Electrical percolation threshold

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

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. 

Electrochemical redox studies of electroactive species solubilized in the water core of reverse microemulsions of water, toluene, cosurfactant, and AOT [28,29] have illustrated a percolation phenomenon in faradaic electron transfer. This phenomenon was observed when the cosurfactant used was acrylamide or other primary amide [28,30]. The oxidation or reduction chemistry appeared to switch on when cosurfactant chemical potential was raised above a certain threshold value. This switching phenomenon was later confirmed to coincide with percolation in electrical conductivity [31], as suggested by earlier work from the group of Francoise Candau [32]. The explanations for this amide-cosurfactant-induced percolation center around increases in interfacial flexibility [32] and increased disorder in surfactant chain packing [33]. These increases in flexibility and disorder appear to lead to increased interdroplet attraction, coalescence, and cluster formation. 

A somewhat different water, decane, and AOT microemulsion system has been studied by Feldman and coworkers [25] where temperature was used as the field variable in driving microstructural transitions. This system had a composition (volume percent) of 21.30% water, 61.15% decane, and 17.55% AOT. Counterions (sodium ions) were assigned as the dominant charge transport carriers below and above the percolation threshold in electrical... 

Similar to the percolation threshold, the effective electrical conductivity of a porous Ni-YSZ cermet anode depends on the morphology, particle size, and distribution of the starting materials as well. In general, the effective conductivity increases as the NiO particle size is reduced when other parameters are kept constant. As shown in Figure 2.4 (samples 1 and 2), the cermet conductivity increased from -10 S/cm to 103 S/cm as the NiO particle size was decreased from 16 to 1.8 pm while using the same YSZ powder (primary particle size of -0.3 pm) and the same Ni to YSZ volume fraction [30],... 

Similarly, other studies concluded that the anode effective electrical conductivity increases with the YSZ particle size when other parameters (Ni to YSZ volume ratio and the particle size of NiO) remain constant, as can be seen in Figures 2.5 [13], 2.4 (compare samples 4, 5, and 6) [30], 2.3 [14], and 2.1 [12], This is because it greatly influences the tendency of NiO clustering and downshifts the percolation threshold. 

As stated, the particle size also influences the distribution of phases and the percolation threshold. In general, the small particles tend to cluster around the large particles to form a continuous path (lower percolation threshold for the smaller particles). Thus, if NiO particles are smaller than YSZ particles, we would expect high electrical conductivity. In contrast, if the YSZ particles are smaller, electrical conductivity would be lower because the small YSZ particles tend to cluster around the larger Ni particle, making them electrically isolated. 

Alignment of CNTs markedly affects the electrical properties of polymer/CNT composites. For example, the nanocomposites of epoxy/MWCNTs with MWCNTs aligned under a 25 T magnetic field leads to a 35% increase in electric conductivity compared to those similar composites without magnetic aligned CNTs (Kilbride et al., 2002). Improvements on the dispersion and alignment of CNTs in a polymer matrix could markedly decrease the percolation threshold value. 

Tab. 4.3 Percolation threshold and conductivity for electrical transport using different types of nanocarbons in polymer composites.

Hu et al. showed a decrease in electrical resistivity of PVA by four orders of magnitude with a percolation threshold of 6 wt% [68], while biodegradable polylactide-graphene nanocomposites were prepared with a percolation threshold as low as 3 5wt% [46]. For polystyrene-graphene composites, percolation occurred at only 0.1 °/o of graphene filler, a value three times lower than those for other 2D-filler [69]. Figure 6.7(b) shows the variation of conductivity of the polystyrene-graphene composite with filler content. A sharp increase in conductivity occurs at 0.1 % (the percolation threshold) followed by a saturation. The inset shows the four probe set up for in-plane and trans-... 

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. 

Pang FI, Chen T, Zhang G, Zeng B, Li Z-M. An electrically conducting polymer/graphene composite with a very low percolation threshold. Materials Letters. 2010 Oct 31 64(20) 2226-9. 

This model, when applied to Nation as a function of water content, indicated a so-called quasi-percolation effect, which was verified by electrical impedance measurements. Quasi-percolation refers to the fact that the percolation threshold calculated using the single bond effective medium approximation (namely, x = 0.58, or 58% blue pore content) is quite larger than that issuing from a more accurate computer simulation. This number does not compare well with the threshold volume fraction calculated by Barkely and Meakin using their percolation approach, namely 0.10, which is less than the value for... 

The percolation model, which can be applied to any disordered system, is used for an explanation of the charge transfer in semiconductors with various potential barriers [4, 14]. The percolation threshold is realized when the minimum molar concentration of the other phase is sufficient for the creation of an infinite impurity cluster. The classical percolation model deals with the percolation ways and is not concerned with the lifetime of the carriers. In real systems the lifetime defines the charge transfer distance and maximum value of the possible jumps. Dynamic percolation theory deals with such case. The nonlinear percolation model can be applied when the statistical disorder of the system leads to the dependence of the system s parameters on the electrical field strength. 

Polymer nanotubes composites are now extensively studied. Indeed, one may associate the properties of the polymer with those of nanotubes. This is the case of the mechanical reinforcement of standard polymer for example, but also one can take advantage of the specific electronic properties of the nanotubes. Therefore, we prepared composites with either saturated polymers like polymethylmethacrylate and MWNTs [27]. The electrical conductivity of these compounds as a function of the nanotube content exhibits for example a very low percolation threshold, (a few % in mass) and therefore they can be used as conducting and transparent layers in electronic devices such as Light Emitting Diodes (LEDs). Another type of composite that we have studied is based on the use of a conjugated polymer, polyphenylene-vinylene (PPV) known for its photoluminescence properties and SWNTs. We prepared this composite by mixing SWNTs to the precursor polymer of PPV. The conversion into PPV was subsequently performed by a thermal treatment at 300°C under dynamical vacuum [28],... 

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 percolation threshold (0C) determined from concentration dependence of electrical resistance was near 6% mass MWNT. 

Fig. 5.9. Electrical conductivity variation versus weight fraction of SWNTs in the blend (filled circles). The percolation threshold is found to be 11%. The solid line is the fit of the percolation model [132].

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] ... 

The percolation behavior is manifested by the rapid increase in the dc electrical conductivity a and the static dielectric permittivity ss as the system approaches the percolation threshold (Fig. 7). 

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