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Cement-based piezoresistive composites have attracted significant attention as smart construction materials for embedding self-sensing capability in concrete infrastructure. Although a number of studies have been conducted using multi-walled carbon nanotubes (MWCNTs) as a functional filler for self-sensing cement-based composites, studies addressing the influence of the internal moisture state on the electrical properties are relatively scant. In this study, we aim to experimentally investigate the effect of internal moisture state on the electrical resistivity of cement-based composites containing MWCNTs as an electrically conductive medium to raise a need for calibration of self-sensing data considering the internal moisture state. To this end, the moisture dependence of electrical resistivity in under-percolated cement-based composites was mainly evaluated, along with other material properties such as strength, shrinkage, and flowability. Results revealed that the electrical resistivity increased almost linearly as the internal relative humidity (IRH) decreased, and the increase was more pronounced below the percolation threshold. In addition, it was found that the strength gained by the microfiller effect of MWCNTs was significantly reduced particularly in under-percolated mixtures, leading to overall strength reductions. Furthermore, this study showed that the more the MWCNT was added, the smaller the flowability was obtained due to the increased viscosity of the mixture. The findings of this study are expected to provide pivotal information for accurate and reliable interpretations of self-sensing data generated by MWCNT-embedded cement-based composites.

Percolative composites with negative permittivity have attracted widespread attentions due to their great potential in electromagnetic shielding and microwave devices. Targeting at achieving epsilon-negative properties, the percolative graphite/barium titanate (GR/BaTiO3) composite is herein designed and prepared using hot-pressing sintered process. It's found that the plasma oscillations of delocalized electrons result in the epsilon negative permittivity behaviors when the GR contents exceeds the 2 wt% (percolation threshold), and frequency dependence of the negative permittivity which is in well agreement with the Drude model. Meanwhile, it's demonstrated that the ac conductivity represents a typical metal-like behavior as the conductive networks formed within the composites by the increasing GR loadings. Moreover, the equivalent circuit analysis reveals the relationships between capacitive-inductive transition and the conversion of permittivity changing from positive to negative. This work provides effective possibility for developing excellent dielectric properties of percolative GR/BaTiO3 composite for capacitors and coil-less electrical inductors applications.

Multi-wall carbon nanotube (MWNT)-reinforced alumina composites were prepared by a sol-spray process combined with a vacuum hot press process. The relative densities of all the samples were higher than 97%. Scanning electron microscopy (SEM) results showed that the MWNTs were well-dispersed in the alumina matrix; specifically, most of them were distributed along the grain boundaries in the form of networks, whereas the others were located in the grains. For 0.5 wt.% MWNTs, the Vicker hardness and fracture toughness were 32.1% and 75.6% higher than those of pure alumina, and the average increment of the thermal diffusivity under different test temperatures is ~ 26.2%. When the content of MWNTs is higher than 0.5 wt.%, the composites showed conductor properties. Moreover, the percolation threshold of the prepared composites was 0.37 wt.% with the nonlinear fitting of conductivity data, which indicates that the MWNTs were well dispersed in the alumina matrix.

Conductive polymer composites enjoy specialized applications such as electrostatic discharge protection. In this work, we create interfacially localized graphene nanoplatelets (GNPs) in a cocontinuous polymer blend of polylactide (PLA) and poly(ethylene-co-vinyl acetate) (EVA). Based on the wetting coefficient analysis, GNPs favor localization in the EVA phase. A two-step compounding sequence is designed such that a PLA/GNP masterbatch is first prepared via solution blending, and then melt compounded with the EVA. In the second step, GNPs transfer from the PLA phase to the EVA phase but become kinetically trapped at the interface, as confirmed by electron microscopy. We achieve an ultralow percolation threshold of 0.048 wt. % GNPs and obtain blends with electrical conductivities of ∼10−5 S/cm at 0.5 wt. % GNP concentration. We systematically study the shear and extensional rheology of the ternary composite system. Cocontinuous blends with interfacial GNPs exhibit higher shear and extensional viscosities compared to samples with GNPs localized entirely within the EVA phase. Rheology, in situ dielectric measurements, and transmission electron microscopic imaging after nonlinear deformations all show the interfacial GNP network undergoes structure recovery and largely remains at the PLA/EVA interface. Moreover, high electrical conductivity is maintained during 2–10 min melt compounding and conductivity recovers with annealing after nonlinear deformations. These results suggest that these robust GNP networks preserve their bulk electrical conductivity during subsequent melt processing.

Pristine carbon nanotubes (CNTs) and functionalized carbon nanotubes (f-CNTs) were introduced into conductive poly(methyl methacrylate)/graphene nanoplatelet (PMMA/GNP) composites to achieve a synergistic effect in the enhancement of the conductivity and the reduction in the percolation threshold by forming a 3-Dimensional(3-D) hybrid structure. Both the in-plane and perpendicular electrical properties were investigated. The synergies of hybrid fillers in the in-plane direction were more dependent on the total filler loading, while those in the perpendicular direction were significantly influenced by the GNP/CNT or GNP/f-CNT ratios. Typically, a schematic diagram of the evolution of the 3-D conductive pathways of PMMA/GNP/f-CNT composite at different GNP/f-CNT ratios was presented to explain this phenomenon. Moreover, tunable conductivity anisotropy (defined as the ratio of in-plane conductivity to perpendicular conductivity) ranging from 0.01 to 1000 was achieved, simply by constructing different conductive structures at various filler loadings or ratios in composites. Graphical abstract The synergistic effect of GNPs and f-CNTs varies with the microstructural conductive network evolution at different filler ratios.

In this paper, we developed a three-dimensional percolation model to investigate the effects of the concentration and morphology of CNTs (carbon nanotubes) on the electrical conductivity of the nanocomposites. In the model, we judged the connections between CNTs by range search algorithm based on KD-Tree structure. At the same time, DIJKSTRA-Melissa algorithm was applied to efficiently find all the conductive paths instead of finding conductive network in traditional methods. From the simulation results, CNTs with higher aspect ratio were easier to form the conductive network. In a certain range of CNT’s concentration, the relationship between the conductivity of the conductive network and the carbon nanotubes was basically consistent with the classical percolation theory. To verify our simulation model, the morphological, electrical properties of Carbon nanotubes (CNTs)/poly(dimethyl siloxane) (PDMS) nanocomposites with different aspect ratio (AR) of MWNTs were systematically studied. In conclusion, these unique advantageous properties could be exploited to suggest potential applications of artificial electronic skin.

