Electric percolation

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

The order parameter values calculated from the data of Fig. 4 are illustrated in Fig. 5. The data there suggest the existence of two continuous transitions, one at a = 0.85 and another at a = 0.7. The first transition at a = 0.85, denoted by the arrow labeled a in Fig. 5, is assigned to the formation of percolating clusters and aggregates of reverse micelles. The onset of electrical percolation and the onset of water proton self-diffusion increase at this same value of a (0.85) as illustrated in Figs. 2 and 3, respectively, are qualitative markers for this transition. This order parameter allows one to quantify how much water is in these percolating clusters. As a decreases from 0.85 to 0.7, this quantity increases to about 2-3% of the water. 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

The filler route has proved to be very efficient to obtain isotropic composites with relatively large improvements in matrix properties at small mass (volume) fractions of nanocarbon. For example, electrical percolation in epoxy has been obtained with only 0.0025 wt% of multi-wall nanotubes (MWNTs) [12]. Similarly, a 2.7-fold increase in matrix modulus has been observed on addition of 0.6 vol% MWNTs to polyvinyl alcohol (PVA) [13]. Although more modest compared to the previous two examples, a... 

The research on nanocarbons dispersed in polymer matrices in recent years has shown that this route is very efficient at small volume fractions above electrical percolation, where it can be the basis for new composite functionalities in terms of processing and properties. It is also clear that there is an inherent difficulty in dispersing these nanoscopic objects at high volume fractions, which therefore limits composite absolute properties to a very small fraction of those of the filler. Independent of their absolute properties, composites based on dispersed nanocarbons have served as a test ground to understand better the basic interaction between nanocarbons and polymer matrices, often setting the foundation to study more complex composite structures, such as those discussed in the following sections. 

Logakis E, Pissis P, Pospiech D, Korwitz A, Krause B, Reuter U, et al. Low electrical percolation threshold in polyethylene terephthalate)/multi-walled carbon nanotube nanocomposites. European Polymer Journal. 2010 May 46(5) 928-36. 

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. 

Bauhofer W, Kovacs JZ. A review and analysis of electrical percolation in carbon nanotube polymer composites. Composites Science and Technology. 2009 Aug 69(10) 1486-98. 

In a related experimental study, Cirkel and Okada compared mechanical and electrical percolation that developed during the gelation of 3 1 (v/v) 2-propanol/ water solutions of Nafion 117 in the acid and Na+ forms.Attention should be paid to the particular manner in which these samples were prepared, as different conditions may yield different results. Also, caution should be applied in comparing these results with those of percolation studies using preformed films, such as that of Hsu et al. ... 

The electrical percolation behavior for a series of carbon black filled rubbers is depicted in Fig. 26 and Fig. 27. The inserted solid lines are least square fits to the predicted critical behavior of percolation theory, where only the filled symbols are considered that are assumed to lie above the percolation threshold. According to percolation theory, the d.c.-conductivity Odc increases with the net concentration 0-0c of carbon black according to a power law [6,128] ... 

This phenomenon has been studied by different combined electrochemical techniques such as -> spectroelec-trochemistry, radioactive -> tracer method, -> electrochemical quartz crystal microbalance, conductivity etc. by varying the experimental parameters, e.g., film thickness, the composition and concentration of the electrolyte solutions, the wait-time at different waiting potentials, and temperature [iii-x]. Several interpretations have been developed beside the ESCR model. The linear dependence of the anodic peak potential on the logarithm of the time of cathodic electrolysis (wait-time) -when the polymer in its reduced state is an insulator -has been interpreted by using the concept of electric percolation [ix]. Other effects have also been taken into account such as incomplete reduction [vii], slow sorp-tion/desorption of ions and solvent molecules [iii-vi], variation of the equilibrium constants of -+polarons and - bipolarons [viii], dimerization [xi], heterogeneous effects [xii], etc. 

Gu, G., Wang, W., and Yan, H. (1996), Electric percolation of water-in-oil microemulsions The application of effective medium theory to system sodium dodecylbenzenesul-fonate (DDBS)/ -pentanol/ -heptane/water,/. Colloid Interface Sci., 178(1), 358-360. 

Usually geometrical connectivity and concentration fluctuations are not related. However, in our case, the electrical percolation is not a simple geometrical connectivity. This fact can explain that electrical percolation and critical points seem to be associated and that (jp % [Pg.80]

Jada, A., Lang, J. and Zana, R. (1989) Relation between electrical percolation and rate constant for exchange of materials between droplets in water-in-oil microemulsions. /. Phys. Chem., 93, 10-12. 

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]. 

For reverse micellar systems, the phenomenon of electrical percolation is observed. This is manifested by the sharp increase in the conductivity of the systems by three-four... 

Figure 10.39. Electrical percolation in rPC/CR mixtures depending on the CNP content [ZRI06]...

Figure 3 Electrical percolation threshold for conductive particles in an insulating matrix.

Upon addition of CNTs and AMs, the storage shear modulus, G, of EP increased (see Figure 13.6) on both sides of Tg, whereas the transition temperature decreased. Thus, the use of AM enhanced the electrical percolation of CNTs without... 

For the composite polymer electrolytes, the conductive carbonaceous filler must be below the electrical percolation threshold, due to the need to obtain an electronically insulating material with suitable ionic conductivity. These fillers are also used to improve the thermal stabilization and serve as mechanical reinforcement to improve the electrolyte/ electrode compatibility. CNT/P(VDF-TrFE) composites showed higher porosity and electrolyte uptake compared to the pristine polymer. CNT also contributed to increase ionic conductivity (2.6 xlO S cm , 0.1 wt.% CNT) and diminished its variations with temperature. 

Sandler, J.K.W., Kirk, J.E., Kinloch, I.A., Shaffer, M.S.P., Windle, A.H., 2003. Ultra-low electrical percolation threshold in carbon-nano tube-epoxy composites. Polymer 44,5893-5899. 

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