A three-dimensional Monte Carlo model for electrically conductive polymer matrix composites filled with curved fibers

A three-dimensional (3-D) Monte Carlo model is developed for predicting electrical conductivity of polymer matrix composites filled with conductive curved fibers. The conductive fillers are modeled as a 3-D network of finite sites that are randomly positioned. The percolation behavior of the network is studied using the Monte Carlo method, which leads to the determination of the critical fiber volume fraction (or the percolation threshold). The effect of fiber curliness on the percolation behavior is incorporated in the current model by using 3-D arm-shaped fibers, each of which needs five independent geometrical parameters (i.e., three coordinates for its vertex and two orientation angles) for its identification. There are three controlling parameters for such fibers, namely the fiber arm length, the fiber aspect ratio, and the fiber arm angle. The new model also considers the sample size and scaling effects. The simulation results reveal an exponential relationship between the fiber aspect ratio and the percolation threshold: the higher the aspect ratio, the lower the threshold. It is also found that the curliness largely influences the percolation threshold: the more curved the fiber, the higher the threshold. However, the effect of curliness diminishes with the increase of the fiber aspect ratio. With the percolation threshold obtained from the Monte Carlo model, the effective electrical conductivity of the composite is then determined by applying the theory of percolation. The numerical results indicate that the composite conductivity decreases as the fibers become more curved and as the fiber aspect ratio decreases. These predicted trends of the percolation threshold and composite conductivity are in good agreement with existing experimental and simulation results.     

AC conductivity of carbon fiber–polymer matrix composites at the percolation threshold

This paper reports results on experimental investigation of the conductivity behavior of carbon fiber filled polymer composites at the percolation threshold. Two types of carbon fiber‐epoxy matrix composites have been studied and comparison of the measured data has been made. These two types of composites differ in the surface modification of carbon fibers (in one case the surface of carbon fibers is covered with polymer beads using the microencapsulation technology, in the other their surface stayed unmodified). Experimental data reveal that surface modification of carbon fibers influences greatly the DC conductivity (percolation threshold moves to higher concentrations) but does not influence the AC electrical properties. From the frequency dependence of conductivity upon fiber concentration it becomes clear that it is not possible to predict the high frequency conductivity (electromagnetic interference shielding properties) based on the DC conductivity. Percolation behavior of conductivity as a function of conductive filler concentration is typical only for DC or low frequency AC conductivity. The percolation threshold gradually vanishes for high frequencies of electromagnetic field. The temperature dependence of electrical properties has also been studied. Composites with concentration near the percolation threshold show the switch‐off effect (at the specific temperature the DC conductivity drops by several orders of magnitude). This switch‐off effect does not occur for high frequency AC conductivity.     

Simulation of percolation threshold and electrical conductivity in composites filled with conductive particles: Effect of polydisperse particle size distribution

A Monte Carlo simulation method was developed in the open source programing language Python to predict the conductive filler concentration at the percolation threshold and the electrical conductivity for different filler concentrations in electrically conductive composites (ECCs) with fiber‐like conductive fillers. The computer method was programmed to consider the aspect ratio distribution of the fibers or a single average aspect ratio for the determination of the percolation threshold. The results for the two cases were compared to values reported in the literature for liquid crystal polymers (LCP) with synthetic graphite (SG) and to results obtained experimentally for polyvinylidene fluoride (PVDF) with polypyrrole (PPy)‐coated amorphous silica fibers (ASF). Additionally, a contact resistance based on the tunneling effects principle was used to predict the electrical conductivity, and the results of the simulations were compared to the experimental data for the same ECCS. It was found that the percolation thresholds predicted through the simulations considering the aspect ratio distribution were within the concentration limits associated with the transition from electrical insulation to conductivity, while the electrical conductivity predictions had similar behavior to the experimental data, although the values were of different magnitudes. POLYM. COMPOS., 61–69, 2016. © 2014 Society of Plastics Engineers     

