The percolation behavior

On the other hand, the electrical anisotropy gradually weakens with the increase of CB concentration because higher CB loading means that more CB particles staying in the matrix to form a better conductive network. When the CB concentration rises up to 8.1 vol%, the conductive network is so perfect that the anisotropic intensity reduces down to 1.12. 

Classical percolation theory attempts to interpret the conductive mechanism in parallel and perpendicular directions which gives the following expression for the DC-conductivity 

As mentioned above, conductive network can be formed via fine contacts of aligned CB coated PET microfibrils. Additionally, the high t values suggest the existence of the tunneling conduction. Hence, contact conduction and tunneling conduction synergetically form the conductive networks of the ACPC material. 

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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 ... 

For a quantitative analysis of the percolation behavior of R, considered in Eq. (20), the permittivity data shown in Fig. 30b have been fitted to an empirical Cole-Cole function [131,132]. The fits are quite good, yielding relatively small broadness parameters between 0.36 and 0.5. The obtained relaxation times rR= R 1 are depicted in Fig. 31 in dependence of filler concentration O. Furthermore, the cross-over times T =a)fl and the limiting low frequency plateau values of the conductivity o ( —>0), obtained from the data in Fig. 30a, are represented in Fig. 31. They have been evaluated by a simple shifting procedure for constructing a conductivity master curve, as... 

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). 

Figure 7. The percolation behavior in AOT-water-decane microemulsion (17.5 21.3 61.2 vol%) is manifested by the temperature dependences of the static dielectric permittivity es (A left axis) and conductivity r (Q right axis). Toa is the temperature of the percolation onset Tp is the temperature of the percolation threshold. Insets are schematic presentations of the microemulsion structure far below percolation and at the percolation onset. (Reproduced with permission from Ref. 149. Copyright 1998, Elsevier Science B.V.)...

Figure 40 Static permittivity of an asphaltene-stabilized model emulsion vs. the applied external electric field. The percolation behavior is clearly seen. (From Ref 170.)...

The percolation behavior seen in (zero crossings (Figure 15.44a). The dispersion of the localized electrons at high energy (>0.06 eV) and the Drude dispersion in the lar-IR are hoth evident. For PPy(TsO), the... 

FIGURE 4 The resistance of 300 keV proton (H") implanted PPP (poly-p-phenylene) [IS]. These data combined, with the data shown in Fig. 3, indicate the percolation behavior of the resistivity as a function of dose. The percolation starts when the one-dimensional clusters come in contact with each other (this figure) and saturates when the three-dimensional carbon structures overlap (Fig. 3). 

The percolation behavior is determined by the shape of the filler and also by geometry and the dimension of the regarded composite sample (Boudenne et al. 2011 Barzic et al. 2014). 

D. Schubel and G. Ilgenfritz 1997 Influence of polyethylene glycols on the percolation behavior of anionic and nonionic w/o microemulsions, Langmuir 13,4246-4250. 

Cg = 0.43% (w/v). The deviation from the power-law behavior appeared below Tp, which was more pronounced for lower volume fractions. Such a deviation has been also observed in a AOT-water-decane microemulsion [6]. Thus, the present nanogel system exhibits the percolation behavior very similar to that of simple microemulsions. 

The author together with V. Sukharev has shown [21] that the percolation behavior of nanocomposites conductivity is different from the one typical for composites containing larger particles (Fig. 4). It has been demonstrated that the threshold filler concentration values are lower for nanocomposites than for composites with micron-size particles, and the slope of the curve in the... 

The results on MWCNT-polymer nanocomposites reported in this chapter demonstrate the versatility of the latex concept to prepare nanocomposites with a broad range of "home-made" or industrially manufactured polymers, namely, amorphous, semi-crystalline, and blended polymer matrixes. Note that blending can further be done in very different fashions, i.e., in situ, while the emulsion polymerization proceeds, by mixing of two different polymer latexes synthesized independently from each other, or by a "masterbatch approach." This study confirms that the CNT-polymer interactions are of major importance to influence the percolation behavior of the nanocomposites, as well as the viscosity, morphology, and the intrinsic conductivity of the polymer matrix. 

This behavior has been called percolation (Figs. 19.2 and 19.3). The percolation behavior of carbon blacks shows a dependence on the specific surface area. Carbon blacks with a large surface area display a much lower percolation point (which can be expressed in percentage by weight or volume, wt % or vol 9f) 9J. 

It is not possible on the basis of percolation theory to explain the percolation behavior of the spherical ICP primary particles that exist in totally disperse form below the percolation point. The percolation theory is based on the assumption that particles that do not enter into any interaction with the matrix are statistically distributed within it. This enabled the theoreticians to arrive at a mathematical description of the percolation behavior from a purely statistical and mechanistic point... 

Several simulation approaches have been employed to model the effect of uniaxial orientation of rodlike fillers on the percolation behavior in 2D and 3D. In 2D, simple anisotropic stick orientation distributions can be obtained by allowing the angle 0, between stick i and the longitudinal axis to be selected randomly in the interval where... 

Fig. 8. Specific conductivity as a function of the volume fraction (j) demonstrating the percolative behavior at different temperatures (30°C (o), 60°C (+), 90°C (x), 120°C () and 150°C (A)) (Reproduced from (Zech et al., 2010 a) with permission, copyright Wiley-VCH Verlag, 2010).

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