Incorporation of rigid nanoparticles is the most effective means of improving polymer properties. Montmorillonite (MMT) and multi-walled carbon nanotubes (MWCNTs) are legendary in this field for their individual exceptional properties. A synergistic phenomenon is induced between these two particles when they are simultaneously incorporated into polymers. At a definite nanofillers concentration, called the percolation threshold, there is a sudden change in nanocomposite properties due to the formation of a 3D-structured network of the nanoparticles within the matrix. In this work, the properties of poly(lactic acid) (PLA) nanocomposites filled with different fractions of MMT/MWCNTs hybrid (0.5–2.0 wt%) were analyzed. In particular, the percolation threshold of the MMT/MWCNTs hybrid was uniquely identified by differential scanning calorimetry, thermogravimetric analysis and dynamic mechanical thermal analysis. The structural studies by X-ray diffraction and Fourier-transform infrared spectroscopy were also associated with the percolation threshold of MMT/MWCNTs in PLA. At 1.0 wt% MMT/MWCNTs concentration, the complete exfoliation of the particles was maintained, and the thermal characteristics such as glass transition, crystallization and melting temperatures reached their plateau at this hybrid concentration. Moreover, the thermal degradation and viscoelastic parameters showed their peak values at this critical point, which is correlated with the formation of the percolation threshold within the matrix. The morphological studies confirmed the homogeneous dispersion of MMT/MWCNTs in PLA up to a concentration of 1.0 wt%. At 2.0 wt% MMT/MWCNTs, few aggregations occurred in the PLA-based composite, confirming that the percolation threshold was formed at a lower concentration of MMT/MWCNTs nanoparticles.

The development of high-efficiency microwave absorbers for C and X bands still remains a challenge, limiting the settlement of corresponding electromagnetic pollution and radar stealth. In this work, a reduced graphene oxide (RGO)/Cu/Fe3O4 composite is successfully proposed by a one-step solvothermal method with a GO dispersion content of 5 mL, where Fe3O4 exhibits high magnetic loss from natural resonance at the C band, and Cu nanorods and RGO are introduced as dual conductive phases to produce suitable dielectric properties by regulating the percolation threshold. The results show that the existence of Cu nanorods significantly reduces the conductivity and dielectric loss of the composites, optimizing the coordination of attenuation capacity and impedance matching in the C and X bands. Consequently, the obtained RGO/Cu/Fe3O4 composite shows outstanding microwave absorption performance with the maximum effective absorption bandwidth (EAB) value of 5.2 GHz at a thin thickness of 3.1 mm, which covers 84% of the C band and 46% of the X band (4.64-9.84 GHz). The performance is superior to the vast majority of previous absorbers in the corresponding bands.

This paper reports the experimental study carried out to establish the dependence of the thermal conductivity of polypropylene-based nanocomposites filled with carbon nanotubes on the main parameter of the temperature regime of their manufacturing ‒ the level of overheating a polymer melt relative to its melting point. The study has been conducted for nanocomposites that were manufactured by applying a method based on the mixing of components in the polymer melt applying a special disk extruder. During the composite manufacturing process, the level of melt overheating varied from 10 to 75K, with the mass share of filler ranging from 0.3 to 10.0%. It is shown that increasing the overheating of a polymer melt causes an increase in the thermal conductivity of the composites. However, when the overheating has reached a certain value, its further growth does not increase the thermal conductivity of nanocomposites. Based on the established pattern, the rational level of this overheating has been determined. That resolves the tasks of manufacturing highly heat-conducting nanocomposites and implementing appropriate energy-saving technology. Data have been acquired on the effects of the impact of the amount of polymer melt overheating on the values of the first and second percolation thresholds for the examined nanocomposites. It is established that the value of the first percolation threshold is more sensitive to the specified amount of overheating. The dependences of the density of the examined composites on the level of polymer melt overheating have been derived. The correlation between a given dependence and the nature of a corresponding change in the thermal conductivity of the composites has been established. Applying the proposed highly heat-conducting nanocomposites is promising for micro and nanoelectronics, energy, etc.

Abstract Electronic devices’ widespread usage has led to a new form of pollution, known as electromagnetic (EM) pollution, causing serious problems like equipment malfunctioning and affecting its reliability. This review article presents a comprehensive literature survey on the various polycarbonate (PC)-based materials for electromagnetic interference (EMI) shielding applications comprising of PC-based composites, blend composites, foams, and more recently, multilayered architectures. Following the state-of-the-art literature available from the previous decade, it is apparent that the properties (conductivity, permittivity and permeability) of nanofiller/fillers and nanocomposite processing/fabrication techniques control the EMI shielding properties in PC-based materials. Researchers have explored a variety of fillers, but high aspect ratio carbonaceous nanofillers have gained significant attention. Through morphological modifications of PC composites, one can obtain a percolation threshold as low as 0.021 wt% of carbon nanotubes (CNTs). However, higher connectivity of conductive filler need not necessarily lead to high EMI shielding performance. Thus, detailed insight into the shielding mechanism is also highlighted. This review article will help researchers design PC-based materials with superior EMI shielding performance coupled with good mechanical stability. Graphical abstract

We aim to express the tunneling resistance in polymer nanocomposites by carbon nanotube (CNT) concentration, interphase depth, CNT curliness, tunneling distance, interfacial tension, network portion and CNT size. The suggested equation is applied to determine the tunneling resistance in some specimens and to estimate the inspirations of dissimilar parameters on the tunneling resistance. The samples do not show a determinate trend between tunneling resistance and filler concentration. Some factors including tunneling distance, percolation onset, CNT content and CNT curliness directly manage the tunneling resistance. Therefore, short tunneling distance, small percolation onset, low CNT content and low CNT curliness produce the poor tunneling resistance. Nonetheless, the resistance of tunnels inversely depends on the portion of attached CNTs, CNT conductivity, CNT length, interphase depth, CNT radius and interfacial tension (i.e. the high levels of these parameters cause the low tunneling resistance). Among the studied parameters, tunneling distance and percolation threshold are the most important parameters manipulating the tunneling resistance, whereas the concentration and length of CNTs have the least effects. As a result, low tunneling distance and small percolation threshold are vital to reduce the tunneling resistance and obtain the conductive nanocomposites.

In this study, nanocomposites with aligned graphene platelets were fabricated to investigate their potential for use in strain measurement. Mechanical mixing was applied, followed by sonication, to disperse the graphene platelets in epoxy resin. Subsequently, an electrical field was applied to the graphene and epoxy compound for 20 min to align the graphene platelets. The electrical conductivity of nanocomposites with different graphene loadings was measured with an electrometer. The results indicated that when the graphene loading was 0.15 wt%, the electrical conductivity of the nanocomposites was close to the percolation threshold. When the electrical conductivity of a material approaches the percolation threshold, its electrical resistance varies considerably in accordance with the extent of axial elongation. Coupon specimens of the nanocomposites with 0.15 wt% aligned graphene platelets were prepared and then subjected to tensile tests. During the tests, conventional strain gauges were adhered to the specimens to evaluate the strain variation and determine the electrical resistance of the specimens. The results revealed that the nanocomposites with aligned graphene exhibited high resistance to axial deformation, demonstrating their potential for use in strain measurement.