新型炭黑填充抗静电和导电聚丙烯复合材料

以炭黑为导电填料,在聚丙烯中加入适量的环氧树脂和玻璃纤维,制备了新型的抗静电和导电聚丙烯复合材料。测定了不同复合体系的渗滤阈值,用扫描电镜(SEM)对相形貌进行了观察,并研究了环氧树脂和玻璃纤维用量对体积电阻率的影响。SEM照片表明在新型复合材料中,炭黑优先分布在环氧树脂中,环氧树脂包覆在玻璃纤维表面,通过玻璃纤维间的搭接形成导电通路。这种独特的结构使该复合材料的渗滤阈值低于聚丙烯/炭黑和聚丙烯/环氧树脂/炭黑复合体系的渗滤阈值。玻璃纤维和环氧树脂含量分别需要达到约10%,复合材料才能具有抗静电和导电作用。     

Electrical and mechanical percolation in graphene-latex nanocomposites

Conductive composites based on few layer graphene are of primary interests. In this work latex based composites were produced leading to a specific cellular morphology. Highly conductive graphene-based composite materials have been produced through a solvent-free procedure. Both the mechanical and conductivity behaviors were successfully described using a percolation approach that confirms the presence of a three dimensional filler network efficiently spread across the material. The influence of the aspect ratio between the conductive filler and the latex nanosphere drove the study. It was demonstrated experimentally that the tuning of the cell dimensions of the composite morphology influences the percolation threshold and the reachable maximum conductivity and reinforcement. These experimental results are consistent with phenomenological models based on the statistical percolation theory.     

Determination of percolation threshold and electrical conductivity of polyvinylidene fluoride (PVDF)/short carbon fiber (SCF) composites: effect of SCF aspect ratio

Composites of polyvinylidene fluoride (PVDF) and short carbon fibers (SCFs) with different aspect ratios of the SCFs were prepared by the solution casting technique. The electrical percolation thresholds of the composites are highly influenced by the SCF aspect ratio calculated using both the Sigmoidal Boltzmann model and classical percolation theory. It was observed that the percolation threshold of PVDF/SCF composites decreases with an increase in the aspect ratio of the SCFs in the PVDF matrix. Different theoretical models were used to check the alignment of the SCFs in the PVDF matrix. The applicability of the theoretical models was tested to predict the composition‐dependent electrical conductivity at different SCF loadings and aspect ratios and the predictions were compared with experimental results. The effect of the fiber aspect ratio on the AC electrical conductivity was also investigated. Finally, the transparency of the composites was tested with the help of UV?visible spectroscopy and exhibits an SCF loading dependence in the PVDF matrix. © 2016 Society of Chemical Industry     

Electrically conductive composites based on epoxy resin containing polyaniline–DBSA‐ and polyaniline–DBSA‐coated glass fibers

Four kinds of polyaniline (PANI)‐coated glass fibers (GF–PANI) combined with bulk PANI particles were synthesized. GF–PANI fillers containing different PANI contents were incorporated into an epoxy–anhydride system. The best conductivity behavior of the epoxy/GF–PANI composites was obtained with a GF–PANI filler containing 80% PANI. Such a composite shows the lowest percolation threshold at about 20% GF–PANI or 16% PANI (glass fiber‐free basis). The PANI‐coated glass fibers act as conductive bridges, interconnecting PANI particles in the epoxy matrix, thus contributing to the improvement of the conductivity of the composite and the lower percolation threshold, compared with that of a epoxy/PANI–powder composite. Particularly, the presence of glass fibers significantly improves the mechanical properties, for example, the modulus and strength of the conductive epoxy composites. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1329–1334, 2004     

Electrical conductivity modeling of carbon black/polycarbonate,carbon nanotube/polycarbonate,and exfoliated graphite nanoplatelet/polycarbonate composites

