles from aggregating. The use of the composite becomes problematic if hydrocarbons are to be directly converted Ni catalyzes cracking, and the resulting carbon deposition deactivates the fuel cells. Therefore either pure H2 has to be used or the fuel has to be externally reformed. A third way is internal conversion of CHV with H20 to synthesis gas. The necessary steam addition, however, reduces the overall efficiency. Another problem of Ni cermets, if they are to be used at lower temperatures, is a potential oxidation of the Ni. Alternatives are Cu/Ce02 cermets in which Cu essentially provides the electronic conductivity and Ce02 the catalytic activity. Note that an efficient current collecting property of the electrode presupposes a metal concentration above the percolation threshold. 

By the method of introducing Pt into the DLC, the platinum metal is assumed to be distributed over the carbonaceous material bulk as discrete atoms or clusters [154], Essentially, Pt is not a dopant in the DLC, in the sense that the term is used in semiconductor physics. Nor is the percolation threshold surpassed, since the admixture of Pt (not exceeding 15 at. %) did not affect the a-C H resistivity, as was shown by impedance spectroscopy tests p 105 Q, cm, like that of the undoped DLC (see Table 3). It was thus proposed that the Pt effect is purely catalytic one Pt atoms on the DLC surface are the active sites on which adsorption and/or charge transfer is enhanced [75], (And the contact of the carbon matrix to the Pt clusters is entirely ohmic.) This conclusion was corroborated by the studies of Co tetramethylphenyl-porphyrin reaction kinetics at the DLC Pt electrodes [155] redox reactions involving the Co central ion proceed partly under the adsorption of the porphyrin ring on the electrode. 

Abstract. It is shown that reinforcement of PTFE by 15% of multiwall carbon nanotubes (MWNT) results in more than 2 times increase of strength parameters compared to starting PTFE matrix. Non-trivial temperature dependences of electrical resistance and thermal electromotive force were observed. Percolation threshold determined from dependence of the composite specific resistance on MWNT concentration was near 6% mass. Concentration and nature of oxygen-containing MWNT surface groups influence the strength parameters of the composite material. 

The electrical percolation behavior for a series of carbon black filled rubbers is depicted in Fig. 26 and Fig. 27. The inserted solid lines are least square fits to the predicted critical behavior of percolation theory, where only the filled symbols are considered that are assumed to lie above the percolation threshold. According to percolation theory, the d.c.-conductivity Odc increases with the net concentration 0-0c of carbon black according to a power law [6,128] ... 

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. 

The reduced value of the scaling exponent, observed in Fig. 29 and Fig. 30a for filler concentrations above the percolation threshold, can be related to anomalous diffusion of charge carriers on fractal carbon black clusters. It appears above a characteristic frequency (O when the charge carriers move on parts of the fractal clusters during one period of time. Accordingly, the characteristic frequency for the cross-over of the conductivity from the plateau to the power law regime scales with the correlation length E, of the filler network. 

An explanation of the observed relaxation transition of the permittivity in carbon black filled composites above the percolation threshold is again provided by percolation theory. Two different polarization mechanisms can be considered (i) polarization of the filler clusters that are assumed to be located in a non polar medium, and (ii) polarization of the polymer matrix between conducting filler clusters. Both concepts predict a critical behavior of the characteristic frequency R similar to Eq. (18). In case (i) it holds that R= , since both transitions are related to the diffusion behavior of the charge carriers on fractal clusters and are controlled by the correlation length of the clusters. Hence, R corresponds to the anomalous diffusion transition, i.e., the cross-over frequency of the conductivity as observed in Fig. 30a. In case (ii), also referred to as random resistor-capacitor model, the polarization transition is affected by the polarization behavior of the polymer matrix and it holds that [128, 136,137]... 

This paper represents an overview of investigations carried out in carbon nanotube / elastomeric composites with an emphasis on the factors that control their properties. Carbon nanotubes have clearly demonstrated their capability as electrical conductive fillers in nanocomposites and this property has already been commercially exploited in the fabrication of electronic devices. The filler network provides electrical conduction pathways above the percolation threshold. The percolation threshold is reduced when a good dispersion is achieved. Significant increases in stiffness are observed. The enhancement of mechanical properties is much more significant than that imparted by spherical carbon black or silica particles present in the same matrix at a same filler loading, thus highlighting the effect of the high aspect ratio of the nanotubes. 

The recognition of the unique properties of carbon nanotubes (CNTs) has stimulated a huge interest in their use as advanced filler in composite materials. In particular, their superior mechanical, thermal and electrical properties are expected to provide much higher property improvement than other nanofillers (18-22). For example, as conductive inclusions in polymeric matrices, CNTs shift the percolation threshold to much lower loading values than traditional carbon black particles. 

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