The electrical properties of ternary epoxy composite materials (CMs) with carbon nanotubes (CNT) and additional inorganic fillers such as carbonyl iron (Fe) and titanium dioxide (TiO2) particles have been investigated The study of electrical conductivity at direct current (DC) showed the increase of percolation threshold in ternary composites compared with two-phase CNT/epoxy CMs. On the other hand, sufficient enhancement of DC conductivity was observed for ternary CNT-based CMs at CNT content higher than 4 wt%. The impedance spectroscopy study at frequency range 10 Hz–2 MHz revealed the increase of conductivity with frequency for most CMs and each CM has a frequency, below which the conductivity stays constant. The equivalent circuit model has been used to model the complex impedances of the CMs and good matching of modeled and measured impedance diagrams was achieved, allowing it to determine the equivalent electrical parameters of the CMs. The impedance spectra show a transition from pure dielectrics at 0 wt% CNT to conductive material for 3–5 wt% CNT in three-phase epoxy composites. The sufficient higher values of permittivity were found for three-phase epoxy composites compared with two-phase CNT/epoxy CMs. The observed negative value of permittivity for 5%CNT/Fe/epoxy CM at higher frequencies is related to metal-like behavior of composite and described within the Drude model. The developed multi-phase epoxy composites may be promising for applications in electronics such as capacitors and electric field grading materials, electromagnetic interference shielding and microwave absorptive materials.

Electrically conductive polypropylene nanocomposites filled with carbon-based nanofillers such as carbon nanotubes, graphene and carbon black are widely being used in different applications such as electromagnetic interference shielding, wearable electronics, sensors, soft actuators, structural health monitoring and energy storage capacitors. The electrical conductivity of polypropylene nanocomposites depends on multiple factors, and can be tailored by using different processing and pre/post-processing techniques. There has been a lot of research in the past decade or so to maintain the electrical conductivity of polypropylene nanocomposites at the lowest possible filler concentration. Low percolation threshold is critically important for several technical applications as a key factor to well tailor mechanical properties, maintain optical transparency, and bring cost-effectiveness in manufacturing. This review article presents a comprehensive insight of the methodologies that have been used by different researchers to achieve low/ultralow electrical percolation thresholds in carbon-based polypropylene nanocomposites. Most importantly, different parameters that directly influence the percolation threshold and electrical conductivity such as the type, size, aspect ratio, functionalization and nucleating ability of carbon nanofillers, inter-particle interactions, density, crystallinity, viscosity of matrices, nanocomposite morphology, interaction of nanofillers with the polymer matrix, as well as post-processing techniques like annealing have also been discussed in detail. Percolation threshold and its theory, as well as the conduction phenomena such as the tunneling effects are also mentioned. The research has been characterized based on carbon filler types and critical comparisons have been made between the studies using similar methodologies.

Graphene is currently attracting attention for radiation absorption particularly at gigahertz and terahertz frequencies. In this work, composites formed by graphene-augmented γ-Al2O3 nanofibers embedded into the α-Al2O3 matrix are tested for X-band absorption efficiency. Composites with 15 and 25 wt % of graphene fillers with shielding effectiveness (SE) of 38 and 45 dB, respectively, show a high reflection coefficient, while around the electrical percolation threshold (∼1 wt %), an SE of 10 dB was achieved. Furthermore, based on the dielectric data obtained for varying fractions of graphene-/γ-Al2O3-added fillers, a functionally graded multilayer is constructed to maximize the device efficiency. The fabricated multilayer offers the highest absorption efficiency of 99.99% at ∼9.6 GHz and a full X-band absorption of >90% employing five lossy layers of 1-3-5-15 and 25 wt % of graphene/γ-Al2O3 fillers. The results prove a remarkable potential of the fillers and various multilayer designs for broad-band and frequency-specific microwave absorbers.

To suppress the high dielectric loss of graphene oxide (GO)/poly(vinylidene fluoride) (PVDF) while still maintaining a high dielectric constant (k) near the filler percolation threshold, herein, GO...

Electrical responses of pre-percolation PEDOT:PSS polymer 30 micron thick films with incorporated single-walled carbon nanotubes were studied by means of impedance spectroscopy technique. The quantitative description of conductivity features is attempted using equivalent circuit modeling. The proposed model is applied to the experimentally investigated nanocomposite systems with different loadings of the nanofiller.

Graphene oxide (GO) was mixed with 3 mol% yttria tetragonal zirconia polycrystal (3YTZP) using two powder processing routines: a colloidal method in an aqueous solution and a combination of ultrasonication with high-energy planetary ball milling in wet conditions. Highly densified 3YTZP composites with reduced GO (rGO) were consolidated by Spark Plasma Sintering. The in-situ reduction of GO was successfully achieved during the high-temperature sintering process and a detailed study of the restoration of the graphene structure in the sintered composites has been made by Raman spectroscopy. Although no differences between the composites prepared by the two processing methods were found in the distribution of the rGO throughout the 3YTZP matrix for high rGO contents (i.e. the composites with 5 and 10 vol% rGO), a better distribution of the graphene phase was found in the composites with 1 and 2.5 vol% rGO prepared by planetary ball milling. This result, together with a better reduction of the GO in these composites, led to the obtaining of rGO/3YTZP composites with a better behavior in terms of electrical conductivity: an electrical percolation threshold below 2.5 vol% rGO and a high electrical conductivity value (~610 S/m for 10 vol% rGO).

In this work, carbon nanotube (CNT) based nanocomposites with high mass fraction are proposed by in-situ bridging carbon matrix into CNT paper through optimized chemical vapor infiltration (CVI). Nanoinfiltration behavior of CNTs is basically investigated under the CVI process. The contact between each CNT can be strengthened and the conductive pathways can be established, resulting in the better mechanical and electrical properties. Compared with the pristine CNT paper, the CNT/C composite after pyrolysis process confirms a remarkable advance in tensile strength (up to 310 ± 13 MPa) and Young's modulus (up to 2.4 ± 0.1 GPa). Besides, a notable feature of electrical conductivity also shows an improvement up to 8.5 S/cm, which can be attributed to the mass fraction of CNT (41 wt%) breaking the limits of percolation thresholds and the efficient densification of this sample to establish the conductive pathways. This study has a broad application in the development of the multi-functional electrical and engineering materials.

