Percolative Metal-Insulator Transition in Excimer Laser Irradiated Polyimide

Ball, Z.; Sauerbrey, R.; Hm, Phillips; Dl, Callahan

doi:10.1103/physrevlett.73.2099

Cited by 37 publications

(19 citation statements)

References 23 publications

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“…where r 0 is the conductivity of the bulk electrolyte, x is the volume portion of the electrolyte in the composite, x c is the percolation threshold, and s is an empirical constant: With s 2 ( Figure 5) it reproduced surprisingly well the data for percolation on regular 3D lattices and even experimental data for some composites, much farther from the percolation threshold that one would have generally expected [29,30]. Thus in the range far from 100% volume portion of the component this could be a reasonable approximation.…”

Section: Ionic Conductivitymentioning

confidence: 59%

How good are the Electrodes we use in PEFC?

Eikerling

Ioselevich

Kornyshev³

2004

Fuel Cells

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Basically, companies and laboratories implement production methods for their electrodes on the basis of experience, technical capabilities and commercial preferences. But how does one know whether they have ended up with the best possible electrode for the components used? What should be the (i) optimal thickness of the catalyst layer? (ii) relative amounts of electronically conducting component (catalyst, with support – if used), electrolyte and pores? (iii) “particle size distributions” in these mesophases? We may be pleased with our MEAs, but could we make them better? The details of excellently working MEA structures are typically not a subject of open discussion, also hardly anyone in the fuel cell business would like to admit that their electrodes could have been made much better. Therefore, we only rarely find (far from systematic) experimental reports on this most important issue. The message of this paper is to illustrate how strongly the MEA morphology could affect the performance and to pave the way for the development of the theory. Full analysis should address the performance at different current densities, which is possible and is partially shown in this paper, but vital trends can be demonstrated on the linear polarization resistance, the signature of electrode performance. The latter is expressed through the minimum number of key parameters characterizing the processes taking place in the MEA. Model expressions of the percolation theory can then be used to approximate the dependence on these parameters. The effects revealed are dramatic. Of course, the corresponding curves will not be reproduced literally in experiments, since these illustrations use crude expressions inspired by the theory of percolation on a regular lattice, whereas the actual mesoscopic architecture of MEA is much more complicated. However, they give us a flavour of reserves that might be released by smart MEA design.

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Section: Ionic Conductivitymentioning

confidence: 59%

How good are the Electrodes we use in PEFC?

Eikerling

Ioselevich

Kornyshev³

2004

Fuel Cells

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“…For example: oil recovery from porous media, 1 epidemic modeling, 2 networks, 3,4 fracture, 5 metal-insulator transition, 6 ionic transport in glasses and composites, 7 ground water flow in fractured rocks 8 and many others. Percolation refers to the formation of long-range connectedness in a system and is known to exhibit a continuous phase transition from a disconnected to a fully connected phase at a sharply defined percolation threshold value.…”

Section: Introductionmentioning

confidence: 99%

Continuous Percolation Transition in Random Cluster Growth Model

Roy¹,

Santra²

2013

Croat. Chem. Acta

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Abstract.A random cluster growth model is developed in terms of two parameters, the initial seed concentration ρ and the growth probability g of individual clusters. The model is studied on a two dimensional square lattice. For every ρ value, a critical value of g = g c is determined at which a percolation transition is observed. A scaling theory for this model is developed and numerically verified. The scaling functions are found to scale with ρ, g as well as the system size L with appropriate critical exponents. The values of the critical exponents are found to belong to the same universality class of percolation. Finally a phase diagram is developed in the ρ − g parameter space for percolating and non-percolating regions separated by a line of second order phase transition points. (doi: 10.5562/cca2313)

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“…Examples include flow through porous material, oil production, and conductivity of semiconducting materials or metal-insulator mixtures [1,2,3,4,5,6,7,8,9,10]. These problems have been studied using a random resistor network model with bonds that have a resistance chosen from a probability distribution mimicking the nature of the physical problem under consideration.…”

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confidence: 99%

Current flow in random resistor networks: The role of percolation in weak and strong disorder

Buldyrev

Braunstein

et al. 2005

Phys. Rev. E

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We study the current flow paths between two edges in a random resistor network on a L×L square lattice. Each resistor has resistance e ax , where x is a uniformly-distributed random variable and a controls the broadness of the distribution. We find (a) the scaled variable u ≡ L/a ν , where ν is the percolation connectedness exponent, fully determines the distribution of the current path length ℓ for all values of u. For u ≫ 1, the behavior corresponds to the weak disorder limit and ℓ scales as ℓ ∼ L, while for u ≪ 1, the behavior corresponds to the strong disorder limit with ℓ ∼ L d opt , where d opt = 1.22 ± 0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale ξ ∼ a ν , below which strong disorder and critical percolation characterize the current path.

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Percolative Metal-Insulator Transition in Excimer Laser Irradiated Polyimide

Cited by 37 publications

References 23 publications

How good are the Electrodes we use in PEFC?

How good are the Electrodes we use in PEFC?

Continuous Percolation Transition in Random Cluster Growth Model

Current flow in random resistor networks: The role of percolation in weak and strong disorder

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