Adding conductive carbon fillers to electrically insulating thermoplastic polymers increases the resulting composite's electrical conductivity, which would enable them to be used in electrostatic dissipative and semiconductive applications. In this study, varying amounts of carbon black (CB: 2 to 10 wt %), multiwalled carbon nanotubes (CNT: 0.5 to 8 wt %), or exfoliated graphite nanoplatelets (GNP: 2 to 15 wt %) were added to polycarbonate (PC) and the resulting composites were tested for electrical conductivity (EC = 1/electrical resistivity). The percolation threshold was ～ 1.2 vol % CNT, ～ 2.4 vol % CB, and ～ 4.6 vol % GNP. In addition, three EC models (Mamunya, additive, and general effective media) were developed for the CB/PC, CNT/PC, and GNP/PC composites. The general effective media (GEM) model showed the best agreement with the experimental results over the entire range of filler concentrations (above and below the percolation threshold) for all three composite systems. In addition, the GEM model can be easily adapted for composites containing combinations of different conductive fillers. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

镀镍碳纤维/镀镍石墨粉填充PC/ABS材料导电性能的研究

在PC/ABS材料中填充镀镍碳纤维（NiCF）和镀镍石墨粉,制备一种新型填充型导电复合材料,分析了NiCF与镀镍石墨粉的填充量及NiCF长度对复合材料导电性能的影响。结果表明,随着NiCF和镀镍石墨粉填充量的增加,复合材料的体积导电率会下降,即导电性能得到提高。与镀镍石墨粉相比,NiCF对复合材料导电性的影响更显著。NiCF/镀镍石墨粉/PC/ABS复合材料存在渗滤效应,当NiCF含量在10%~15%范围内时,材料的体积导电率急剧下降,导电性能迅速提高。当复合材料颗粒长度为10mm左右时,注塑成型的材料导电性能最佳。     

Electrical conductivity and percolation threshold of hybrid carbon/polymer composites

The electrical conductivity and percolation threshold of single and hybrid carbon filled composites are experimentally investigated. Polystyrene, carbon fiber (CF) and carbon black (CB) at three CF/CB ratios of 1.67, 3.33, 6.67 were compounded in a twin screw extruder micro‐compounder and compression molded into sheets. The through‐plane and in‐plane electrical conductivity of the composites are measured by 2 and 4 probe techniques. The percolation threshold of the single filler and hybrid composites are determined from the experimental results using a percolation model. The hybrid composites have a higher value of electrical conductivity and lower percolation threshold than the single CF filler composite except for the CF/CB ratio of 6.67. The percolation threshold for the cases of single filler and hybrid composites are modeled. The hard core / soft shell model is used and it is assumed that the percolation in a particle filled system depends on the ratio of tunneling distance to particle diameter. This ratio is determined by modeling single filler composites using the experimental data and kept constant in the modeling of the hybrid system. Finite size scaling is used to determine the percolation threshold for the infinite size hybrid system containing (nanosize) particles and micron size fibers for three CF/CB ratios. The simulation results show that the percolations of hybrid composites have the same trends observed in the experimental results. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41744.     

Synthesis of glass fiber‐multiwall carbon nanotube hybrid structures for high‐performance conductive composites

The conductive polyamide 66 (PA66)/carbon nanotube (CNT) composites reinforced with glass fiber‐multiwall CNT (GF‐MWCNT) hybrids were prepared by melt mixing. Electrostactic adsorption was utilized for the deposition of MWCNTs on the surfaces of glass fibers (GFs) to construct hybrid reinforcement with high‐electrical conductivity. The fabricated PA66/CNT composites reinforced with GF‐MWCNT hybrids showed enhanced electrical conductivity and mechanical properties as compared to those of PA66/CNT or PA66/GF/CNT composites. A significant reduction in percolation threshold was found for PA66/GF‐MWCNT/CNT composite (only 0.70 vol%). The morphological investigation demonstrated that MWCNT coating on the surfaces of the GFs improved load transfer between the GFs and the matrix. The presence of MWCNTs in the matrix‐rich interfacial regions enhanced the tensile modulus of the composite by about 10% than that of PA66/GF/CNT composite at the same CNT loading, which shows a promising route to build up high‐performance conductive composites. POLYM. COMPOS. 34:1313–1320, 2013. © 2013 Society of Plastics Engineers     

