Percolation level

Since L and X are constant, in the absence of brush-like ordering. Pc Xc, which represents a critical number of chains required to build up the network above the percolation level. Hence we have... 

As it has been already shown the adsorption-induced change in the value of percolation electric conductivity of adsorbent and tangent of inclination angle in its pre-relaxation VAC are determined by adsorption-related change in the value of the percolation level and correlation length of the system, i.e. by functions c(0 and f ( c>0. One can readily conclude for 4c t) that when Nt < 4a - 4 co < i-e. at small Nt and... 

Semiconductive materials having conductivity between 10 and 10 S/cm have been studied more extensively. They are obtained by dispersion of conductive fillers—metallic and carbon based—in an insulating matrix. High filler contents are required, from 10 to 15% for fibres and 30% for spheres, to reach a percolation level leading to microwave losses. 

The effect of S WNT addition to PANi fibers on conductivity was also investigated (Figure 8). A percolation threshold of 0.35% (w/w) SWNTs was determined using the basic percolation power law [32]. The value for conductivity percolation threshold obtained here is in good agreement with another polymer-nanocomposite system that showed a 0.5 w/w % percolation level [33]. In addition, a significant increase in electrical conductivity was observed even at low SWNTs loadings, while the neat PANi-AMPSA fibers prepared here had similar conductivities ( 500 Scm ) compared to those obtained in a previous study (600 Scm ) [11]. 

Table 5.2 gives results for a series of CB grades, with respect to volume fractions 0.10 and 0.20, i.e., below and above the so-called percolation level of around 0.13. As we will see later, significant changes occur in a number of macroscopic properties, when filler content is above this level. In fact, most practical rubber compounds have filler content significantly above the percolation level (for instance =0.184 for the 50 phr N330 SBR compound described in Table 5.1). 

Present experimental evidence is somewhat inconclusive, except for elasticity where the classical theory works reasonably well in the majority of cases, and for viscosity where existing theories are unsatisfactory on both the classical and the percolation level. The exponent k = 0.8 determined for the divergence of the viscosity seems to be the most accurately known exponent of gelation at present. 

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