Universality of ac conduction in anisotropic disordered systems: An effective-medium-approximation study

Bustingorry, Sebastián

doi:10.1103/physrevb.71.132201

Cited by 2 publications

(2 citation statements)

References 37 publications

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“…The magnitude is consistent with theoretical arguments and prior experimental observations of disordered carbon-filled systems, n ≈ 0.75-1. 48,[64][65][66] From the theoretical constructs, n is related to the dispersion of the carrier mobility, where n ) 1 is for an ideal process and is reflective of transport via a single mechanism across the network within the critical region (Φ -Φ c ,1). The decrease of n as Φ -Φ c increases is consistent with a multiplication of paths and processes for transport through the network.…”

Section: Resultsmentioning

confidence: 99%

Thermal−Electrical Character of in Situ Synthesized Polyimide-Grafted Carbon Nanofiber Composites

et al. 2008

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Notwithstanding the success of polymer−carbon nanotube (CNT) nanocomposites, a solid understanding of the impact of external perturbations, including temperature and stress, on the electrical response, its reproducibility, and the subsequent relationship to the topology of the percolative morphology and molecular details of the CNT−CNT contact junction is not complete. Using an in situ synthesis approach, two series of polymide (CP2)−carbon nanofiber (CNF) composites are prepared with quantitatively (small-angle X-ray scattering) comparable CNF dispersions, but differing in the structure of the CNF−polymer interface. Amino-functionalized CNFs (FCNFs) enable direct formation of CP2 grafts onto the CNFs, whereas pristine CNFs (PCNFs) result in a relatively weak interface between the carbon nanofiber and CP2 matrix. In general, low-frequency ac impedance measurements are well described by the percolation bond model, yielding a percolation threshold below 1 vol % (0.24 and 0.68 vol % for PCNF−CP2 and FCNF−CP2, respectively). However, the design of the interface is determined to be crucial for controlling the electrical behavior in four substantial ways: magnitude of the limiting conductivity, linearity of the I−V response, magnitude and direction of temperature-dependent resistivity, and reproducibility of the absolute value of the resistivity with thermal cycling. These observations are consistent with a direct CNF−CNF contact limiting transport in the PCNF−CP2 system, where the CP2 grafts onto the FCNF from a dielectric layer, limiting transport within the FCNF−CP2 system. Furthermore, the grafted CP2 chains on the FCNF reduce local polymer dewetting at the CNF surfaces when the temperature exceeds the CP2 glass transition. This appears to stabilize the structure of the percolation network and associated conductivity. The general behavior of these interfacial extremes (pristine and fully functionalized CNFs) set important bounds on the design of interface modification for CNFs when the intended use is for electrical performance at elevated temperatures or under extreme current loads.

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Section: Resultsmentioning

confidence: 99%

Thermal−Electrical Character of in Situ Synthesized Polyimide-Grafted Carbon Nanofiber Composites

et al. 2008

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“…They are numerically very successful and therefore of huge practical relevance, [27,28]. One not only uses such concepts to describe transport (especially in the percolation problem), [29][30][31], but also optical phenomena, [32,33].…”

Section: Introductionmentioning

confidence: 99%

Effective-medium approximation for lattice random walks with long-range jumps

Thiel

Sokolov

2016

Phys. Rev. E

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We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective-medium approximation (EMA) to find the disorder-averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In the case of a power-law scaling between transition rates and distance, lattice variants of Lévy-flights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions and demonstrate very good agreement with numerical simulations.

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Universality of ac conduction in anisotropic disordered systems: An effective-medium-approximation study

Cited by 2 publications

References 37 publications

Thermal−Electrical Character of in Situ Synthesized Polyimide-Grafted Carbon Nanofiber Composites

Thermal−Electrical Character of in Situ Synthesized Polyimide-Grafted Carbon Nanofiber Composites

Effective-medium approximation for lattice random walks with long-range jumps

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