Carbon nanomaterials are effective conductive fillers for permanent antistatic composites due to their long-term stability in electrical conductivity under ambient temperature and humidity. Where graphene or graphene-like materials have been demonstrated to be the most promising conductive fillers. However, the preparation of graphene and further dispersion into polymer matrices to obtain interconnected conductive networks is still a big challenge for conductive composites. A facile green path (all solid states), microsphere rolling transfer method, has been adopted to introduce nano-graphite conductive fillers for polyethylene. The nano-graphites were well dispersed into polyethylene matrices to give interconnected networks with low loading. The conductivity reinforcements of nano-graphite fillers even overtake those of complicated graphene fillers. The percolation threshold of the conductive composites with nano-graphite fillers for polyethylene has been demonstrated to be as low as 0.85 wt%. The electrical conductivity of the conductive composites was measured to increase by 13 orders of magnitude with 2.05 wt% nano-graphite fillers (0.02 S/m), much higher than traditional solid mixing methods and approaching to the best effects from complicated solution mixing of graphene fillers. The nano-graphite conductive networks are easily adjusted and the method is feasible to almost all conventional solid resins and industrial production.

This research focuses on the uncertainty quantification of electrical percolation behavior in wavy carbon nanotube (CNT)-filled polymer nanocomposites with a three-dimensional representative volume element accounting for both tunneling resistance (quantum carrier tunneling) and stochasticity in CNT waviness. The developed percolation model is validated with existing experimental data, and model parameters for electrical conductance converge to the optimal value with Markov Chain Monte Carlo (MCMC) based on Bayesian inference. The predicted 95% confidence interval of electrical conductance indicates a different trend between two-and three-parameters of the electrical conductance model. The main trend of correlation between the percolation threshold (φc) and a parameter of the phase transition (critical exponent, t) indicates a statistically linear relationship via evaluation of the Pearson correlation coefficient. Moreover, the correlation between intrinsic conductance of CNTs (σo) and t also strongly affect the magnitude and slope of electrical conductance in uncertainty quantification. This work can contribute to a robust and reliable design of the PNC considering the physical uncertainty satisfying the target electrical performance through controlling φc, σo, and t.

Lightweight, high-strength, and multifunctional polymer composite foams are urgently needed in numerous high-tech areas. Herein, we proposed a facile, clean, and energy-saving strategy to prepare the microcellular polystyrene/carbon nanotube (PS/CNT) composite foams with segregated conductive networks by an ingenious combination of microwave-assisted foaming and welding of expandable PS beads. The properties (e.g., expansion ratio, cellular structure, electrical conductivity, and fusion strength) of composite foams can be readily tailored by changing the CNT content and irradiation parameters. Benefiting from the unique structure of the microporous PS phases embedded in the conductive CNT networks, the 3D geometric PS/CNT foam part with a density of 0.095 g cm−3 showed an ultralow percolation threshold of 0.0014 vol% and a high specific electromagnetic interference shielding effectiveness (EMI SE) of 211.5 dB cm3 g−1 at 12.4 GHz with only 0.046 vol% CNT loading. The material presented an absorption-dominant shielding feature due to the synergistic action of the perfect CNT networks and the microcellular structure in PS beads. More importantly, the intense microwave sintering induced sufficient interdiffusion and entanglement across the interfacial regions among neighboring PS beads, thus providing the composite foams with a significantly enhanced compression stress of 7.1 MPa and a tensile strength of 2.2 MPa. Consequently, this study might offer a promising approach to manufacture high-performance and multifunctional composite foams for wearable electronic applications.

This paper provides a new approach to model the formation of networks by carbon nanotubes (CNTs) in three dimensions. Network formation by the CNTs plays a vital role in understanding the overall behaviour of the nanocomposites. It is often complicated to analyze the 3D distribution of the fillers inside a nanocomposite experimentally. This 3D atomistic visualization of CNTs through simulations will prove highly beneficial to understand the effect of filler concentration and other experimental parameters. The proposed approach is at the atomistic scale, i.e. each CNT will be built using the appropriate number of carbon atoms depending on its aspect ratio and dimensions. This method aims to be more realistic by eliminating 2D approximation techniques and the cylinder approximation method for the CNTs. Inter filler distances in uniformly distributed short-chopped CNTs are analyzed using this approach. Probable least resistive paths were estimated, and an extended analysis reveals that the minimum filler concentration for initiating electrical conductivity in such short fillers to be around 0.6 vol%.

Graphene nano-platelets (GNPs) can substantially improve the performance of epoxy resin, but improving effects are highly dependent on GNP dispersion uniformity in the matrix. The aim of the current study is to explore the influence of matrix viscosity on the dispersion of GNPs. Thus, epoxy matrix with three disparate viscosities was reinforced with GNPs varying from 0 to 3 wt%, and the influence of matrix viscosity on dispersion uniformity and thus properties of composites were identified. Significant differences in rheological and electrical percolation thresholds were found with a change in the matrix viscosity. The lowest rheological percolation threshold (0.3 vol%) and electrical percolation threshold (0.53 vol%) were always observed in specimens based on a low viscosity matrix. X-ray Diffraction (XRD) results also showed that lower viscosity resulted in better GNPs distribution. The visual state of GNPs dispersion with a change in matrix viscosity was also evaluated through Scanning Electron Microscopy (SEM) and optical microscopy. Optical microscopy images confirmed that while the GNP agglomeration diameter is 42.3 µm in high-viscosity resin, it markedly decreased to 15.1 µm by using low viscosity resin. Transmission Electron Microscopy (TEM) quantitative measurements pertaining to the number of GNP stacked layers also showed that when a low viscosity matrix was used, only 11 layers stack on each other and form thinner clusters compared to 13 and 39 layers in medium and high ones.

Multiwall carbon nanotube (MWCNT) based metacomposites with negative permittivity have received significant interest over the past decade due to their unique electromagnetic properties. Here, markedly percolating Bi2SiO5 (BSO)/MWCNT metacomposites with adjustable negative permittivity were prepared by the facile hydrothermal method. Three-dimensional conductive networks formed by interconnected MWCNT are present in BSO/MWCNT metacomposites with 10 and 20 wt% of MWCNT. The detailed microstructure and resistivity studies of the metacomposites led to realize that the adjustable negative permittivity of the BSO/MWCNT metacomposites attributes to the low-frequency plasmon resonance of free Drude carriers. In this work, the effect of the direct-current biasing voltage in the radio frequency region is investigated on the negative permittivity characteristics. For below percolation threshold ( f c ) metacomposites, the Maxwell-Wagner polarization effects increase in low-frequency region immediately after dc bias is applied. In case of above percolation threshold ( f c ) metacomposites, the Drude free carrier concentration increases due to the formation of conductive network among MWCNT led to the rise of negative permittivity values in the low frequency region. This work provides a novel strategy for the adjustment of the negative permittivity value, which can expand the potential application in the field of sensors based on the changes in permittivity properties.

