Percolation threshold composite

Yuen et al. 2008 (43) MWCNT CVD CNT Company, Incheon, Korea As-received In situ method Ex situ method CNT Loading levels 0.25 to 4.76 wt% Film Bulk Film Bulk Electrical Conductivity Percolation threshold 0.25 wt% for in situ prepared composites Percolation threshold 0.74 wt% for ex situ prepared composites EMI SE (2-18 GHz) 32.06 dB at 2.18 GHz for bulk composite prepared by in situ method 58.73 dB at 14.84 GHz for 10 layers of stacked composite film prepared by in situ method Higher EMI shielding effectiveness of layered composite attributed to energy loss by multi-reflections in the layered composites... 

Slobodian et al. 2007(57) MWCNT Sun Nanotech Co. Ltd. Purified Solvent Casting Followed by compression molding CNT loading levels 2 to 20 wt% Bulk Composites Percolation threshold Solvent Percolation MWCNT Hansen solubility parameters were used as a guide to characterize percolation thresholds ... 

Composites can be divided into two subgroups statistical mixtures and matrix-inclusion type composites. The effective dielectric function of the first subgroup can be calculated by equations, which are symmetrical with respect to phase indices. Statistical mixtures exhibit the so called percolation Phenomenon which is extremely important in conductor-insulator composites. Percolation threshold is a critical... 

The composites with the conducting fibers may also be considered as the structurized systems in their way. The fiber with diameter d and length 1 may be imagined as a chain of contacting spheres with diameter d and chain length 1. Thus, comparing the composites with dispersed and fiber fillers, we may say that N = 1/d particles of the dispersed filler are as if combined in a chain. From this qualitative analysis it follows that the lower the percolation threshold for the fiber composites the larger must be the value of 1/d. This conclusion is confirmed both by the calculations for model systems [27] and by the experimental data [8, 15]. So, for 1/d 103 the value of the threshold concentration can be reduced to between 0.1 and 0.3 per cent of the volume. 

The defects caused by the high contact resistance especially manifest themselves in the metal-filled composites where the value of the percolation threshold may reach 0.5 to 0.6 [30]. This is caused by the oxidation of the metal particles in the process of CPCM manufacture. For this reason, only noble metals Ag and Au, and, to a lesser extent, Ni are suitable for the use as fillers for highly conductive cements used in the production of radioelectronic equipment [32]. 

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. 

In the case of the filler localization in one of the polymer components of the mixture, an increase of the portion of the second unfilled polymer component in it entails sharp (by a factor of lO10) rise of a in the conducting polymer composite. In this case the filled phase should be continuous, i.e. its concentration should be higher than the percolation threshold. 

As already noted, the main merit of fibers used as a filler for conducting composite materials is that only low threshold concentrations are necessary to reach the desired level of composite conductivity. However, introduction of fiber fillers into a polymer with the help of ordinary plastic materials processing equipment presents certain difficulties which are bound up mainly with significant shearing deformations entailing fiber destruction and, thereby, a decrease of parameter 1/d which determines the value of the percolation threshold. 

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... 

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. 

Grunlan JC, Mehrabi AR, Bannon MV, Bahr JL (2004). Water-based single-walled-nanotube-filled polymer composite with an exceptionally low percolation threshold. Adv. Mater. 16 150-154. 

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-... 

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). 

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. 

With the U-Type systems (i.e. with the low chain alcohols) the trends in the conductivity - curve are consistent with percolative conduction originally proposed to explain the behaviour of conductance of conductor-insulator composite materials (27). In the latter model, the effective conductivity is practically zero as long as the conductive volume fraction is smaller than a critical value called the percolation threshold, beyond which k suddenly takes a non-zero value and rapidly increases with increase of Under these conditions. 

Wool and Cole (6) described a simulation model based on percolation theory for predicting accessibility of starch in LDPE to microbial attack and acid hydrolysis. This model predicted a percolation threshold at 30% (v/v) starch irrespective of component geometry, but the predicted values are not in accordance with results of enzymatic or microbial attack on these materials (Cole, M.A., unpublished data). Since a model that incorporates component geometry provides a better fit to experimental data than a geometry-independent model does, development of advanced models should be based on material geometry and composition, rather than on composition alone. 

In marked contrast to conventional injection moulding, where orientation effects normally depress conductivity, in this investigation the injection-moulded composite material yielded not only a lower percolation threshold than compression moulded samples, but in the injection direction, also gave conductivity values two to three orders of magnitude higher than the latter. 

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],... 

Percolation threshold pc corresponding transition to metal conductivity in composite films from Teflon with Au nanoparticles is 30 vol.% [36]. The similar transition to semiconductor conductivity in films of polyvinyl alcohol containing nanocrystals CuS takes place at pc 15-20 vol.% [88]. In cryochemically synthesized films PPX with Ag nanocrystals conductivity of metal type is achieved already in films with Ag content 7 vol.% conductivity of these composite films increases with the lowering temperature proportional to (1 — j.Ty1 similarly to that of block metals, but coefficient a is 2.5 times less than value x0, characteristic for block silver [86]. 

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