Carbon materials with quasi-graphene layers: the dielectric, percolation properties and the electronic transport mechanism

We investigate the dielectric properties of multi-walled carbon nanotubes (MWCNTs) and graphite filling in SiO₂ with the filling concentration of 2-20 wt.% in the frequency range of 10²-10⁷ Hz. MWCNTs and graphite have general electrical properties and percolation phenomena owing to their quasi-structure made up of graphene layers. Both permittivity ε and conductivity σ exhibit jumps around the percolation threshold. Variations of dielectric properties of the composites are in agreement with the percolation theory. All the percolation phenomena are determined by hopping and migrating electrons, which are attributed to the special electronic transport mechanism of the fillers in the composites. However, the twin-percolation phenomenon exists when the concentration of MWCNTs is between 5-10 wt.% and 15-20 wt.% in the MWCNTs/SiO₂ composites, while in the graphite/SiO₂ composites, there is only one percolation phenomenon in the graphite concentration of 10-15 wt.%. The unique twin-percolation phenomenon of MWCNTs/SiO₂ is described and attributed to the electronic transfer mechanism, especially the network effect of MWCNTs in the composites. The formation of network plays an essential role in determining the second percolation threshold of MWCNTs/SiO₂.     

Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System

We study short-range percolation models. In a finite box we define the percolation threshold as a random variable obtained from a stochastic procedure used in actual numerical calculations, and study the asymptotic behavior of these random variables as the size of the box goes to infinity. We formulate very general conditions under which in two dimensions rescaled threshold variables cannot converge to a Gaussian and determine the asymptotic behavior of their second moments in terms of a widely used definition of correlation length. We also prove that in all dimensions the finite-volume percolation thresholds converge in probability to the percolation threshold of the infinite system. The convergence result is obtained by estimating the rate of decay of the limiting distribution function's tail in terms of the correlation length exponent ν. The proofs use exponential estimates of crossing probabilities. Substantial parts of the proofs apply in all dimensions. Received: 1 May 1996 / Accepted: 25 July 1996     

Temperature- and magnetic field-dependent electrical transport studies of poly(-3,4 ethylenedioxythiophene) nanoparticles

Large-scale silver nanowires (AgNWs) with a width of 50–60 nm and a typical length of 10 ± 5 μm were synthesized conveniently through a simple polyol reduction method, and the weight of obtained AgNWs was close to 10 g in this one-pot reaction with 500 ml of solution. The as-prepared AgNWs were incorporated into polyvinylidene fluoride matrix (PVDF) to fabricate the AgNWs/PVDF composites, and dielectric behaviors of the composites were investigated. The results revealed that a low percolation threshold of 1.8 vol% was observed in the AgNWs/PVDF composites, which was due to the large aspect ratio of one-dimension structured AgNWs. A giant dielectric constant of 80,000 at 1 kHz was obtained with 1.8 vol% of AgNWs mainly caused by the percolation effect. Besides, the large micro-capacitor networks and strong interfacial polarization at percolation threshold contributed to the enhanced dielectric constant.     

化整为零:聚合物/粘土纳米复合材料的微观结构和阻隔性能

在聚合物基体中掺入少量的层状硅酸盐所制备的聚合物／粘土纳米复合材料，其阻隔性能明显地优于纯聚合物及其传统的复合材料。实验及分析结果表明，聚合物／粘土纳米复合材料的微观结构和阻隔性能主要受控于粘土剥离后的径厚比．一简单的重整化群模型被用来评估粘土几何因素（诸如径厚比、取向、剥离程度等）对聚合物／粘土纳米复合材料阻隔性能的影响，所得到的逾渗阈值及最佳粘土含量与实验结果吻合。     

Influence of aspect ratio on barrier properties of polymer-clay nanocomposites

The barrier properties of polymer-clay nanocomposites, with far less inorganic contents of layered-silicate fillers, are remarkably superior to those of neat polymers or their conventional counterparts. A simple renormalization group model is proposed to assess the influence of geometric factors (such as aspect ratio, orientation, and extent of exfoliation) of layered-silicate fillers on the barrier properties of polymer-clay nanocomposites. The results show that the aspect ratio of exfoliated silicate platelets has a critical role in controlling the microstructure of polymer-clay nanocomposites and their barrier properties. The estimated percolation thresholds of clay content for minimum permeability are in good agreement with experimental data.     

Radiative and electrical properties of granular materials: application to mixtures of insulating and conducting polymers

The study of the radiative and electrical properties of granular materials coated with polypyrrole (PPy) a conducting polymer, shows the influence of the processing conditions concerning the nature of the substrate and the deposition parameters. Binary mixtures with varying compositions of mono and bidisperse particles, coated with or without PPy (which are conductive and insulating, respectively) present electrical percolation thresholds which can also be found when the radiative aspect is considered. The principal component analysis carried out on the spectral values allows us to corroborate the experimental factors and to distinguish the mixtures according to their compositions.     