International audience; The chemical vapor deposition of carbon onto a commercial α-Al2O3 powder bed produces a pristine film of few-layered-graphene (FLG) uniformly covering the α-Al2O3 grains. This obviates both the manipulation of nanocarbons, lengthy mixing steps and the risk of damaging any pre-existing graphene platelets. The powders are consolidated to 99 % by SPS, producing samples where a FLG film is located along the grain boundaries of the submicron α-Al2O3. Compared to the pure α-Al2O3, the composites are moderately stronger and similarly tough and hard due to crack-deflection and crack-bridging and they are electrically conducting with a percolation threshold below 0.74 vol.% of carbon. The high conductivity values reflect the high quality of the thin FLG film and its continuous nature over very long distances. The samples are characterized by Raman spectroscopy, X-ray photoelectron spectroscopy, scanning and transmission electron microscopy.

Magnetic carbon nanotube (marked as “MWCNT@Fe3O4”) has been prepared by depositing magnetic Fe3O4 on carbon nanotube. In order to align MWCNT@Fe3O4 in polyimide (PI) film, weak magnetic field by permanent magnet has been applied during the film curing process. The orientation mechanism of MWCNT@Fe3O4 between the magnetic carbon nanotubes and the PI film matrix has been theoretically studied. Experimental results showed that MWCNT@Fe3O4 was formed in a chain-like alignment in the PI film matrix by the magnetic field, which significantly improved the dielectric properties of composite films. The dielectric permittivity of parallel-aligned films (1.6 wt%) was increased from 5.5 to 52.75 at 58 Hz and percolation threshold of 1.6 wt% was almost 6 times that of the film in random alignment. The dielectric loss of the aligned films before reaching the percolation threshold was between 10–2 and 1. The magnetic alignment can greatly enhance the dielectric permittivity of composite films and suppress their dielectric loss. As for magnetic properties, the relationship between different arrangements and saturation magnetization is as follows: randomly aligned > parallel aligned. PI(//)-0.4wt% film shows the best tensile strength of 70 MPa, 5% elongation at break improvement, and 23% improvement in elastic modulus. This study provides an effective method to align MWCNT in PI film matrix, and the MWCNT@Fe3O4/PI composite film has a promising application prospect in flexible electronic devices.

Conductive Al2O3/graphene composites were manufactured by SPS from Al2O3 powders coated with a few graphene layers. Composite powders with a total carbon content of 0.1, 0.6 and 1.0 wt. % were manufactured by chemical vapour deposition. The effect of the graphene content on the microstructure, mechanical and electrical properties of the compacts were studied. Graphene, homogenously located along the grain boundaries, dramatically hindered the Al2O3 grain growth. The continuous interconnected graphene network enhanced electrical properties, achieving percolation threshold as low as 0.6 wt. % of graphene. The content of 1 wt. % of graphene increased electroconductivity by 13 orders of magnitude as compared to the monolithic alumina. The indentation fracture toughness increased by 20 % in specimens with 0.6 wt. % graphene content as compared to pure alumina. The presence of 1.0 wt. % of graphene resulted in a slight decrease of elastic modulus and hardness, but strength decreased by 40 %.

In this study, an effective method has been described and adopted to quantify the diameter and length of graphene nanofiller. The experimentally measured graphene parameters were modelled by using the Weibull distribution. The fitted graphene nanofiller length and diameter were used to predict the electrical conductivity of the graphene-loaded polypyrrole. The reliability of the dispersion of the filler in the matrix is, aided by the adequate distribution of the filler. An analytical model was developed to study the conductivity of the polypyrrole-graphene (PPy-Gr) composite. In the model, the interfacial effect of the composite constituents was considered and the electrical conductivity of the composite was determined by the simple-sum method. The percolation threshold and the electrical conductivity dependencies of the composites were evaluated by concurrently varying the potential barrier, filler electrical conductivity and the interfacial thickness and the matrix conductivity. The current model produced results, which are in good agreement with experimental measurements of different polymer-composites. It is envisaged that the method employed in this study, can be extended to other polymer-filler mixture as a predictive, optimization and design tool, for polymer composites of any type.

In this paper, Paul’s model is advanced to forecast the tensile modulus of polymer nanocomposites reinforced by carbon nanotubes (CNT) above percolation onset. The developed model assumes the CNT network density by CNT aspect ratio (α), percolation onset and CNT density (n). The experimental results from several samples containing a filler network confirm the predictability of the advanced model. However, undesirable results are reported for the samples without the filler network. Also, both α and n directly manipulate the nanocomposite’s modulus above percolation onset, because they positively influence the polymer-CNT interfacial area and network size. The reasonable effects of α, n and percolation onset on the predicted moduli of nanocomposites validate the developed Paul model.

Graphene products have been used as conductor filler in polymers matrix, resulting in a conductive composite for optoelectronic applications. In this work, the effect of oxygen content of reduced graphene oxide (rGO) products on its dispersion in poly(3-hexylthiophene) (P3HT) and the electrical properties of the P3HT-rGO composites is studied. Graphene oxides (GOs) with different concentrations of oxygen species were first prepared by a modified Tour method. Each GO product was reduced with the same amount of L-ascorbic acid to obtain the corresponding rGO. By using X-Ray Photoelectron Spectroscopy (XPS) and Raman spectroscopy, oxygen-related species and their concentration in GO and rGO products have been identified. The sizes of graphene sheets in those two carbon products are estimated by Dynamic Light Scattering (DLS) method. We find that the dispersion degree of the rGO product in a hydrophobic P3HT matrix depends on content of carboxyl (–COOH) and epoxy (C–O–C) groups on GO as well as on the graphene sheet size. At the same time, the most reduced and conductive rGO product (rGO-4) comes from a GO with the lowest oxygen content and lowest concentration of –COOH species, giving the largest graphene sheet sizes and spacing between the sheets. The homogeneous P3HT-rGO-4 composite material shows a micrometer sized laminated structure and a percolation threshold point around 20 wt%. The electrical conductivity of the composite is close to 10–1 S m−1, two orders of magnitude larger than the pristine P3HT. It is concluded that the electrical properties of rGO products can be improved by tailoring the type and concentration of oxygen species in GO.

