Percolation Theory and Its Application in Electrically Conducting Materials

Balberg, I.

doi:10.1002/9783527648689.ch5

Cited by 6 publications

(10 citation statements)

References 71 publications

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“…The transport properties-in particular, the electrical conductivity-of binary systems with conducting fillers inside an insulating host matrix are closely connected with their percolating properties (for reviews, see, e.g., [5,6] and the references therein). One of the first works devoted to the percolation and conductivity of twodimensional (2D) systems of objects of different shapes, particularly rods, is [7].…”

Section: Introductionmentioning

confidence: 99%

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

et al. 2018

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The electrical conductivity of two-dimensional films filled with rodlike particles (rods) was simulated by the Monte Carlo method. The main attention has been paid to the investigation of the effect of the rod alignment on the electrical properties of the films. Both continuous and lattice approaches were used. Intersections of particles were forbidden. Our main findings are (i) both models demonstrate similar behaviors, (ii) at low concentration of rods, both approaches lead to the same dependencies of the electrical conductivity on the concentration of the rods, (iii) the alignment of the rods essentially affects the electrical conductivity, (iv) at some concentrations of partially aligned rods, the films may be conducting only in one direction, and (v) the films may simultaneously be both highly transparent and electrically anisotropic.

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Section: Introductionmentioning

confidence: 99%

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

et al. 2018

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“…The percolation threshold corresponds to the critical content at which the conductive path throughout the entire sample occurs. In the first case, the conduction mechanism is similar to the electron mechanism in metals (a contribution of quasi-free electron) [37][38][39][40][41]. However, the PU-based nanocomposites were not electrically conductible; therefore, the percolation threshold was not achieved (data not published).…”

Section: Thermal Conductivitymentioning

confidence: 99%

Self-Healing Polyurethane-Based Nanocomposites Modified with Carbon Fibres and Carbon Nanotubes

Szatkowski

Pielichowska

Błażewicz

2020

Advances in Polymer Technology

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Self-healing polyurethanes (PUs) were synthesized as a matrix of nanocomposites containing two fibrous carbon components, i.e., functionalized carbon nanotubes (CNF-OH) and short carbon fibers (CF). Two types of PUs differing in the content of flexible chain segments (40% and 50%) were used. Changes in mechanical strength were analyzed to assess the ability to self-healing of PU-based matrix nanocomposites with experimentally introduced damage in the form of an incision. The healing process was activated by heating the damaged samples at 60°C, for 30 minutes. The addition of CNT-OH and CF caused a slight reduction in the self-healing ability of the nanocomposites as compared to the neat PUs. After heating to 60°C, the nanocomposites self-healed up to 72% of the initial strength of the undamaged samples. The introduction of fibrous components to the polymer matrix improved the thermal conductivity of nanocomposites and facilitated heat transfer from the environment to the interior of the samples, necessary to initiate self-healing. Low content of carbon components in the PU matrix, i.e., 3 wt% of CF and 2 wt% of CNF-OH increased the total work up to fracture of samples after healing by about 53%.

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“…Polymeric materials composed of two or more components with percolation pathways within each component are desired across materials science for numerous applications such as photovoltaics, − thermoelectrics, ion transporting materials, , porous catalysts, membranes, and conducting composites . Percolation, whether it is for electrical, , thermal, mass, or ionic , transport, through bulk materials is determined by the structure and connectivity of a network comprised of the constituent polymer meso- or microstructure. ,− The most common method to prepare polymeric materials with percolating pathways is by blending two or more polymers in a common solvent and fabricating films or nanofibers. − ,− Other methods employing conducting-fillers have also been explored to create polymer based percolation networks . However, the morphology within these materials is dictated by several interdependent kinetic processes that cannot be independently controlled. − Thus, it is very difficult to control the assembly of each of the components in the nanoscale as well as the assembly of these nanoscale assemblies into a meso- or microstructures.…”

Section: Introductionmentioning

confidence: 99%

“…We have measured and modeled the time-of-flight (TOF) charge carrier mobility of P3HT and PS nanoparticle assemblies to probe bulk charge percolation, and used conducting atomic force microscopy (cAFM) to probe electrical percolation in the nanoscale. We fit data from TOF and cAFM experiments at various values of η to a power law scaling relation for percolation behavior. ,,− Moreover, we have developed a simple resistor network model ,, to reproduce nanoscale percolation measurements by cAFM and make further predictions. Using this model, we have analyzed the structure of percolating networks in binary polymer nanoparticle glasses in terms of their average or predominant local motifs, describing them as ( p i , p 1 ‑i )-connected networks.…”

Section: Introductionmentioning

confidence: 99%

“…We fit data from TOF and cAFM experiments at various values of η to a power law scaling relation for percolation behavior. 14,27,39−41 Moreover, we have developed a simple resistor network model 13,42,43 to reproduce nanoscale percolation measurements by cAFM and make further predictions. Using this model, we have analyzed the structure of percolating networks in binary polymer nanoparticle glasses in terms of their average or predominant local motifs, describing them as (p i , p 1-i )-connected networks.…”

Section: ■ Introductionmentioning

confidence: 99%

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Tunable Percolation in Semiconducting Binary Polymer Nanoparticle Glasses

et al. 2016

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Binary polymer nanoparticle glasses provide opportunities to realize the facile assembly of disparate components, with control over nanoscale and mesoscale domains, for the development of functional materials. This work demonstrates that tunable electrical percolation can be achieved through semiconducting/insulating polymer nanoparticle glasses by varying the relative percentages of equal-sized nanoparticle constituents of the binary assembly. Using time-of-flight charge carrier mobility measurements and conducting atomic force microscopy, we show that these systems exhibit power law scaling percolation behavior with percolation thresholds of ∼24-30%. We develop a simple resistor network model, which can reproduce the experimental data, and can be used to predict percolation trends in binary polymer nanoparticle glasses. Finally, we analyze the cluster statistics of simulated binary nanoparticle glasses, and characterize them according to their predominant local motifs as (p(i), p(1-i))-connected networks that can be used as a supramolecular toolbox for rational material design based on polymer nanoparticles.

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Percolation Theory and Its Application in Electrically Conducting Materials

Cited by 6 publications

References 71 publications

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

Self-Healing Polyurethane-Based Nanocomposites Modified with Carbon Fibres and Carbon Nanotubes

Tunable Percolation in Semiconducting Binary Polymer Nanoparticle Glasses

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