Percolation Threshold Of Composites Research Articles

Enhanced Thermal Conductivity of Composite Materials by Filling Sheet and Fiber Under Effect of Filler Contact

Abstract The most common nongranular fillers are sheet and fiber. When they are distributed along the heat flux direction, the thermal conductivity of the composite increases greatly. Meanwhile, the filler contact also has a large effect on the thermal conductivity. However, the effect of filler contacts on the thermal conductivity of the composite with directional fillers has not been investigated. In this paper, combined effects of the filler contact, content, and orientation are investigated. The results show that the effect of filler orientations on the thermal conductivity is greater than filler contacts in the low filler content, and the exact opposite in the high filler content. The effect of filler contacts on fibrous and sheet fillers is far greater than cube and sphere fillers. This rule is affected by the filler contact. The filler content of 8% is the ideal percolation threshold of composites with fibrous and sheet fillers. It is lower than cube filler and previous reports. The space for the thermal conductivity growth of composites with directional fillers is still very large. The effect of the interfacial thermal resistance should be considered in predicting the thermal conductivity of the composite under high interfacial thermal resistances (>10−4).

Improved conductivity and piezoresistive properties of Ni-CNTs cement-based composites under magnetic field

A novel type of cement-based composite with preferentially orientated nickel-coated carbon nanotubes (Ni-CNTs) was fabricated by induction of magnetic field (MF) method for piezoresistive sensor in structural health monitoring system. The microstructures of Ni-CNTs and their aligned features in the as-fabricated composites were observed by scanning electron microscope (SEM), transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD), respectively. The four-electrode method was applied to measure the conductivity and piezoresistive properties of as-fabricated composites. Besides, the effects of several influencing factors, including Ni-CNTs orientation and content, loading rate on the conductivity and piezoresistive properties of Ni-CNTs cement-based composites were determined. The results indicate that the CNTs coated with crystalline nickel are orientated preferentially along the MF direction, of which the orientation angles are concentrated between −30°-20°, presenting a Gaussian distribution. The conductivity and piezoresistive properties of oriented Ni-CNTs cement-based composites are anisotropic. The electrical resistivity and percolation threshold of composites have a sequence: perpendicular to MF > without MF > parallel to MF. Under cyclic compressive loading, Ni-CNTs cement-based composites parallel to MF direction exhibit the best piezoresistive properties. The optimum content level of CNT for the piezoresistivity is 1.20 vol%, which is slightly higher than the percolation threshold. Also, the strain sensitivity of composites parallel to MF is most sensitive to the loading rate.

Removal of Surfactant from Nanocomposites Films Based on Thermally Reduced Graphene Oxide and Natural Rubber

Electrically conducting elastomer composites based on natural rubber and reduced graphene oxide (rGO) is reported. These composites were prepared by a latex method and an easy washing process. The latex method consists of the mixing of an aqueous suspension of rGO, stabilized by sodium dodecyl sulfate and pre-vulcanized natural rubber, followed by solvent casting. The percolation threshold of composites was estimated at 1.54 wt.% of rGO. The washing process allowed elimination of the surfactant completely from nanocomposites. The absence of surfactant in nanocomposites was demonstrated by Raman spectroscopy and dynamo-mechanical analysis. The surfactant-free nanocomposites showed improved mechanical and electrical properties.

Numerical Simulation of the Percolation Threshold in Non-Overlapping Ellipsoid Composites: Toward Bottom-Up Approach for Carbon Based Electromagnetic Components Realization

A Monte Carlo (MC) model for the calculation of the percolation threshold in the composite filled with ellipsoids of revolution is developed to simulate the real experimental situation of percolative composites in which functional additives do not penetrate each other. The important advantage is that the MC model can be easily applied to multi-components composites, e.g., containing graphene nanoplatelets, carbon black and carbon nanotubes, by means of utilising the ellipsoids of different aspect ratios with the filling fraction corresponding to concentrations of each type of inclusion. The developed model could be used in a pre-experimental step for producing effective close-to percolation and percolated nanocomposites for various electromagnetic applications to avoid time and resources consuming the “sort-out” experimental phase of composition optimization, and could be utilized as the first step of the bottom-up material approach to touch the macroscopic platform for antennas/circuit realization.

