Percolation system polymer composite

It has been possible to directly image the percolation network at the surface of a CB-polymer composite. An early report is that of Viswanathan and Heaney [24] on CB in HOPE in which it was shown that there are three regions of conductivity as a function of the length L, used as a metric for the image analysis. Below I = 0.6pm, the fractal dimension D of the CB aggregates is 1.9 0.1. Between 0.8 and 2 pm, the data exhibit D = 2.6 0.1 while above 3 pm, D = 3 corresponding to homogeneous behavior. Theory predicts D = 2.53. It is not obvious that the carbon black-polymer system should be explainable in terms of standard percolation theory, or that it should be in the same universality class as three-dimensional lattice percolation problems [24]. Subsequent experiments of this kind were made by Carmona [25, 26]. 

Fig. 1.1 Relative differential resistance change, AR/R, predicted by percolation theory as a function of the relative volume change, AV/V, of a carbon black-polymer composite upon swelling. The volume of carbon black is assumed to be unaffected by swelling, and the polymer matrix is assumed to have a conductivity 11 orders of magnitude lower than that of carbon black. The three separate lines are for composites with differing initial volume percentages of carbon black, as indicated. The percolation threshold for the system is at CB content=0.33. The total volume change results in a change in the effective carbon black content. When, this value drops below the percolation threshold, a sharp increase in response is observed. Of course, the position of this sharp increase depends on the value of the percolation threshold (Reprinted with permission from Lonergan et al. 1996, Copyright 1996 American Chemical Society)...

Rubin Z, Sunshine S A, Heaney M B, Bloom I and Balberg I (1999) Critical behavior of the electrical transport properties in a tunneling-percolation system, Phys Rev B 59 12196-12199. Balberg I (2002) A comprehensive picture of the electrical phenomena in carbon black-polymer composites, Carbon 40 139-143. 

Bauhofer W, kovacs JZ (2009) A review and analysis of electrical percolation in carbon nanotube polymer composites. Compos Sci Technol 69 1486 Behnam A, Guo J, Ural A (2007) Effects of nanotube alignment and measurement direction on percolation resistivity in single-walled carbon nanotube films. J Appl Phys 102 044313 Berhan L, Sastry SM (2007) Modeling percolation in high-aspect-ratio fiber systems. L Soft-core versus hard-core models. Phys Rev E 75 041120 Berman D, Orr BG, Jaeger HM, Goldman AM (1986) Conductances of filled two-dimensional networks. Phys Rev B 33 4301... 

Electrical Percolation Data for Some CNT/Polymer Composite Systems Reported Since 2008... 

In paper [19] it has been shown that the universality of the critical indices of the percolation system is connected directly with the fractal dimension of this system. The self-similarity of the percolation system assumes the availability of a number of subsets having the order ( = 1,2,4), which in the case of the structure of polymeric materials are identified as follows. The percolation cluster network or matrix physical entanglement cluster network is the first subset n = 1) in the polymer matrix. The loosely packed matrix, into which the cluster network is immersed, is the second one (n = 2). For polymer composites, the filler particles network, which is naturally absent in epoxy polymers, is the third subset (n = 4). In such a treatment the percolation cluster critical indices P and v are given as follows (in three-dimensional Euclidean space) [19] ... 

The high aspect ratio of nanorods can facilitate charge transport, while the handgap can he tuned by vaiying the nanorod radius. This enables the absorption spectmm of the devices to be tailored to overlap with the solar emission spectmm, whereas traditionally polymer absorption has been limited to only a small fraction of the incident solar irradiation. At present, the nanorods in polymer solar cells are typically incorporated into a homopolymer matrix. An alternative to this approach is to incorporate the nanorods into either a polymer blend or diblock copolymer system. The photovoltaic properties of nanorod polymer composites could potentially be improved due to the percolation of nanorods, and the presence of continual electrical pathways, from the DA interfaces to the electrodes. To test this hypothesis, we use the distribution of nanorods from the self-assembled stmcture in Figure 1(b) as the input into a drift-diffusion model of polymer photovoltaics. 

Theoretical investigations addressing the percolation of rods are important for predicting insulator-conductor transitions in real composite systems with rodlike fillers. Such systems include early fiber-reinforced polymer composites and the more recent polymer nanocomposites containing carbon nanotubes and metallic nanowires. Since the early 1980s, extensive analytical and computational studies have been conducted for sticks in 2D, and also for rods in As... 

White et al recently conducted simulation and experimental studies to investigate the L/D dependence of 4>c in polymer composites with finite-aspect ratio silver nanowire fillers. Their simulation program determines the percolation threshold for very large systems of isotropic soft-core cylinders (comprising 10 -10 rods) with aspect ratio ranging between 5 and 80. The authors then compared the simulated thresholds to analytical results from the excluded volume theory for inter-penetrable cylinders (eqn [7]), as well as experimental results from their silver nanowire/polystyrene composites (Figure 5j. 

Most theoretical studies of electrical percolation in composite systems with rodlike fillers assume that the particles are rigid, straight cylinders or spherocylinders. However, this assumption offers a poor description of some important composite systems. For example, electron microscopy studies have revealed that nanotubes embedded in a polymer matrix are generally curved or wavy, rather than straight, as observed in Figure 9. Several authors have conducted theoretical studies to probe the effect of filler waviness on the percolation threshold of composite materials.The percolation threshold was found to increase with inaeasing filler waviness, and this effect was more pronounced for smaller aspect ratios. However, the reported increase in the percolation threshold due to waviness is still small relative the wide spread of experimental threshold values for CNT/polymer composites. Simulations of CNT/ polymer composites also show that filler waviness lowers the composite conductivity. These studies were conducted for highly idealized systems, so the extent of this reduction is not well established. 

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