Electrical properties of percolation clusters: exact results on a deterministic fractal

Clerc, Jean-Pierre; Giraud, G.; Laugier, J.M.; Luck, J. M.

doi:10.1088/0305-4470/18/13/032

Cited by 50 publications

(23 citation statements)

References 23 publications

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“…3(b)]. These values are very close to the theoretical value of 2.0 for a random percolating network formed by particle aggregates 21, 29, 30…”

Section: Resultssupporting

confidence: 83%

“…It is well known that the φ c of polymer nanocomposites can be extremely low2–4, 21–26, 29 when fractal networks are present in the polymer matrices, especially when these networks are made from fractal aggregates 3, 4, 20–26. Moreover, for some of the polymer composites, it was found that the position of φ c is strongly influenced by the difference in surface tension between the matrix and the particles 2–4, 25.…”

Section: Resultsmentioning

confidence: 99%

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Novel phthalocyanine crystals as a conductive filler in crosslinked epoxy materials: Fractal particle networks and low percolation thresholds

Chen

Brokken-Zijp

Michels

2005

J Polym Sci B Polym Phys

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Novel nanosized crystals of aquocyanophthalocyaninatocobalt (III) (Phthalcon 11) were used as a conductive filler in crosslinked epoxy materials. The crosslinked composite materials had a very low percolation threshold (u c % 0.9 vol %). The relationship between the volume conductivity and the filler fraction follows the scaling law of the percolation theory and suggests that the conducting particle networks were formed by random percolation of primary aggregates. The occurrence of the low u c can be explained by the presence of a fractal Phthalcon 11 particle network formed from fractal aggregates during crosslinking. The position of the percolation threshold and the volume conductivity of these crosslinked materials were found to depend heavily on the processing conditions applied. These dependencies are explained in terms of specific particle-matrix interactions and the particle-particle interactions and by taking into account different mechanisms of particle network formation. V V C 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] 2006

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“…3(b)]. These values are very close to the theoretical value of 2.0 for a random percolating network formed by particle aggregates 21, 29, 30…”

Section: Resultssupporting

confidence: 83%

Section: Resultsmentioning

confidence: 99%

Novel phthalocyanine crystals as a conductive filler in crosslinked epoxy materials: Fractal particle networks and low percolation thresholds

Chen

Brokken-Zijp

Michels

2005

J Polym Sci B Polym Phys

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“…In [3] it was shown that the two classes of response were general forms of behaviour resulting from systems that could be described by a scaled hierarchy of R-C circuits. A specific circuit construction of this type representing a percolation system generalised from [6], was studied in [4], and this seems the most appropriate for the oil samples investigated here. FPR behaviour occurs when the system is above the percolation limit, i.e.…”

Section: Dielectric Spectroscopymentioning

confidence: 99%

Anomalous dielectric response of very small quantities of virgin, aged and failed silicone oil

Haidar

Fothergill

Dissado

et al. 2003

IEEE Trans. Dielect. Electr. Insul.

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractA technique is described for making dielectric spectroscopy measurements of very small quantities (< 1 µl) of oil. The technique utilises surface tension to hold the oil between the plates of a capacitor, the inter-electrode distance being controlled by a micrometer.Breakdown strength can also be estimated using this technique. Three samples of silicone oil, used in cable sealing ends, were tested: virgin, used and failed. A major component in the frequency dependent impedance had the form ( ) (

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“…Nevertheless, applications in materials science and engineering are expected. To cite just a few possible scenarios, electrical properties of percolation clusters in random media and disordered systems can be studied considering fractal networks [23]. Sierpinski gasket can be used to model two dimensional superconductor materials [24].…”

Section: Final Commentsmentioning

confidence: 99%

Self-similar resistive circuits as fractal-like structures

Santos

Mendes

Freire

2017

Rev. Bras. Ensino Fís.

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In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski's configurations with resistors.Comment: 9 pages, 15 figure

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Electrical properties of percolation clusters: exact results on a deterministic fractal

Cited by 50 publications

References 23 publications

Novel phthalocyanine crystals as a conductive filler in crosslinked epoxy materials: Fractal particle networks and low percolation thresholds

Novel phthalocyanine crystals as a conductive filler in crosslinked epoxy materials: Fractal particle networks and low percolation thresholds

Anomalous dielectric response of very small quantities of virgin, aged and failed silicone oil

Self-similar resistive circuits as fractal-like structures

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