Self-Assembled Morphologies and Percolation Probability of Mixed Carbon Fillers in the Diblock Copolymer Template: Hybrid Particle-Field Molecular Dynamics Simulation

The self-assembly of polymer composites of mixed carbon fillers including single-walled carbon nanotube (SWCNT) and carbon black nanoparticles (CB NPs) in diblock copolymer (BCP) template are investigated using hybrid particle-field molecular dynamics simulations in this work. Simulations show, in agreement with experiments, that composites of BCP template with SWCNT have lower percolation threshold than that of BCP template with CB NPs. Moreover, the ratio between SWCNT and CB NPs has a strong influence on the percolation threshold of composites. The results of percolation probability show that adding more SWCNT (compared with CB NPs) to the BCP template could decrease the percolation threshold. However, a synergistic effect of percolation of the mixed carbon fillers in BCP template has been found. In particular, a nonlinear relation following the Boltzman function has been found, and the lowest percolation threshold exists with the volume ratio 4:1 (SWCNT/CB NPs) compared with the volume ratios of 1:1, ...

Graphene nanoplatelets and fullerene in polypropylene matrix as nanosized dielectric probe

Composite materials of polypropylene, graphene nanoplatelets (GNP) or fullerene C60 were synthesized by in situ polymerization. GNP particles consist of 3–5 graphene layers and have aspect ratio 40. In composites with pristine GNP particles their aspect ratio is 110, whereas ultrasonic processing reduces it to 40–50. This change of aspect ratio of filler particles and their aggregates results in different properties of composites with pristine and sonicated GNP. Percolation threshold for composites with pristine GNP is 0.25% vol. In composites with sonicated GNP it is 2–3% vol. This is due to reduction in the size of filler particles aggregates and more uniform distribution of particles in polymer matrix after ultrasonic treatment. The presence of nanocarbon filler (GNP or fullerene) makes α‐transition, associated with the glass transition of the amorphous phase of polypropylene, clearly resolved. Its intensity increases with the concentration of nanofiller, which acts as a dielectric probe. POLYM. COMPOS., 36:1006–1011, 2015. © 2015 Society of Plastics Engineers

A Numerical Study on Electrical Percolation of Polymer-Matrix Composites with Hybrid Fillers of Carbon Nanotubes and Carbon Black

The electrical percolation of polymer-matrix composites (PMCs) containing hybrid fillers of carbon nanotubes (CNTs) and carbon black (CB) is estimated by studying the connection possibility of the fillers using Monte Carlo simulation. The 3D simulation model of CB-CNT hybrid filler is established, in which CNTs are modeled by slender capped cylinders and CB groups are modeled by hypothetical spheres with interspaces because CB particles are always agglomerated. The observation on the effects of CB and CNT volume fractions and dimensions on the electrical percolation threshold of hybrid filled composites is then carried out. It is found that the composite electrical percolation threshold can be reduced by increasing CNT aspect ratio, as well as increasing the diameter ratio of CB groups to CNTs. And adding CB into CNT composites can decrease the CNT volume needed to convert the composite conductivity, especially when the CNT volume fraction is close to the threshold of PMCs with only CNT filler. Different from previous linear assumption, the nonlinear relation between CB and CNT volume fractions at composite percolation threshold is revealed, which is consistent with the synergistic effect observed in experiments. Based on the nonlinear relation, the estimating equation for the electrical percolation threshold of the PMCs containing CB-CNT hybrid fillers is established.

In situ polymerized poly(propylene)/graphene nanoplatelets nanocomposites: Dielectric and microwave properties

Composite materials of isotactic polypropylene and graphene nanoplatelets were synthesized by in situ polymerization in liquid propylene with the use of metallocene catalyst system. Graphene nanoplatelets were prepared by chemical oxidation of graphite and subsequent reduction. Preliminary ultrasonic treatment of GNP suspensions in toluene results in better dispersion of particles, both in liquid polymerization medium and in polymer matrix. GNP particles consist of 3–5 graphene layers and have aspect ratio 40. In composites with pristine GNP particles their aspect ratio is 110, whereas ultrasonic processing reduces aspect ratio to 40–50. Ultrasonic processing provides, apparently, a more uniform distribution of GNP particles, which in nanocomposite are largely individualized. This change of aspect ratio of filler particles and their aggregates results in different properties of composites with pristine and sonicated GNP. Percolation threshold for composites with pristine GNP is 0.25 vol.%. In composites with sonicated GNP percolation threshold is 2–3 vol.%. This is due to reduction in the size of filler particles aggregates and much more uniform distribution of particles in polymer matrix after ultrasonic treatment.