Thermal and electrical conductivity of poly(l-lactide)/multiwalled carbon nanotube nanocomposites

Multiwalled carbon nanotubes (MWCNTs) are considered to be the ideal reinforcing agent for high-strength polymer composites, because of their fantastic mechanical strength, high electrical and thermal conductivity and high aspect ratio. Polymer/MWCNTs composites are easily molded, and the resulting shaped plastic articles have a perfect surface appearance compared with polymer composites made using usual carbon or glass fibers. Good interfacial adhesion between the MWCNTs and the polymer matrix is essential for efficient load transfer in the composite. The ultrahigh strength polymer composites demand the uniform dispersion of the MWCNTs in the polymer matrix without their aggregation and the good miscibility between MWCNT and polymer matrix. This approach can also be applied to biodegradable synthetic aliphatic polyesters such as poly(l-lactide) (PLLA), which has received a great deal of attention due to environmental concerns. In this study, PLLA was melt-compounded with MWCNTs. A high degree of dispersion of the MWCNTs in the composites was obtained by grafting PLLA onto the MWCNTs (PLLA-g-MWCNTs). After oxidizing the MWCNTs by treating them with strong acids, they were reacted with l-lactide to produce the PLLA-g-MWCNTs. The mechanical properties of the PLLA/PLLA-g-MWCNT composite were higher than those of the PLLA/MWCNT composite. The electrical conductivity of the composites was determined by measuring the volume resistivity, which is a value of the resistance expressed in a unit volume by two-probe method. The thermal diffusivity and heat capacity of composites was measured by laser flash method, and the effects of modification of the MWCNT in PLLA matrix are discussed.     

Effect of temperature on the electron field emission from aligned carbon nanofibers and multiwalled carbon nanotubes

Effect of temperature and aspect ratio on the field emission properties of vertically aligned carbon nanofiber and multiwalled carbon nanotube thin films were studied in detail. Carbon nanofibers and multiwalled carbon nanotube have been synthesized on Si substrates via direct current plasma enhanced chemical vapor deposition technique. Surface morphologies of the films have been studied by a scanning electron microscope, transmission electron microscope and an atomic force microscope. It is found that the threshold field and the emission current density are dependent on the ambient temperature as well as on the aspect ratio of the carbon nanostructure. The threshold field for carbon nanofibers was found to decrease from 5.1 to 2.6 V/μm when the temperature was raised from 300 to 650 K, whereas for MWCNTs it was found to decrease from 4.0 to 1.4 V/μm. This dependence was due to the change in work function of the nanofibers and nanotubes with temperature. The field enhancement factor, current density and the dependence of the effective work function with temperature and with aspect ratio were calculated and we have tried to explain the emission mechanism.     

Percolation thresholds and percolation conductivities of octagonal and dodecagonal quasicrystalline lattices

The octagonal and dodecagonal quaislattices were generated by means of the grid method. Monte Carlo simulation and cluster counting procedure were used for numerical determination of the site and bond percolation thresholds. Two types of connectivity called ferromagnetic and chemical were studied. The estimated site percolation thresholds are 0.5435… and 0.585… for octagonal lattice and 0.617… and 0.628… for dodecagonal lattice respectively. The obtained spanning fraction curves (for site percolation) seem to approach the 50% value at the percolation threshold. The site percolation conductivity for these lattices was studied by means of a transfer-matrix approach. The critical behavior was found to be the same as for the periodic lattices.     

An alternative proof of some percolation threshold (p c ) using the idea of self-organized criticality

Summary By means of a well-developed method in self-organized criticality, we can obtain the lower bound for the percolation threshold (p _c) of the corresponding site percolation problem. In some special cases, we have proved that such lower bounds are indeed the percolation thresholds. We can reproduce some well-known percolation thresholds of various lattices including the Cayley trees and Kock curves in this framework.     

A percolation approach to study the high electric field effect on electrical conductivity of insulating polymer

The effect of percolation threshold on the behaviour of electrical conductivity at high electric field of insulating polymers has been briefly investigated in literature. Sometimes the dead ends links are not taken into account in the study of the electric field effect on the electrical properties. In this work, we present a theoretical framework and Monte Carlo simulation of the behaviour of the electric conductivity at high electric field based on the percolation theory using the traps energies levels which are distributed according to distribution law (uniform, Gaussian, and power-law). When a solid insulating material is subjected to a high electric field, and during trapping mechanism the dead ends of traps affect with decreasing the electric conductivity according to the traps energies levels, the correlation length of the clusters, the length of the dead ends, and the concentration of the accessible positions for the electrons. A reasonably good agreement is obtained between simulation results and the theoretical framework.     

