Conductivity and percolation in epoxy resin/conductive filler composites

Abstract

Composites of the polymer/filler type, when the filler is a conductive material such as metal particles, exhibit electrical conductivity that increases with concentration of the conductive phase. These complex materials are considered to be chaotic mixtures of conductive particles randomly distributed in an insulating matrix. The conductivity of these materials in dc electric fields is studied in terms of percolation theory, where electrical conductivity σ is rapidly increased at a critical concentration, defined as P _c, of the conductive phase, according to σ≈(P­P _c)^α. In this work, various epoxy resin/conductive filler composites were prepared. The filler was metal powder of copper, aluminium, or zinc. The conductive behaviour of these materials was studied at temperatures varied from 20 to 140°C. Data obtained from these measurements are analysed using percolation theory and introducing new parameters β and σ_c into the above relation. A semiempirical algorithm is introduced for the determination of α, β, σ_c, and P _c.     

Strain effects on percolation conduction in conductive particle filled composites

The effect of uniaxial and multiaxial mechanical strain on the electrical conductivity of particle filled polymer composites is investigated in the framework of concentration-driven percolation. For composites consisting of low aspect ratio, rigid conductive particles in a compliant polymer matrix, a simple argument leads to the conclusion that the effective volume fraction of conductive particles (the ratio of total particle volume to the total volume of the deformed composite) plays a dominant role, with conductivity remaining isotropic despite the directional bias of the strain state. As such, conductivity is expected to exhibit classical power, law-dependence on concentration, which in this case takes the form of a strain-dependent effective volume fraction. Consideration of deformation effects on particle agglomerates suggest, however, that particle-to-particle network connections are likely to be affected most significantly along directions experiencing the most severe strains, introducing a directional bias in network connectivity at a higher length scale. To assess the importance of this possible directional bias, random resistor network models are used to study the conductivity of uniaxially strained composites. For conservative assumptions on the severity of the bias in bond probabilities, network conductivities exhibit approximately isotropic, concentration-driven behavior for moderate strains, supporting the predictive utility of the simple percolation conduction-effective volume fraction approach. Further corroboration is provided by experiments in the literature on silicone-graphite composites subjected to uniaxial compressive strain, where good agreement is obtained through moderate strains for the theoretically correct value of the conduction exponent in concentration-driven percolation.     

Joining of Si-Ti-C-O fibre-assembled ceramic composites with 72Ag-26Cu-2Ti filler metal

Si-Ti-C-O fibre-assembled ceramic composites were joined with 72Ag-26Cu-2Ti filler metal at 1123 K and 1223 K in vacuum. The composites consisted of Si-Ti-C-O fibres, which were assembled unidirectionally, and oxide material filling the spaces between the fibres. During the joining process, frothing occurred at the joining interfaces. Joining interfaces were observed by SEM and analysed by electron probe microanalysis and X-ray diffraction. The strength of the joints was evaluated by four-point bending tests. Most of Si-Ti-C-O fibre/filler metal interfaces and the oxide material/filler metal interfaces were firm without cracking and separation. At the fibre/metal interfaces, a high concentration of titanium was confirmed. Among the specimens joined at 1123 K, the average strength, measured by the bending test, was 96 MPa. It was inferred that the defects at the joining interfaces formed by frothing had decreased the strength of the joints. Metallizing of the surfaces to be joined with the same filler metal as a pretreatment before joining, was effective in preventing frothing during joining and improving the joining strength. The average strength of the joints with pretreatment was 211 MPa.     

Joining of carbon fibre-reinforced silicon nitride composites with 72Ag-26Cu-2Ti filler metal

Unidirectionally reinforced carbon fibre/Si₃N₄ matrix composites were joined with 72Ag-26Cu-2Ti filler metal. Joining interfaces were observed by SEM and analysed by energy dispersive spectroscopy. The strength of the joints was evaluated by four-point bending tests. Most of the interfaces of Si₄N₄ matrix/filler metal were firm without cracking and separation. At the interfaces, reaction between the composites and filler metal was limited. Only a concentration of titanium at Si₃N₄ matrix/filler metal interface was confirmed. On the fracture surfaces, many holes left as traces of pull-out of carbon fibres and pulled out fibres could be observed. The maximum joining strength and the average strength, measured by the bending test, were 159 MPa and 107 MPa, respectively. The pull-out process of fibres from the matrix and the reasons for the large scatter in the strength of joints, were discussed. The fibre pull-out behaviour could be related to fibre distribution density at the joining interface.     

Influence of filler particle shape on elastic moduli of PP/CaCO3 and PP/Mg(OH)2 composites

The effects of filler particle shape on the Young's and shear moduli of PP/CaCO₃ and PP/Mg(OH)₂ composites were studied in the concentration interval up to 50 vol/vol % filler. Calcium carbonate had irregular, approximately spherical particles and magnesium hydroxide had particles either in the form of hexagonal plates or micro-needles. The analysis based on the classical models together with structural observations enabled explanation of the composition dependences of elastic moduli of the blends studied. It was found that immobilization of PP matrix on the filler surface prominently influenced the values ofG′ andE′ moduli of PP/CaCO₃ and PP/Mg(OH)₂ composites. The presence of the strongly immobilized PP with increasing geometrical anisotropy of the filler particles enabled a hyperstructure creation in the composites PP/Mg(OH)₂.     