Ising Model for Conductive Percolation in Electrically Conductive Adhesives by Considering Random Arrangement of Conducting Particles

Problem statement: Thermodynamically, particles in composites will arrange in a way such that the Helmholtz free energy is minimized. However, even a single structure has the lowest free energy, it should not ignore the probability of other structures having larger energies to occur, although at small chances. Approach: All possible arrangements of particles in the composites, therefore, must be taken into account in the theory or simulation development. Results: The composite energy depends on the interaction between components in the composites. To consider the effect of interactions on energy, in this study we used a simple Ising model incorporated with the Bragg-Williams approximation. We used the model to predict the average packing fraction and the percolation threshold in composites as well as other quantities related to percolation phenomenon. Conclusion/Recommendations: We found several predictions that have not been reported by previous authors. This model can be important in the understanding conductivity development in electrically conductive adhesive composites.

Effect of electrostatic heterocoagulation of PVM/MA grafted carbon black and attapulgite nanorods on electrical and mechanical behaviors of waterborne polyurethane nanocomposites

In our previous report, poly(methyl vinyl ether-alt-maleic anhydride) grafted CB (GCB) with stable dispersion in water was successfully prepared. In the present study, waterborne polyurethane (WPU) nanocomposites including GCB and attapulgite (ATT) were prepared by liquid mixing method. Anionically charged GCB nanoparticles were heterocoagulated on the surface of cationically charged ATT nanorods at low pH value and improved the stabilization of ATT nanorods in water as a dispersing aid. The microstructure development in matrix that depended on various weight ratios of the nanoparticles ultimately influenced the electrical conductivity and mechanical properties of WPU nanocomposites. Composites containing equal concentrations of GCB and ATT showed reduced electrical conductivity, but significant increase in storage modulus. When the weight ratio of GCB to ATT was 5:1, both electrical conductivity and storage modulus of composite were improved simultaneously. The percolation threshold of composites containing a 5:1 (w/w) GCB/ATT ratio was lower than that of composites with GCB alone. The proposed mechanism for the effect of GCB and ATT on electrical or mechanical behaviors in composite was discussed in details. The clear evidence of microstructure development was also observed by transmission electron microscope.

Monte Carlo model for the study of percolation thresholds in composites filled with circular conductive nano-disks

The subject of the study described in this paper is the percolation threshold of composites with conductive nano-scale fillers. Specifically, a three-dimensional continuous Monte Carlo algorithm was developed to determine the percolation threshold of polymers filled with two-dimensional conductive circular nano-disks. The Monte Carlo simulation provides the threshold value of the filler loading when at least one percolation network is formed. A scaling study was carried out to determine the minimum dimension of the representative unit volume that ensures a percolation threshold that is independent of the unit cell size. The effect of the aspect ratio of the nano-particles and the tunneling distance on the percolation threshold was investigated employing the developed model. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

Simulation of percolation threshold in composites filled with conducting particles of various morphologies