Electrical Resistivity of Composites

Percolation and Bruggeman's effective media theories, as they apply to the electrical conductivity of composites, are reviewed, and a general effective media (GEM) equation, which combines most aspects of both percolation and effective media theories, is introduced. It is then shown that the GEM equation quantitatively fits electrical resistivity (conductivity) as a function of the volume fraction data for binary composites. The parameters used to fit the experimental data are the electrical resistivities of the two phases, the percolation threshold for the lower resistivity phase (ô _c ), and an exponent t. Preliminary work, showing how the GEM equation can be used to model the piezoresistivity of composites by postulating that ô _c is a function of the independent variable, is also presented.     

PP/AlN复合材料导热机理研究

以氮化铝(AlN)粉末、聚丙烯(PP)为原料,通过共混-模压法制备了PP/AlN导热复合材料,并对其导热性能进行检测。研究发现,该复合材料的导热系数与AlN添加量之间不是线性关系而是呈幂函数关系,与介电逾渗理论基本吻合。根据检测数据并参考介电逾渗理论,提出了导热逾渗模型,并利用该模型和其他导热预测模型对PP/AlN复合材料的导热系数进行了计算。结果表明:复合材料的导热系数随AlN质量分数的增加呈幂函数增加趋势;实际检测结果与导热逾渗模型的预测结果基本相符,使该理论得到了验证。     

Conducting aluminum‐filled nylon 6 composites

This work is concerned with the preparation and characterization of composite materials prepared by compression molding of a mixture of aluminum flakes and nylon 6 powder. The electrical conductivity, density, hardness and morphology of composites were investigated. The electrical conductivity of the composites is < 10⁻¹¹ S/cm unless the metal content reached the percolation threshold, beyond which the conductivity increased markedly by as much as 10¹¹. The volume fraction of conductive filler at the percolation threshold was calculated from experimental data, by fits to functions predicted by the percolation theory. Decreasing the average particle diameter of filler leads to increased percolation threshold (it varies from 23 to 34 vol% for the three different fillers studied) and decreased maximal conductivity of composites. The density of the composites was measured and compared with values calculated assuming different void levels within the samples. Furthermore, it is shown that for certain sizes of particle filler, the hardness decreases initially with the increase of metal concentration, possibly because of poor surface contact with the nylon matrix, but, starting from a certain value, there is a hardness increase. For the smallest particle filler, the hardness of samples is not influenced by the presence of the filler.     

The effect of filler concentration on the electrical,thermal, and mechanical properties of carbon particle and carbon fiber‐reinforced poly(styrene‐co‐acrylonitrile) composites

Composite materials of poly (styrene‐co‐acrylonitrile) (luran) matrix with carbon fibers (CF)/carbon particles (CP) were prepared and their properties were evaluated. The mechanical and thermal properties of these composites were studied by dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). Although, by increasing the filler concentration no significant difference was found in melting and crystallization temperatures of the luran. The storage and tensile modulus of the composites increased linearly with filler concentration up to 40 wt % that was approximately three times higher than that of the virgin luran. There is a shift in glass transition temperature of the composite with increasing the filler concentration and the damping peak became flatter that indicated the effectiveness of the filler–matrix interaction. The volume resistivity and thermal conductivity (TC) of the composites were also measured. At a given carbon filler content the CF–Luran composites have much less volume resistivity as compared to CP–Luran composites. The decreased percolation threshold and volume resistivity in case of CF–Luran composites indicated that conductive paths existed in the composites. The conductive pathways were probably formed through interconnection of the carbon fillers. The volume resistivity was also decreased as a function of temperature. The thermal conductivity was increased linearly as a function of temperature with increasing filler concentration up to 40% of CF and CP. This increase was more profound in case of CF–Luran as compared to CP–Luran composites. This was owing to greater thermal networks of fibers as compared to particles. POLYM. COMPOS., 28:186–197, 2007. © 2007 Society of Plastics Engineers     