Metastability Thresholds for Anisotropic Bootstrap Percolation in Three Dimensions

In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the ‘easiest growth direction’ in the model. In contrast to anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metastability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.     

Effect of dispersion state of carbon nanotube on the thermal conductivity of poly(dimethyl siloxane) composites

Herein, the effect of dispersion uniformity of multi-walled carbon nanotube (MWCNT) on the thermal conductivity of poly(dimethyl siloxane) (PDMS) composites was investigated by comparing experimentally obtained and calculated results based on simple models. Two different MWCNTs, i.e., raw and oxidized/masterbatched MWCNTs, were used and compared. For raw MWCNT, the dispersion in PDMS was poor, resulting in the significant reduction in the aspect ratio of MWCNT. However, for composites using masterbatched MWCNT, the thermal conductivity was always about 10% greater than those prepared with raw MWCNT and the aspect ratio calculated by the model equation was also 1.7 times greater. Above 1.5 phr masterbatched MWCNT concentrations, the aspect ratio of 430 was maintained. Finally, the results suggest that the thermal conductivity can be correlated with the degree of dispersion and aspect ratio obtained from the model equation used.     

Impedance study of polymethyl methacrylate composites/multi-walled carbon nanotubes (PMMA/MWCNTs)

The dielectric behavior of polymethyl methacrylate/multi-walled carbon nanocomposites (PMMA/MWCNTs) was investigated using impedance spectroscopy technique. The composites were prepared using melt mixing with MWCNTs loading ranging from 0.01 to 10 wt%. The experimental results showed that the measured impedance reflects the insulating behavior of the host material (PMMA) with no appreciable effects of the filler less than 8.5 wt%. However, for the sample containing 10 wt%, the calculated value of dc conductivity increases with increasing temperature from 2.0×10⁻⁶ (Ω m)⁻¹ to attain a value of 4.8×10⁻⁶ (Ω m)⁻¹ at 110 °C. The percolation threshold derived from the dielectric data was estimated to be higher than 8.5 wt% and lower than 10 wt%. A temperature dependent electrical relaxation phenomenon was only observed in the sample containing 10 wt% of MWCNTs. The frequency dependence of the ac conductivity data followed a power law.     

Numerical studies of gravity destabilized percolation in 2D porous media

Two dimensional simulations of percolation are realized on square networks of pore throats with a random capillary pressure distribution. We analyse the influence of a destabilizing gravity field (g) and of the standard deviation of the distribution of the capillary pressure thresholds (W_t). The fragmentation process is not taken into account in this study. For an increase of g or/and when W_t decreases, two transitions are analyzed with three different regimes displacement patterns: Invasion percolation, invasion percolation in a gradient, and invasion in a pure gradient. The transitions are controlled both by the ratio g/W_t and by the sample size (L). A scaling law between the saturation at the percolation threshold and g/W_t allows delineating the three regimes in agreement with theoretical argument of the percolation in a gradient.     

New critical frontiers for the potts and percolation models

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.     

Physical properties of carbon composite materials with low percolation threshold

Electrical and thermal properties of binary systems consisted of stearine and expanded graphite (EG) of different bulk densities (0.003 and 0.4 g/cm³), stearine and fine-crystalline graphite (CG) were examined. Heat capacity measurements display that phonon spectrum of graphite does not change after chemical and heat treatment in the temperature range from 300 to 700 K. It was shown that the value of samples’ percolation threshold depends on aspect ratio of using the electroconducting filler: EG as electroconducting filler is 20 times more effective than common crystal graphite.     

Electrical,optical and mechanical properties of PS/GNP composite films

In this study, the electrical, optical and mechanical properties of polystyrene (PS) thin films added graphene nanoplatelet (GNP) have been investigated. Surface conductivity (σ), absorbance intensity (A) and tensile modulus of these composite films have increased with increasing the content of GNP in the composite. The increase in the electrical and optical properties of the PS/GNP composite films has been interpreted by site and classical percolation theory, respectively. The electrical and the optical percolation thresholds of PS/GNP composite films were determined as R_σ?=?23.0?wt.% and R_op?=?13.0?wt.%, respectively. While the conductivity results have been attributed to the classical percolation theory, the optical results have attributed to the site percolation theory. The electrical (β_σ) and the optical (β_op) critical exponents were calculated as 2.54 and 0.40, respectively. The tensile modulus and the tensile strength of the PS/GNP composites increased with the increasing of GNP content in the PS. But, the toughness of the composites fluctuated with GNP addition.