AbstractThree‐dimensional (3‐D) Monte Carlo simulation has been performed for predicting the percolation threshold in electrical conductivity of polymer composites filled with randomly oriented conductive particles of various morphologies. The conductive fillers like graphite nanoplatelets have been simulated as interpenetrating thin disks and oblate ellipsoids of revolution. For large aspect ratios we find close agreement between disks and oblate ellipsoids of revolution for the average number of bonds per object BC ≈ 2.3, that is in agreement with previous calculations for other shapes of filler (e. g. oblate prisms). The vermicular particles of thermoexfoliated graphite (TEG) have been simulated as the chains of disks jointed in a special manner. The values of percolation threshold have been calculated for various configuration of graphite chains (fragments of vermicular TEG particles) using the Monte Carlo method. The percolation threshold was shown to be determined by the number of disks m and angle between connected disks. It was found that critical volume fraction strongly depends on disks' aspect ratio ε, their orientation within a chain and length of this chain: ϕc decreases with increase of m and ε. The comparison of numerical results with our previous experimental data showed a reasonably good agreement.Die dreidimensionale (3‐D) Monte‐Carlo‐Simulation wurde zur Ermittlung der Perkolationsschwelle bei der elektrischen Leitfähigkeit von Polymer‐Kompositen, die mit regellos orientierten leitfähigen Teilchen unterschiedlicher Struktur gefüllt sind, eingesetzt. Leitfähige Füllstoffe wie Graphit‐Nanoplatten werden als durchdringende Dünnplatten und abgeplattete Sphäroide simuliert. Bei den großen Seitenverhältnissen wurde eine gute Übereinstimmung zwischen Platten und abgeplatteten Sphäroiden für die Durchschnittszahl der Verbindungen pro Objekt BC ≈ 2.3, entsprechend den vorigen Berechnungen für die anderen ähnlichen Formen wie abgeplattete Prismen gefunden. Weiterhin wurden die fadenförmigen Teilchen eines thermoexfolierten Graphits als Ketten von den auf besondere Weise verbundenen m Platten simuliert. Durch das Monte‐Carlo‐Verfahren wurde die Perkolationsschwelle für unterschiedliche Formen von Graphit‐Verbindungen (Bestandteile der wurmförmigen TEG‐Teilchen), bestimmt von m‐Zahl der Platten und vom Winkel zwischen den verbundenen Platten, berechnet. Es wurde festgestellt, dass die Fraktion des kritischen Volumens von den Platten‐Seitenverhältnissen ε, der Platten‐Orientierung in der Kette und von der Ketten‐Länge abhängig ist: ϕc wird durch die Erhöhung von m und ε reduziert. Die numerischen Ergebnisse wurden dann mit den experimentellen Werten verglichen.

New electromagnetic wave shielding effectiveness at microwave frequency of polyvinyl chloride reinforced graphite/copper nanoparticles

A novel functional nanoconducting composite from polyvinyl chloride reinforced graphite–copper nanoparticles (PVC/GCu) was fabricated in order to produce a material suitable for electromagnetic interference (EMI) shielding applications. The microstructure of the nanocomposites was investigated by means of scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR). The thermal stability of the nanocomposites could improved with the incorporation of GCu nanoparticles. The electrical conductivity increases with increasing GCu content within composites. The percolation threshold of composites is low of about 2 wt.%. Hall-effect studies indicate that increase in GCu content in the composites causes increase in carrier concentration, mobility of the carriers and the composites behave as n-type semiconductor. The nanocomposites showed a high dielectric constant and a high dissipation factor in the frequency range of 1–20 GHz which makes it useful in charge storing and decoupling capacitors applications. The EMI shielding effectiveness (SE) of the PVC/GCu nanocomposites was tested over a frequency range of 1–20 GHz, and 22–70 dB shielding efficiency was obtained for the composites, suggesting that they may be used as an effective lightweight EMI shielding material in aerospace and radar evasion applications.

Effect of conductivity of filler on the percolation threshold of composites

Polytetrafluoroethylene (PTFE)-silver composites were prepared and the influence of conductivity, particle size, and interfacial area of Ag particle on the percolative behavior were investigated. Silver particles of two different grain sizes (3.5 and 5 μm) were individually mixed with PTFE and the corresponding variations in the dielectric properties were studied. The composite containing Ag particles of size 3.5 μm showed the percolation at 7 vol %, while for Ag particles of size 5 μm, the percolation is at 10 vol %. In both cases near the percolation, the interparticle distances were in the range of ∼3.3–3.8 μm.