The present study investigates the effects of grafting a long-chain organosilane (OS) onto the reduced graphene oxide (rGO) on dielectric and electromechanical performance of polydimethylsiloxane (PDMS). Accordingly, two types of OS-rGO particles were synthesized with different grafting densities and characterized by various tests such as Fourier transform infrared spectroscopy, Raman spectroscopy, and thermo-gravimetric analyses. As-prepared particles were introduced into PDMS using the solution mixing method to manufacture composites with different concentrations of particles. Dielectric results revealed that the composites containing OS-rGO particles offer better dielectric performance in terms of higher “dielectric efficiency” and dielectric breakdown strength than composites containing rGO or neat PDMS. The higher the grafting density of OS, the better the dielectric and electromechanical performance is obtained. By examining the electrical conductivity of particles, it was discussed that the spacer length of silane creates a space-filling insulating layer around the conductive rGO particles, traps free electric charges at the particle-polymer interface, postpones the electrical percolation threshold to higher concentrations, and reduces the dielectric loss through suppressing the leakage current of charges in the composite. Actuation strain of PDMS containing 3 wt% of OS-rGO with high grafting density was almost twice that for the neat PDMS.

A simple and efficient method for calculating the conductivity of systems of carbon nanotubes forming a random resistor circuit in the case where the percolation threshold is reached in the system is proposed in this paper. This method uses the recursive removal of the dead-end branches of a cluster, which is necessary to determine the elements of the percolation cluster participating in the system’s conductivity. The calculated conductivities presented in this paper are obtained using Monte Carlo simulation. In the future, the developed method can be used to calculate the conductivity of polymer–carbon nanocomposites.

The study uses the phenomenon of high voltage partial discharge to investigate the phenomenon of percolation and visualisation of the percolation channel. The phenomenon of partial discharges is very similar to the quantum tunneling phenomenon observed in metal-dielectric nanocomposites. In both cases the flow of alternating current occurs in the absence of direct contact between the metallic phase particles.A measuring stand was developed and constructed to test models of metal dielectric nanocomposites using high voltage partial discharge. The stand consists of a 110 kV high voltage transformer, a voltage regulator protecting the constant rate of high voltage rise, a measuring system consisting of a measuring probe, voltmeters and a computer. The communication between the measuring probe and the voltmeter was made in digital technology with the use of fiber optic technology, which allowed the meter to communicate with the computer without any errors and eliminated the interference caused by a strong electromagnetic field resulting from the use of high voltage.Systems modelling metal-dielectric composites were built, consisting of metallic elements in the form of disks, randomly distributed on the surface of the dielectric matrix. The number of disks was increased in series of 40 in each. The maximum number of disks was 1520. The dependence was determined of one of the important parameters characterising an partial discharge, i. e. the initial voltage, at which an electric current starts to flow between electrodes, on the concentration of the metallic phase. On the basis of these results, a percolation threshold was established for a matrix with a random distribution of metallic phase elements, the value of which is about 50 %. Films and pictures of partial discharges with visible percolation channels were taken with the camera with which the stand was equipped.

During this research, O2-functionalised graphene nanoplatelets and multiwalled carbon nanotubes have been used to generate a nanoreinforced hybrid nanocomposite polymer. The addition of increasing contents of graphene nanoplatelets resulted in strength increases of over 260% in compression and 190% in tension over that of parent epoxy resin. It has been determined that the percolation threshold of nanomaterials is lower when appropriate high-shear mixing methods are used to disperse the nanomaterials. This research has determined the properties of the matrix material composition and the graphene nanoplatelet concentration aspect ratio and surface treatment method to achieve enhanced properties. The resulting electrically conductive hybrid nanocomposite formulations produced had an optimum concentration of graphene nanoplatelets and multiwalled carbon nanotubes. This research has been used as a demonstrator for the fabrication of advanced adhesive systems for the space launch system.

Cellulose nanocrystal (CNC)-reinforced poly(butylene adipate-co-terephthalate) (PBAT) nanocomposites with CNC contents of 1, 3, and 5 wt% were prepared through either solution casting or dilution of a PBAT/CNC masterbatch through melt mixing. The efficiency of these preparation approaches on CNC dispersion quality was examined using transmission electron microscopy and rheological analysis. It was found that solution-casted nanocomposites possessed a much finer CNC dispersion, while melt mixing could cause the formation of CNC agglomerates. In the nanocomposites, the rheological percolation threshold through small-amplitude oscillatory shear experiments was determined to be around 2.18 and 3.15 wt% CNC, respectively. The PBAT melt crystallization was also promoted with CNC regardless of the preparation method. The oxygen permeability of PBAT remarkably reduced with the CNC incorporation, specifically in the solution-casted nanocomposites with finer CNC dispersion. The thermal degradation, thermomechanical, and mechanical properties of the nanocomposites were also compared although no significant differences were observed.

Carbon nanotubes (CNTs) remain one of the most efficient reinforcing material for enhanced mechanical and electrical properties. In this study, the effects of multi-walled CNTs (MWCNTs) fillers on mechanical, structural, and electrical properties of polymethyl methacrylate (PMMA)/MWCNTs composites were studied. The PMMA/MWCNTs composites, containing varying MWCNTs concentration of 0.1, 0.3, and 0.5 wt%, were prepared by a solution casting method. The mechanical properties of the composites such as tensile strength, elongation, Young modulus, tear resistance, fracture energy, impact strength, and hardness were investigated. Results showed that the mechanical properties of the composites were enhanced significantly. At 0.5 wt% MWCNTs, the tensile strength, elongation, tear strength, hardness, fracture energy and impact strength increased by 397%, 567%, 89%, 27%, 12%, and 36%, respectively, while the Young modulus decreased by 26% compared to pure PMMA polymer sample. Both the dc electrical conductivity and the activation energy increased with increased concentration of MWCNTs. From the electrical conductivity measurements, the percolation threshold was found to equal ~ 0.55 wt% MWCNTs. Based on the Fourier-transform infrared spectroscopy analysis, enhancement of mechanical and electrical properties is attributed to the formation of covalent bonds between polymer strands and MWCNTs. Moreover, a mechanism was proposed to describe the influence of MWCNTs on electrical and mechanical properties of PMMA/MWCNTs composites.

