Charge transport properties in carbon black/polymer composites

The charge transport properties of polymer matrix–carbon black composites are investigated in this study. Direct current conductivity is examined with varying parameters: the temperature and the conductive filler content. Conductivity data are analyzed by means of percolation theory, and both percolation threshold and critical exponent are determined at each of the examined temperatures. The temperature dependence of conductivity and the agreement of experimental results with the variable range hopping model reveal hopping conduction as the predominant transport mechanism, below and in the vicinity of the critical concentration of carbon black particles. At higher concentrations, the contribution of hopping transport to the overall conductivity is reduced and a balance between hopping and conduction via geometrical contact occurs. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2535–2545, 2007     

二维渗流相关长度ξ(p)的幂估计(英文)

相关长度ξ(p)是渗流理论中最重要的一个量。本文对它给出了一个幂估计     

Cardy's formula for some dependent percolation models

We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice  (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice 𝕋 with flips when a site disagrees with six, five and sometimes four of its six neighbors. Received: 24 December 2001     

Cu-MgF2复合纳米金属陶瓷薄膜的电导特性研究

用射频磁控共溅射法制备了Cu体积分数分别为 10 % ,15 % ,2 0 %和 3 0 %的Cu MgF2 复合金属陶瓷薄膜 .用x射线衍射、x射线光电子能谱和变温四引线技术对薄膜的微结构、组分及电导特性进行了测试分析 .微结构分析表明 :制备的Cu MgF2 复合薄膜由fcc Cu晶态纳米微粒镶嵌于主要为非晶态的MgF2 陶瓷基体中构成 ,Cu晶粒的平均晶粒尺寸随组分增加从 11 9nm增至 17 8nm .5 0— 3 0 0K温度范围内的电导测试结果表明 :当Cu体积分数qM 由 15 %增加到 2 0 %时 ,Cu MgF2 复合薄膜的电阻减小了 8个量级 ,得出制备的复合薄膜渗透阈qCM 应处于 15 %和 2 0 %之间 .qM 在 10 %和 15 %之间的薄膜呈介质导电状态 ,而在 2 0 %和 3 0 %之间的薄膜则呈金属导电状态 .从理论上讨论了复合薄膜中杂质电导和本征电导的激活能及其对电导的贡献 ,并讨论了Cu MgF2 复合纳米金属陶瓷薄膜的渗透阈 ,得到了和实验一致的结果     

Size dependence of self-diffusion in the hard-square lattice gas

A striking size dependence of the mean-square displacement of diffusing particles in the two-dimensional lattice gas of hard squares has been observed by Monte Carlo simulation. It is shown that the size effect is due to the formation of a stable cage structure in small lattices when the particle concentration is high. The formation of cages is governed by a new type of percolation problem related to bootstrap percolation.     

Raman spectra of olivine solid solutions (FexMg1−x )2SiO4 and spin-vibration interaction

Room temperature Raman spectra of synthesized powder (Fe_xMg_1?x )₂SiO₄ solid solutions are obtained. Frequency trend of all modes versus composition shows clearly the existence of a step at x = 0.3. A step-like behavior of vibration frequencies at the given composition that coincides with the percolation threshold for the olivine lattice is related to the appearance of magnetic excitations in the disordered magnetic medium owing to the spin-vibration interaction.     

The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster tends to 1/2 as the intensity of the Poisson process tends to infinity. This confirms a conjecture of Benjamini and Schramm [5].     

Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.     

Fractals in physics: Squig clusters,diffusions, fractal measures,and the unicity of fractal dimensionality

The three topics discussed in this paper are largely independent. Part 1: Fractal squig clusters are introduced, and it is shown that their properties can match to a remarkable extent those of percolation clusters at criticality. Physics on these new geometric shapes should prove tractable. As background, the author's theories of squig intervals and squig trees are reviewed, and restated in more versatile form. Part 2: The notion of latent fractal dimensionality is introduced and motivated by the desire to simplify the algebra of dimensionality. Scaling noises are touched upon. A common formalism is presented for three forms of anomalous diffusion: the ant in the fractal labyrinth, fractional Brownian motion, and Lévy stable motion. The fractal dimensionalities common to diverse shapes generated by diffusion are given, in Table I, as functions of the latent dimensionalities of the support of the motion and of the diffusion itself. Part 3: It is argued that every fractal point set has a unique fractal dimensionality, but it is pointed out that many fractals involve diverse combinations of many fractal point sets. Such is, in particular, the case for fractal measures and for fractal graphs, often called hierarchical lattices. The fractal measures that the author had introduced in the early 1970s are described, including new developments.     

Computer Simulation of the Structure of Porous Electrodes with an Immobilized Enzyme and Nanosized Support Particles

The efficiency of the operation of a porous electrode with an immobilized enzyme is defined, in particular, by a lucky structure of its active layer, which can contain nanosized particles of the support. The composites of such a kind are prepared with the aid of methods of colloidal chemistry. The aim of this particular investigation is to perform a computer simulation of processes of coagulation of particles of the support and their possible heterocoagulation with molecules of the enzyme. Algorithms of the formation of nanocomposite structures in solution are suggested. Calculations show that the concentration of the enzyme molecules in the nanocomposite structures cannot exceed a certain critical value. On the other hand, at a fixed value of the concentration of the enzyme molecules, the concentration of the support particles must not fall below a certain threshold quantity, which provides for the passing of current through the active layer. In order for all the enzyme molecules, rather than for a fraction of these, in the composite to take part in the process of bioelectrocatalysis, the concentration of support particles must be increased even higher, to an optimum value.__________Translated from Elektrokhimiya, Vol. 41, No. 6, 2005, pp. 738–747.Original Russian Text Copyright © 2005 by Chirkov, Rostokin.