Impedance spectroscopy and optical characterization of polymethyl methacrylate/indium tin oxide nanocomposites with three-dimensional Voronoi microstructures

This study describes the optical and ac electrical characterization of polymethyl methacrylate (PMMA)/indium tin oxide (ITO) nanocomposites containing a Voronoi-type segregated network microstructure. Optical transmission microscopy, scanning electron microscopy (SEM), and impedance spectroscopy were used to investigate the microstructure and electrical properties of the composites. The complex refractive index values of the composites were measured by using a modified version of the internal reflection intensity analysis (IRIA) method. SEM images of the composites reveal that the microstructure consists of polyhedral-shaped PMMA particles, where the ITO nanoparticles become concentrated along the edges of the PMMA to form a percolated network. Electrical measurements as a function of filler content indicate that the percolation threshold is <0.50 vol % ITO. The in-plane and through-plane refractive indices obtained by the modified IRIA method suggest that the microstructure is isotropic. The estimated extinction coefficients increase with higher ITO content, which is expected for a percolating system. A microstructural model, which takes into account the accumulation of the ITO nanoparticles at the edges of the polyhedron-shaped PMMA particles, is proposed that can predict the percolation threshold in composites that have Voronoi-type segregated network microstructures.

Anomalous electrical conductivity and percolation in carbon nanotube composites

Transport properties of disordered multiphase materials, such as electrical and thermal conductivities, have been an active research area in statistical physics for decades. In a composite consisting of conductive fillers dispersed in an insulating matrix, there is a well-defined insulator– conductor transition when an infinite conductive network or path throughout the matrix is formed. This process can be well described by percolation theory [1, 2]. Recently, carbon nanotube (CNT)-reinforced composites and suspensions have attracted a great deal of attention due to their excellent properties and many potential applications. CNTs have a unique set of mechanical and physical properties, including extremely high Young’s modulus, strength, electrical, and thermal conductivities. The current experiments showed that CNT-reinforced composites exhibit an electrical percolation with addition of 0.1 vol.% or less fillers, at which electrical conductivity rises sharply by several orders of magnitude [3–7]. Here, the percolation threshold of CNTs is closely dependent on their geometric factors (e.g., volume fraction, size, shape, and orientation) and the interaction between them. It is a critical issue in producing conductive composites for use in films, coatings, and paints since the lower percolation threshold can reduce the loading of expensive CNTs, leading to lighter composites. In comparison with composites reinforced with isotropic particles, however, the percolation threshold of composites containing highly anisotropic conductor fillers such as CNTs is still not well understood. The term ‘‘percolation’’ refers to the onset of a sharp transition or an infinite network (or cluster) at which longrange connectivity suddenly appears [1]. The electrical conductivity near the percolation threshold is anomalously greater than that predicted by traditional theoretical models, such as Maxwell, Hamilton-Crosser models [8]. Intuitively, the electrical percolation process in CNT composites is similar to traditional ones with the addition of isotropic conductive particles, but with an ultra-low percolation threshold. As shown in Fig. 1, near the percolation threshold, the probability or fraction of a CNT, P, on the infinite cluster obeys a power law and can be described as P 1⁄2/ /cðaÞ bðaÞ; ð1Þ

Comparison of the effective conductivity between composites reinforced by graphene nanosheets and carbon nanotubes

Both graphene nanosheets and carbon nanotubes have exceptional electric and thermal conductivities, rendering them excellent candidates as second-phase fillers in composite materials to substantially enhance their effective conductivities. Their markedly different geometries, however, can have significant effect on the effective conductivities of composites, which we investigate using an effective medium approximation. It is demonstrated that graphene nanosheet is more effective in conductivity enhancement than carbon nantubes, and both fillers lead to substantially higher conductivity and much reduced percolation threshold in composites. The effects of conductivity anisotropy and interfacial resistance are also discussed.

Study of the Electrical and Tribologic Properties of CNTs-HDPE Composites

CNTs-HDPE composites were prepared by the blend method. SEM was used to investigate the microstructure of the composites. The electrical and tribologic properties of the composites were studied respectively. The experiments showed that the percolation threshold of composites is about 3wt%, which is much lower than that of the carbon black-HDPE composites, and that the temperature-dependent electrical conductivity of composites had the PTC and double NTC characters, being also different from the carbon black-HDPE composites. These results are due to the unique structure and characters of CNTs. The frictional experiments demonstrated that the addition of CNTs would enhance the wear resistance of the composites.