Morphology and electrical properties of carbon black/poly(ethylene terephthalate)/polypropylene composite

This work attempts to develop a carbon black (CB) filled conductive polymer composite based on poly(ethylene terephthalate) (PET) and polypropylene (PP). The process follows by localizing the CB particles in the minor phase (PET), and then the conductive masterbatch was elongated to form conductive microfibrils in PP matrix during melt extrusion process. After compression molding, a fine conductive three‐dimensional microfibrillar network is constructed. For comparison purpose, CB, PET, and PP are mixed using different pattern. The morphology and the volume resistivity of the obtained composites are evaluated. Electrical conductivity investigation shows that the percolation threshold and resistivity values are dependent on the CB concentration. The best morphological observation shows that the PET phases forms well‐defined microfibrils, and CB particles overwhelmingly localize in the surfaces of the PET microfibrils, which led to a very low percolation threshold, i.e., 4.5 phr, and a reasonable conductivity. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Electrical conductivity and mechanical strength of composites consisting of phenolic resin,carbon fibers,and metal particles

Composites of phenolic resin of novolac type as matrix, with metal particles of Zn as conducting filler, without or with 15% v/v carbon fibers were manufactured by hot pressing. The porosity ratio, the hardness, the flexural and shear strength, and the electrical conductivity of the composites were determined. The percolation threshold was determined based on two models of electrical conductivity versus the content of metal particles of Zn, namely, an analogous to polymer gelation model and the other based on the power law. The composites of carbon fibers combined with Zn particles have higher electrical conductivity than the corresponding without carbon fibers and high strength, lower than that of the composite reinforced with carbon fibers without Zn particles, but still acceptable. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

A modified model of electrical conduction for carbon black–polymer composites

A modified model of electrical conduction for carbon black‐polymer composites is proposed based on the general effective media theory and the number of carbon black particles per aggregate to describe their nonlinear conductive behavior. In order to consider the interactions between carbon black particles, a simple self‐consistent approach is used to improve the model. Expressions of electrical conductivity and percolation threshold are derived from the modified model. The predicted results of electrical conductivity and percolation threshold are in good agreement with experimental data reported in previous literature. Moreover, the dependences of electrical conductivity and percolation threshold on the number of carbon black particles per aggregate are discussed. Copyright © 2010 Society of Chemical Industry     

炭黑质量分数对炭黑/聚丙烯复合材料导电性影响

采用熔融共混制备炭黑(CB)/聚丙烯(pp)导电复合材料,研究炭黑质量分数对复合材料导电性的影响。结果表明,复合材料具有明显渗滤效应,渗滤值在8%左右,炭黑经偶联处理后,渗滤值降低到5%,体积电阻率降低3个数量级;同时发现"逾渗阈值"现象出现的原因,与热力学理论吻合较好,即随着炭黑含量的增加,复合体系界面能出现饱和、过剩,当体系界面过剩达到一定值后,粒子开始形成导电网络,宏观表现为复合材料体积电阻率突降。     

Mechanical,Thermal and Electrical Resisitivity Properties of Thermoplastic Composites Filled with Carbon Fibers and Carbon Particles

Composites consisting of carbon fibers (CF) and carbon particles (CP) in polypropylene (PP) matrix were melt-compounded. Composites were analyzed for their mechanical, electrical and thermal properties. Results indicate that the addition of these fillers improved the mechanical properties of the composites. Thermal conductivity was enhanced as the concentration of fillers was increased. Carbon fibers render the composites electrically conductive so we observed a percolation threshold near 10 wt.% of CF for PP/CF (PP and CF composite) and near 25 wt.% of CP for PP/CP (PP and carbon particle composite). All the results indicated that carbon fibers are more effective in improving the properties as compare to the carbon particles.