Influence of the filler particle shape on the elastic moduli of PP/CaCO3 and PP/Mg(OH)2 composites

The effects of enhancing the interfacial adhesion between fillers and PP matrix on the Youngs and shear moduli were observed within wide concentration intervals of both filler and adhesive agent. Calcium carbonate and magnesium hydroxide were used as-received and/or with the surface hydrophobized by the long-chain fatty acids. A copolymer of polypropylene and maleic anhydride containing about 1 wt/wt% of grafted maleic anhydride was used for the interface modification. The analysis, based on the classical models, showed the necessity of their simple modification considering the increase in the amount of immobilized matrix with enhancing interfacial adhesion. Maleated polypropylene influenced both the matrix-filler interface and matrix bulk due to the interactions of carboxyl groups with basic centres on the filler surface or on the impurities in the matrix bulk. The greater extent of the immobilized matrix on the filler surface caused the creation of the particles hyperstructure at a lower Mg(OH)₂ content than in systems with zero adhesion.     

Crushed sand in concrete – Effect of particle shape in different fractions and filler properties on rheology

Studies of sand particle characteristics (shape, voids content, filler particle size distribution) and rheology of concrete (slump-flow, yield stress and plastic viscosity) show that the 0.125/2 mm particle shape and ≤0.125 mm filler properties are the most important factors for concrete workability when the sand grading 0/8 mm is kept constant. By normalizing the maximum variation of rheology (slump-flow value in mm) obtained in mixes where different size fractions are exchanged, the fraction ≤ 0.125 mm was found to have around 6–8 times larger effect on rheology per unit volume % exchanged, compared to the coarser sand fractions: ≤0.125 mm = 35.2 mm/%; 0.125/2 mm = 4.9 mm/%; 2/5 mm = 6.0 mm/% and 5/8 mm = 3.8 mm/%.     

Strengthening in deformation-processed Cu-20% Fe composites

Three Cu-20% Fe composites with different iron powder sizes were fabricated using powder metallurgy processes. The strengths of these composites after extensive deformation processing by rod swaging and wire drawing were shown to be anomalously higher than those predicted by rule of mixtures equations. However, the strengths obey a Hall-Petch type relationship with the iron filament spacings. The strengths of the Cu-20% Fe composites after equivalent deformation processing increased with decreasing initial iron powder size. Comparison of a Cu-20% Fe composite with a similar Cu-20% Nb composite showed that Cu-20% Fe was stronger after an identical degree of deformation processing. This increase in strength of a Cu-20% Fe composite over that of a Cu-20% Nb composite correlated with the greater shear modulus of iron compared to niobium using a barrier model for hardening.     

Three-dimensional electrical percolation behaviour in conductive short-fibre composites

The percolation behaviour and electrical conductivity in unidirectional composites made of short conductive fibres embedded in an insulating matrix were examined by Monte Carlo simulation as a function of aspect ratio, volume fraction and angle. The unidirectional composite exhibited a highly anisotropic percolation behaviour with respect to the fibre direction for both fibre normal and fixed-length distribution. For the direction parallel to the fibre, the electrical conductivity increased exponentially with the volume fraction and the exponent increased as the aspect ratio increased. The conductivity in the transverse direction exhibited a sharp transition, from zero to nearly the same level as parallel conductivity at the critical volume fraction. The percolation threshold for the transverse direction also increased with aspect ratio up to 20, above which it decreased in parabolic manner. Both the threshold volume fraction and transient increase in conductivity in the transverse direction varied parabolically with aspect ratio, the maximum being an aspect ratio of 20.     

Production of biopolymer composites by particle bonding

This paper describes a new technology to produce biopolymer composites at room temperature. During the process, micrometer-scale raw material is coated with zein that has strong adhesive property, which is then compressed to form a rigid material. Since this technology does not require purification of the raw materials, various types of compounds can be used as component materials. The coating of particles with zein makes use of the unique property of zein in aqueous ethanol solution. Zein molecules adsorb to the surface of hydrophilic particles when the ethanol content of solvent mixture increases. Formation of aggregates is followed to form large agglomerates. Removal of solvents from the agglomerates yields the final product. Biopolymer composites thus formed showed a broad range of compressive strengths depending on the hardness of the starting raw material used as a base component.     

Electrical conductivity of composites: a percolation approach

A percolation model has been developed for describing electrical conductivity in particle and short-fibre metal-ceramic composites. Results apply quantitatively to three-dimensional microstructures with fully controlled characteristics (particle shape, orientation and distribution).     

Electrical percolation phenomena in cement composites containing conductive fibres

Electrical conductivity measurements on cement composites containing carbon fibres or steel fibres were conducted. Percolation phenomena associated with electrical conductivity were observed. The conductivity of the systems studied increased by several orders of magnitude, at a specific concentration of conductive fibre, i.e. the percolation concentration. The percolation concentration is shown to be dependent on conductive fibre geometry instead of system composition. The results provide an important guide for the manufacture of conductive cement composites containing conductive fibres.     

Assessment of percolation and homogeneity in ABS/carbon black composites by electrical measurements

In this study, composites consisting of an insulating poly(acrylonitrile-co-butadiene-co-styrene) polymer matrix and a conducting carbon black (CB) additive were produced by twin-screw extrusion. Both direct current and alternating current electrical measurements were used to evaluate the electrical properties of the composite and to assess whether sufficient mixing was achieved. Electrical measurement results and scanning electron micrographs show that once-extruded composites had a porous structure and poor conductivity while twice-extruded composites were much more homogeneous and had higher conductivity. The percolation threshold of the twice-extruded poly(acrylonitrile-co-butadiene-co-styrene)/CB composites was found to be between 8 and 10% CB. Electrical measurements provided a feedback loop for improving processing of the composite material.