Percolation double

The electrical conductivity of two-phase, incompatible polymer blends containing carbon black has been shown to depend on the relative affinity of the conductive particles to each of the polymer components in the blend, the concentration of carbon black in the filler-rich phase, and the structural continuity of this phase [82]. Hence, by judicious manipulation of the phase microstructure, these three-phase filled composites can exhibit double percolation behaviour. 

Because the conductive filler is located into a single component of the blend, these materials show an onset in the electrical conductivity at very low filler loadings of 2-3%. These findings have been explained by a double percolation effect. The CNT filled blends show superior mechanical properties in the tensile tests and in impact tests (25). 

Partial dissolution of an active mass often leads to poor cyclability by compaction and loss of the double percolation, electronic and ionic conductivity, necessary for a successful operation. This is especially true for PbS04, in diluted H2S04 (discharged battery). Metallic deposition in the separator of a dissolved metal may cause short circuits, accelerated self-discharge, and may prevent subsequent charging. 

Co-continuous polymer blends of 50/50 polyamide6/acrylonitrile-butadiene-styrene copolymer (PA6/ABS) involving multiwall carbon nanotubes (MWNTs) were prepared by melt mixing technique in order to develop conducting composites utilizing the concept of double-percolation. To control the dispersion and to selectively restrict MWNTs in the PA6 phase of the blends, MWNTs were pre-treated with two modifiers which differ in their molecular length scales and... 

In these systems, it is possible to obtain low percolation thresholds if a double percolation is present, that is, particle and phase percolation. This effect may be observed when the conductive particles, localized preferentially in one polymer phase, have a concentration equal or larger than the electric percolation threshold, and when the host polymer phase is the matrix or continuous phase of the polymer blend [155]. There are several models that describe the electroconductivity of these systems the effective medium theory, the onset for percolation theory, and thermodynamic models. Sumita s model considers the formation of chainlike conductive structures [151, 156]. 

The study of electroconductive polymer systems, based on conductive particles and polymer blends, has been quite intensive during the recent past. Gubbels et al. [149] studied the selective localization of CB particles in multiphase polymeric materials (PS and PE). According to these results, the percolation threshold may be reduced by the selective localization of CB. The minimum resistivity was obtained when double percolation (phase and particle percolation) exists in the PS-PE blend. In addition, it was found that the percolation threshold may be obtained at very low particle concentrations, provided that CB is selectively localized at the interface of the blend components. Soares et al. [150] found that the type of CB (i.e., different surface areas) does not affect the conductivity of the blend with 45/55 PS/PIP (polyisoprene) composition. 

Figure 10.40. Adsorption of the CNPs to the CR forms conductive pathways by double percolation [ZRI06], (For a color version of this figure, see WWW. iste. CO. uk/hamide/polymers.zip)...

Droval,G.,FeUer, J.F., Salagnac, P. and Glouannec, P. (2008) Conductive polymer composites with double percolated architectme of carbon nanoparticles and ceramic microparticles for high heat dissipation and sharp PTC switching. Smart Materials and Structures, 17 (2), 1-10. 

Mao et al. had tuned the morphology to improve the electrical properties of graphene filled immiscible polymer blends. PS and PMMA blends filled with octadecylamine-functionalized graphene (GE-ODA) were fabricated to obtain conductive composites with a lower electrical percolation threshold. The dependence of the electrical properties of the composites on the morphology was examined by changing the proportion of PS and PMMA. The electrical conductivity of the composites was optimal when PS and PMMA phases formed a co-continuous structure. For the PS/PMMA blend (50 wt/50 wt), the composites exhibited an extremely low electrical percolation threshold (0.5 wt%) because of the formation of a perfect double percolated structure (Mao et al. 2012). 

PC/SAN 60/40 C150HP MWCNT PC phase Irrespective of mixing protocols, even for pre-dispersing the nanotubes in SAN, all CNTs are located in the PC phase. The formation of double percolation network resulted in lower electrical resistivity Goldel et al. 2009... 

Zhang, C., Yi, X.S., YuL H., Asai, S., and Sumita, M. (1998) Selective localization and double percolation of short carbon fiber filled polymer blends high-density polyethylene/isotactic polypropylene. Mater. Lett., 36, 186. 

