SWCNT percolation threshold

The fact that a minimal change in the SWCNT percolation threshold is observed when introducing QDs raises the question if the SWCNT and QDs are at all interacting. To determine the distribution of SWCNTs and QDs within the PS matrix, scanning electron microscopy (SEM] micrographs of the surface of the PS/ QD/SWCNT composite films were taken. One such micrograph is shown in Figure 6.21. 

Benoit et al. 2001 (41) SWCNT Arc Discharge As-synthesized Casting CNT Loading levels 0.1 to 8 wt% Film Electrical conductivity increases with CNT content by 9 orders of magnitude from 0.1 to 8% mass fraction with percolation threshold 0.33 wt%. Temperature dependence of resistivity for 0.2 to 8 wt% SWCNT composite films showed that percolating network is affected at low temperature, enhancing the relative resistivity ... 

Due to the complexity of the transport properties of an SWCNT network, the physical mechanisms at stake during exposure to gas constitute an important source of debate. The percolation theory is invoked to account for the influence of SWCNT density on the percolation threshold of metallic SWCNTs and on the transport properties of SWCNT networks (Topinka et al, 2009). As a result, the SWCNT network exhibits a metallic or a semiconducting character. 

It is well known that the percolation threshold is strongly dependent on the aspect ratio. One-dimensional (ID) nanostructures, such as nanowires, nanotubes, and nanoribbons, have geometries that are favorable for the maintenance of connectivity at low content of active materials. Carbon nanotubes (CNTs) are a good representative example. Electrical percolation can be achieved in polymer composites with well-dispersed single-walled carbon nanotubes (SWCNTs) at levels as low as 0.03 wt% [69]. Recently, it has been reported that the formation of semiconducting nanofibers facilitates percolation in semiconducting/insulating polymer blends. 

Fig. 8.1 (a) Electrical conductivity of polycarbonate/SWCNT composites as a function of the filler mass fraction. Different commercial applications are also noted in the graph, (b) Power-law application to experimental data for the calculation of the percolation threshold. Reprinted with permission from Ramasubramaniam et al. (2003)... 

Coleman et al. prepared SWCNT/PmPV composites by mixing SWCNT powder, prepared in a Kratschmer reactor, and PmPV dissolved in toluene. The mixture was briefly sonicated, and was left to settle for three days. These authors calculated that the true percolation threshold of the resulting composite was located between 8 wt% and 9 wt% of CNTs (Figure 2.8]. The incorporation of CNTs increased the conductivity by ten orders of magnitude, viz., from 2 X 10 1° S/m for the pure PmPV polymer to 3 S/m at 36 wt% of CNTs. 

This "excluded volume" concept was further illustrated by Winey and her coworkers who prepared SWCNT/PS nanocomposites by homogeneously coating SWCNTs (exfoliated in aqueous solutions without using surfactant) on the surface of softened flakes or pellets of PS, maintained above the glass transition of the polymer. After processing of the coated PS particles by compression molding, it was shown that SWCNTs were predominantly present in the interfacial volume between the pellets and formed a continuous three-dimensional cellular network. The nanocomposites obtained had conductivity values of the order of 10 S/m for 1 wt% of SWCNTs and a percolation threshold of about 0.2-0.3 wt%, i.e., half of the value of one of the reference samples for which SWCNTs of the same batch were homogeneously dispersed into the same PS matrix by an alternative method. ... 

Ultimately, the quality of the CNT will play the most influential role on the conductive nature of the final composite. A substantial increase in ultimate conductivity [beyond the percolation threshold] with a decrease in melt-viscosity was reported for systems in which the inherent SWCNT conductivity was much lower than those used in the composites presented here. The higher inherent conductivity of the CNTs used in the present study could explain the absence of a large increase in ultimate conductivity with decreased melt viscosity. Differences in ultimate conductivities have been shown to vary widely across different CNT batches, thus making comparisons between different systems inaccurate. ... 

Results presented on the influence of the matrix viscosity on the percolation threshold, collected using one batch of SWCNT and one batch of MWCNTs, not only agree with the report on the decrease in percolation threshold with an increase in the processing temperature, but also agree with results reported for carbon blackfilled polymers. The influence that the matrix viscosity has on the formation of equilibrated CNT network structures cannot be overlooked. It has been shown that a reduced matrix viscosity, achieved by higher processing temperatures or introducing low molar mass material, leads to similar reductions in the percolation threshold. 

Changes in the percolation threshold and critical exponent for composites prepared via a latex-based route using different processing techniques have been observed. Composites prepared with both a latex of high-Tg [PS) and low-Tg [poly[methyl acrylate) [PMA)) polymer, and SWCNTs and MWCNTs were compared, and the results are presented in the following sections. 

Figure 4.10 Results from [i) Four-point conductivity measurements for SWCNT/PS composites prepared by various processing techniques and ii) respective data fits of the equation given in Table 4.1 (R values of 0.99 for all fittings. Only points close to the percolation threshold were taken into account for the fitting). Lines given in (i) are fittings using the value of t and (pp determined in (//).

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. 

As an additional factor, the lower melt viscosity at the compression molding temperature of the iPP-g-MA matrix in comparison with the PS system (about 50 Pa s at 170°C for the former in non-emulsified form vs. well-above 10 Pa s at 180°C for the latter) certainly favors the lowering of the experimental percolation threshold, both for SWCNT and MWCNT nanocomposites (see Table 5.1). A lower melt viscosity of the matrix, indeed, reduces the average CNT-CNT distance and was... 

As shown in Table 5.1, the percolation thresholds in both SWCNT-and MWCNT-based nanocomposites of iPP-g-MA and PS roughly... 

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