Percolation threshold values

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. 

From Section IX, our best fits to the measured viscosity data for six glass formers give p =o /i i30 at 7. That is, for each 20 to 40 atoms within a cluster, we expect to find a void of the size Having chosen the percolation threshold value of =0.15, we found that />, 0.2 was a typical result from our relaxation studies of the specific heat near Tg. Then if we consider... 

The combination of electrical properties with good mechanical performance is of particular interest in electroactive pol5mieric technology. Fibers have an intrinsically high structure factor, which results in lower percolation threshold values, avoiding material fracture with low filler content Also, the use of mechanically stronger fibers will result in stronger composites. 

Figure 5.8 shows the dependence of complex viscosity (frequency tu = 1 rad/s, strain = 1%) on the concentration of the nanofillers (i.e., MMT-BAPS, SNT, and Zr02) for the current OI-l nanocomposites prepared as already described. The figure shows significant increases ( 3 decades) for the OI/MMT-BAPS and OI/SNT nanocomposites occurring at 2-3 vol% MMT-BAPS and 8-12 vol% SNT nanofiller concentrations, respectively. For the two types of nanocomposites just mentioned, the critical nanofiller concentrations corresponding to the dramatic rise in viscosity were found to be both higher than the percolation threshold values estimated theoretically as already described [i.e.. Pc... 

The percolation-like behavior of polymer-nanocomposites conductivity is a crucial property for device manufacture since all the electrophysical and a number of other properties change completely once the percolation threshold concentration is reached. The question should always be asked whether to utilize the properties of non-contacting nanoparticles in a polymer matrix below the threshold or those consisting of an interconnected particle network, with topology, connectivity and persistence length changing depending on the filler concentration excess over the percolation threshold value. 

The author with co-workers [39] has investigated systems with the structures Al/Cso/PANI+CdS/ITO and Al/Cgo/PPV-l-CdInS/ITO. Most worthy of note are the dependencies of the short circuit current and the open circuit voltage on the nanoparticles concentration (Fig. 21). Since the fullerene molecule acts as a strong electron acceptor, excitons generated both in the polymer matrix and in the CdS particles are decomposed, electrons are accepted by the Ceo layer and the holes are transported to the anode through the polymer. Once the concentration of the nanoparticles exceeds the percolation threshold value, the system becomes short contacted, since the electrons can pass from the anode to the cathode through the barrier-free connected network of CdS clusters this latter fact leads to the disappearance of the photovoltaic effect, as illustrated in Fig. 21b. The increase in the photocurrent and the open circuit... 

The capacitance change upon absorption in nanocomposites with the filler concentration lower than the percolation threshold is another opportunity to monitor the dielectric permeability change. The effect consists of the existence of the dielectric constant anomaly for the conductive filler concentrations just below the percolation threshold values. The anomaly is due to the giant cross capacitance of big clusters of nanoparticles formed close to the percolation threshold which are not yet in contact with each other (the effect is similar to other critical phenomena, e.g. the behavior of ferromagnetics close to the Curie temperature). The absorption of the gas molecules by the polymer matrix leads to a highly non-linear capacitance change. The use of such polymer-nanocomposite layers placed on the top of field effect transistors (ChemFETs) has been proposed [41], but not yet realized. 

Due to their unique properties, CNTs have attracted considerable attention since their discovery in 1991 by lijima (50). Their high electrical conductivity, great mechanical strength, and low percolation threshold values make them attractive as additive materials for precipitates in lithium-ion batteries (51). 

Figure 5.3 [resp. Figure 5.4]. Upon further CNT addition, the conductivity levels off around 70 S/m (resp. 7 S/m] at 2 wt% of MWCNTs (resp. SWCNTs], irrespective of the type of matrix. Note, however, that the same CNTs dispersed in a PS matrix, following the same experimental procedure, exhibit significantly higher percolation threshold values than in the CNT/iPP-g-MA series, namely, of the order of 0.55 wt% for SWCNT/PS systems and 0.81 wt% for MWCNT/PS nanocomposites.

Even if conductivity results of CNT/polymer nanocomposites are commonly reported in terms of wt%, mainly because of lack of precise CNT density values, percolation is considered to be a volumetric phenomenon. In an attempt to fairly compare conductivity results obtained for systems containing either SWCNTs or MWCNTs dispersed in a given polymer matrix, the percolation threshold values of the various nanocomposites series were calculated in terms of vol% CNT. See ref. [28] for the details of the calculation. 

Table 5.1 Comparison of the percolation threshold values and of the conductivity levels measured for the different systems studied...

Figure 99 Distributions ns of clusters with S water molecules in densely packed lysozyme powder at T = 400 K. Mass fraction of water increases from C = 0.128 (top) to 0.201 (bottom). Circles represent at C = 0.151, when the spanning cluster exists with probability of about 50%, while squares correspond to C = 0.173, when the fractal dimension of the largest cluster is close to the 2D percolation threshold value. The distributions are shifted consecutively by one order of magnitude each, starting from the bottom. Reprinted, with permission, from [401].

Polyamide 6/graphite nanocomposites with markedly low percolation threshold value were recently prepared using an in-situ polycondensation approach. Based on transmission electron microscopy (TEM) results, the thickness of EG filler incorporated in the polymer matrices was found to vary from 10 to 50 nm, and the aspect ratios (diameter to thickness) can be estimated as high as 100-300. The graphite used by Pan et al. is termed foliated graphite (FG). FG can... 

To determine the percolation threshold value for a polymer insulator/ conductive filler composite, several theoretical elaboration methods have been proposed, including percolation theory, mean-field theory and excluded volume theory. Only the percolation theory is introduced in this review. 

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