In a noncrystallizable polymer such as atactic polystyrene, is dose to 8wt%. In semicrystalline PE it is 5 wt%, presumably due to segregation of the CB to the noncrystalline phase or the phase boundaries in PE. This segregation is further enhanced in PE/PS blends when the composition allows for continuity of the PE phase and double percolation of the phases and conductive regions [27, 37]. This has been observed at a 45/55 ratio by weight of PE/PS in a melt-blended composition with more than 0.4 wt% (0.2 vol%) carbon black [27]. The effect seems to depend upon the relative interfacial tensions of the polymers and the CB in a manner consistent with the independent observations of Miyasaka et al. [38]. 

Thongruang, W., Spontak, R.J., and Balik, C.M. (2002) Bridged double percolation in conductive polymer composites an electrical conductivity, morphology, and mechanical property study. Polymer, 43, 3717. 

Depending on the blended polymers, one can achieve two types of carbon black distribution—one where the filler is homogeneously incorporated in one phase of the blend and another where the filler is preferably localized at the interface between the two polymers. This leads to so-caUed double percolation, which is explained by the fact that electrical conductivity was determined both by the filler concentration in the filler-rich phase and also by the structural continuity of this phase (Sumita etal. 1991,1992). 

Sumita Masao, Sakata Kazuya, Hayakawa Y., Asai Shigeo, Miyasaka Keizo, and Tanemura M. Double percolation effect on the electrical conductivity of conductive particles filled polymer blends. Colloid Polym. Sci. 270 no. 2 (1992) 134-139. 

It may be mentioned here that two stage (or double) percolation has been reported by Ray and Moulik [92] and Maiti et al. [93] for (water/AOT/decanol) and water/DTAB (octadecyltrimethylammonium bromide)-butanol/heptane microemulsion systems, respectively. The double percolation process for AOT/ decane/NaCl (0.5%) was also reported by Eicke et al. by conductivity, viscosity, and electro-optical Kerr effect [94]. The two processes demarcated three structural regimes viz, o/w, w/o, and oil or water continuous. 

Double percolation phenomenon has been reported previously for two phase polymer blends loaded with carbon black (P-77). Very low percolation thresholds were reported when conductive carbon black was preferentially localized at the phase boundary (P). Figure 9 shows the volume resistivity of phase-separated nylon/poly-... 

Here, <5 is the percolation exponent (we take 6 = 2.5), and is the percolation threshold for the hard phase. The percolation exponent, 6, typically ranges between 1.5 and 2 (see, e.g., ref. [52]), depending on the type of the system and the property described by a percolation model (modulus, conductivity, etc.). There are instances, however, when the percolation exponent could be larger than 2 (see, e.g., ref. [53]). Various models (e.., double percolation -see ref. [54]) have been proposed to explain these high percolation exponents. In our analysis, we refrain firom ascribmg any specific meaning to exponent 5 = 2.5, and treat it simply as an adjustable parameter that is found fi-om the best fit to experimental data. 

In this multiphase system, the term double percolation is defined to describe the conductive mechanism of polymer nanocomposites with a percolated network of nanofiller in one phase, which enables the formation of the conductive network through the whole polymer matrix. It has been proved that addition of conductive nanofillers into an immiscible polymer blend allows for the formation of cocon-tinuous structure and efficiently decreases the percolation threshold of nanofiUers due to the selective localization of the conductive networks. For example, Petra Poitschke et al. [89] introduced CNTs into Polycarbonate/Poly(styrene-acrylonitrile) (PC/SAN) to prepare CPCs. The percolation threshold of CNTs was less than 1 wt %, which is lower than those of CNTs in single PC matrix (1.2 wt%) and in single SAN phase (2.0 wt%).The localization of the conductive fiUer in polymer matrix depends on the interfacial energies of components and can be predicted by following Eq. (2) [86]. 

In conductive polymer blends, for example, TPO, another phenomenon must be taken into account—the localization of the conductive filler in only one of the available phases. Such composites characteristically acquire conductivity at lower filler loading levels than would be achieved by either of the two individual polymer phases. This advantaged percolation using localization of filler in a single phase of a polymer blend is called double percolation. Filler localization has been reported in a large number of conductive blends (40-54). 

The percolation threshold can be further reduced, and conductivity increased, if one makes use of the concept of double percolation, first theoretically studied by Levon, Margolina, and Patashinsky [164], and experimentally observed by Sumita and coworkers [161], as well as other researchers [157, 158, 162] for the dispersion of carbon black in binary polymer blends. To obtain double percolation, one needs to have a ternary system, with two phase-separating polymers and conducting filler with strong affinity to one of the polymers (we denote it as A, and the second polymer as B). Then, the system could be conducting if (i) filler loading in the A-domain is above percolation threshold and (ii) the volume fraction of the filled A-domains is above... 

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