Intelligent smart materials can not only monitor the damage and degradation of architectural structures in real time but also the health structure. In recent years, carbon nanotubes materials have emerged to possess both excellent mechanical and electrical properties. Moreover, when carbon nanotubes are added to epoxy resin, intelligent composite materials with significant sensitivity are created. In this study, the stress–strain curves and anelasticity of carbon nanotube/epoxy resin composites with different carbon nanotube concentrations is analyzed. Through changing the level of carbon nanotubes using the two-pole method, the percolation threshold of carbon nanotube/epoxy composites was determined. Thereafter, the effect of temperature on the composites’ conductive properties was investigated. Moreover, using the stepwise cyclic loading method, the piezoresistivity of the carbon nanotube/epoxy composites was investigated. The test results show that the elastic limit, the yield point, and the elastic modulus range of the carbon nanotube/epoxy composites is approximately 45 MPa, 50 MPa, and 1–2 GPa, respectively. The anelasticity of the carbon nanotube/epoxy composites increases with the gradual increase of the stress level. The percolation threshold interval of carbon nanotube/epoxy composites ranges from 0.5 to 1.0 wt%. The rate of change of resistance for the different concentrations on carbon nanotube/epoxy specimens corresponds to the temperature. Notably, the carbon nanotube/epoxy composites have better discrimination and pressure sensitivity for different grades of load. When the carbon nanotube content is 0.5 wt%, the sensitivity of the carbon nanotube/epoxy composites pressure-sensitive property is the largest, which is in agreement with the threshold curve. The results of this investigation have implications for the application of carbon nanotube/epoxy composites in structural health monitoring.

We demonstrated a dramatic reduction in the sub-terahertz (sub-THz) transmittance and enhancement in the conductance of the carbon nanotube (CNT) mats at high radiation intensities near the percolation threshold, i.e. at the CNT concentrations where the mat conductivity as a function of the CNT concentration sharply increases. The CNT mat conductivity near the percolation point is determined by the electron (or hole for p-type CNTs) tunneling between the adjacent nanotubes. The symmetry of CNT contacts is broken by the differences in the positions and the sizes and types of the contacting CNTs enabling the rectification of the THz or sub-THz radiation impinging on the CNT mats. As the consequence of such rectification, the tunneling barrier shape changes to a more triangular share enhance the CNT mat AC conductivity and decrease transmission. One application of this effect is films preventing damage to sensitive THz and sub-THz detectors (such as Schottky diodes or TeraFETs) by limiting the maximum power impinging on the detectors. Since the shape of the tunneling barriers is strongly affected by ambience and/or substrate monitoring limiting CNT transmission near the percolation point transmission as function of intensity, temperature, and frequency could be used for humidity, temperature, gas exposure, strain, and multiple sensors of external stimuli. The nanoscale of CNT contacts and gaps enables high speed THz responses.

Abstract Silver nanowires (AgNW) were incorporated into different organic–inorganic hybrids and a silicone composition that served as a reference. Spin coating yielded transparent conductive films, their respective nanowire distribution, thermal activation, and visual transparency were characterized. The percolation threshold of the films scales with the individual average AgNW length. Substantial conductivity was maintained throughout mechanical stretching up to 30%. Microstructured organic–inorganic hybrid composite films were obtained by UV lithography.

Among reported stretchable conductors, electrically conductive composites (ECCs) have the advantages of low cost, simplicity in circuit design and fabrication, and good reliability. However, the resistivity of conventional stretchable ECCs usually increases during stretching as a result of the loss of contact between neighboring conductive fillers. Here we prepared stretchable ECCs filled with silver dendrites. Due to the high aspect ratio, hierarchy structure, and multiple contact points in all dimensions, ECCs filled with silver dendrites have lower percolation threshold compared with conventional ECCs filled with silver particles or flakes. Moreover, ECCs filled with silver dendrites show a unique decrease in resistivity during stretching. The resistivity can decrease from 5 × 10−4 Ω·cm to as low as 1.1 × 10−4 Ω·cm at 100% elongation. Due to the high conductivity during stretching, the ECCs are used to prepare stretchable capacitors and antennas, demonstrating the stable electrical performance of ECCs under strain.

In this paper, the effective length and concentration of carbon nanotubes (CNT) in polymer CNT nanocomposites (PCNT) are formulated by conductivity transferring between nanoparticles and polymer matrix as well as interfacial conductivity. The effective terms and interphase thickness are applied to suggest the percolation threshold of CNT and the volume fraction of networked CNT in PCNT. In addition, a simple model is developed for conductivity of PCNT by the mentioned parameters and the tunneling distance between adjacent CNT. The predictions of conductivity are compared to the experimental results and the significances of all parameters on the conductivity are justified to validate the advanced model. The predictions of developed model show fine agreement with the experimental data. High conductivity transportation and large CNT can improve the conductivity of PCNT. Additionally, the optimized levels of conductivity are obtained by thick interphase and high interfacial conductivity.

Carbon and ice make up a substantial proportion of our Universe. Recent space exploration has shown that these two chemical species often coexist including on comets, asteroids and in the interstellar medium. Here we prepare mixtures of C60 fullerene and H2O by vapor co-deposition at 90 K with molar C60:H2O ratios ranging from 1:1254 to 1:5. The C60 percolation threshold is found between the 1:132 and 1:48 samples, corresponding to a transition from matrix-isolated C60 molecules to percolating C60 domains that confine the H2O. Below this threshold, the crystallization and thermal desorption properties of H2O are not significantly affected by the C60, whereas the crystallization temperature of H2O is shifted towards higher temperatures for the C60-rich samples. These C60-rich samples also display exotherms corresponding to the crystallization of C60 as the two components undergo phase separation. More than 60 volume percent C60 is required to significantly affect the desorption properties of H2O. A thick blanket of C60 on top of pure amorphous ice is found to display large cracks due to water desorption. These findings may help understand the recently observed unusual surface features and the H2O weather cycle on the 67P/Churyumov-Gerasimenko comet.

Electrically conductive polymer composites (CPCs) have been applied extensively in many fields such as electronics, wearable sensors and antistatic agent. It is still challenging to develop CPCs with a low percolation threshold and high electrical conductivity. Here, highly electrically conductive polystyrene (PS) composite with a fiber-based segregated structure is prepared by carbon nanotubes (CNTs) decoration onto the electrospun PS fibers, followed by hot press at a proper temperature. In the electrically conductive PS composite, the CNTs are segregated at the interface among the fiber-shaped matrix, and the one-dimensional fiber possessing the merit of a large aspect ratio, which facilitates the formation of conductive network. The percolation threshold is calculated to be 0.084 vol%, and the electrical conductivity of the CPC reaches 83.3 S/m when the concentration of the CNTs is 1.5 vol%. If the hot press temperature is much higher than the glass transition temperature of PS, the fiber-based segregated structure would be destroyed, increasing the percolation threshold while decreasing the conductivity of the composite. The fiber-based segregated structure provides a new and versatile route for the rational design and preparation of CPCs with a low percolation threshold and high conductivity.

In this work, a compression-induced percolation threshold was found when the thickness of polydimethylsiloxane (PDMS) nanocomposite samples was reduced via a spatial confining forced network assembly (SCFNA) process from 1.0 mm to 0.1 mm. Such as for PDMS/2 wt% short carbon fiber/4 wt% carbon nanotube (CNT) composite, its conductivity was more than 8 times enhanced to 487 S/m from 59.5 S/m, and the mechanical properties of composites have been improved by more than 15% accordingly. Comparatively, when increased the concentration of CNT or Gr from 1 to 4 wt%, the electrical conductivity of PDMS nanocomposites at 1 mm thickness was barely changed as it generally reached saturation and became independent of filler loading. Compared with the traditional blending method, it indicates that the SCFNA process can further promote the maximum electrical conductivity of polymer nanocomposites when the filler concentration has little effect on the conductivity. Especially under the condition of relatively high filler concentration, the electrical conductivity enhancement effect becomes more significant that is contrary to the classical percolation theory. Moreover, the mechanical properties of the nanocomposites can be slightly improved by the mechanical compression, which makes it more suitable for flexible electronic devices' applications.

In independent bond percolation on $${\mathbb {Z}}^d$$ with parameter p, if one removes the vertices of the infinite cluster (and incident edges), for which values of p does the remaining graph contain an infinite connected component? Grimmett-Holroyd-Kozma used the triangle condition to show that for $$d \ge 19$$, the set of such p contains values strictly larger than the percolation threshold $$p_c$$. With the work of Fitzner-van der Hofstad, this has been reduced to $$d \ge 11$$. We improve this result by showing that for $$d \ge 10$$ and some $$p>p_c$$, there are infinite paths consisting of “shielded” vertices—vertices all whose adjacent edges are closed—which must be in the complement of the infinite cluster. Using values of $$p_c$$ obtained from computer simulations, this bound can be reduced to $$d \ge 7$$. Our methods are elementary and do not require the triangle condition.

The relationship between the effective (real) specific surface area of the nanofiller and the elastic modulus for polymer/graphene nanocomposites is studied. The process of aggregation of a graphene 2D nanofiller (the formation of its tactoids) leads to a decrease in its effective specific surface area, since the surface of graphene plates inside the tactoid, which does not interact with the polymer matrix, does not affect the formation of the properties of nanocomposites. This effect is realized only above the percolation threshold of the nanofiller. An interpretation is proposed that allows estimating the number of graphene plates in one tactoid. Further calculations allow the determination of the effective specific surface area of the nanofiller and the degree of reinforcement of the nanocomposite.

The microwave properties of composite materials (CMs) based on epoxy resin and mixed filler carbon nanotubes/barium titanate (CNT/BT) at CNT concentrations up to 5 wt% and 34 wt% of BT were investigated. The complex permittivity of epoxy composites was measured in the frequency range 1–67 GHz via vector network analyzer. The CNT/BT/epoxy composite showed the increase of permittivity with the increase of CNT content in CM. The electromagnetic shielding properties of developed CMs were measured using waveguide spectroscopy in the frequency range from 26 to 37.5 GHz. Increasing of CNT content enhances the conductivity, resulting in an increase of the EMR reflection at the interface air–composite as well as EMR absorption inside of the composite. The increase of the shields’ thickness (up to 2.5 mm) leads to the increase of shielding effectiveness for transmission up to 30 dB for sample with 5% CNT content due to higher EMR absorption inside, while the changes of the reflection index versus frequency depend on CNT content and composite thickness. The reflection loss (RL) of composites was calculated for various thicknesses using the complex permittivity and the obtained results show that composite 2 wt% CNT/BT/epoxy exhibits superior absorptive properties in the frequency range 10–67 GHz. The BT primary role in such CMs (with conductive fillers) is to move the percolation threshold further for conductive filler, increasing its real part of permittivity.

Multi-walled carbon nanotubes (MWCNTs) modified with silane coupling agent A-1120 (MWCNTs-A1120) were prepared. Compared with the raw MWCNTs, acidified MWCNTs (MWCNTs-COOH), and MWCNTs grafted with EDA (MWCNTs-NH2), MWCNTs-A1120 have the best dispersion in fluoroelastomer at the same doping ratio. Therefore, fluoroelastomer/MWCNTs-A1120 composite has the best mechanical properties with tensile strength of 13.92 MPa and elongation at break of 111.78%. Then, the effects of doping amount of MWCNTs-A1120 on the electrical properties of the composites were investigated. The dielectric constant of the composite increases with the increase of MWCNTs-A1120, and the dielectric loss does not change much at the low doping amount such as 0.5 wt%. When the doping amount of MWCNTs-A1120 is 5 wt%, the dielectric constant and the dielectric loss value are greatly increased, and the volume resistivity is greatly decreased, which proves that the conductive network is formed in the composite, so the filling amount of 5 wt% is the percolation threshold. The tensile deformation of the sample also affects the electrical properties of the composites. As the tensile deformation increases, the dielectric constant and dielectric loss of the composite decrease. For the composite with 5 wt% MWCNTs-A1120, excessive tensile deformation will destroy the conductive network structure of the composite, so the composite will change from conductive material to dielectric material. Therefore, such composite is a good candidate for flexible conductive material or flexible dielectric material used in harsh environments such as high temperatures and various aggressive solvents.

The nonlinear rheology of a novel 3D hierarchical graphene polymer nanocomposites was investigated in this study. Based on an isotactic polypropylene, the nanocomposites were prepared using simple melt mixing, which is an industrially relevant and scalable technique. The novel nanocomposites stand out as having an electrical percolation threshold (≈0.94 wt%) comparable to solution mixing graphene-based polymer nanocomposites. Their nonlinear flow behavior was investigated in oscillatory shear via Fourier-transform (FT) rheology and Chebyshev polynomial decomposition. It was shown that in addition to an increase in the magnitude of nonlinearities with filler concentration, the electrical percolation threshold corresponds to a unique nonlinear rheological signature. Thus, in dynamic strain sweep tests, the nonlinearities are dependent on the applied angular frequency, potentially detecting the emergence of a weakly connected network that is being disrupted by the flow. This is valid for both the third relative higher harmonic from Fourier-transform rheology, I3/1, as well as the third relative viscous, v3/1, Chebyshev coefficient. The angular frequency dependency comprised non-quadratic scaling in I3/1 with the applied strain amplitude and a sign change in v3/1. The development of the nonlinear signatures was monitored up to concentrations in the conductor region to reveal the influence of a more robust percolated network.