Electrical Percolation Research Articles

A numerical conductive network model for investigating the strain-sensing response of graphene nanoplatelets-filled elastomeric strain sensors

Strain sensors have attracted great attentions for practical applications such as human-machine interface. It is challenging to model the electrical behavior of elastomeric strain sensors modified with nanomaterials. This study presents a finite element simulation to explore the piezoresistivity of graphene nanoplatelet (GNP)-filled elastomeric nanocomposites. The percolation network model is employed to determine the critical distance necessary for electrical percolation. The finite element percolation network model uses the Euclidian distance between GNPs distributed inside the representative volume element to calculate the resistivity. The influence of various parameters, including GNP alignment direction, aspect ratio, and volume fraction, on the resistivity changes of the nanocomposite is investigated. Results demonstrate that nearly 20% more tunneling distance is allowed for percolation of nanocomposite with 30% larger aspect ratio GNPs. Findings reveal that as the volume fraction of GNPs increases, the critical distance for the electrical percolation decreases significantly.

Development of Electrically Conductive Wood-Based Panels for Sensor Applications.

This study investigates the development of electrically conductive panels for application as emergency detection sensors in smart house systems. These panels, composed of wood chips coated with polymeric methylene diphenyl isocyanate, were modified with carbon black and carbon fibers to enable detection of moisture, temperature, and pressure variations. Manufactured via hot pressing, the panels retained standard mechanical properties and exhibited stable performance under diverse environmental conditions. Carbon black-filled panels achieved electrical percolation at a lower filler concentration (5%) compared to carbon fiber-filled panels. The incorporation of carbon black reduced the electrical resistivity to 8.6 ohm·cm, while the addition of carbon fibers further decreased it to 7.7 ohm·cm. In terms of sensor capabilities, panels containing carbon fibers demonstrated superior sensitivity to moisture and pressure changes. However, carbon black was ineffective for temperature sensing. Among the carbon fiber-filled panels, those with 20 wt.% concentration exhibited the best performance for moisture and pressure detection, whereas panels with 40 wt.% carbon fiber content displayed the most reliable and consistent temperature-sensing properties.

EIS Behavior of Polyethylene + Graphite Composite Considered as an Approximation to an Ensemble of Microelectrodes

The electrical percolation of alternating current through two-phase polyethylene/graphite composite electrodes with different contents of graphite microparticles immersed in aqueous KCl solutions has been studied. Above the graphite content of the first percolation threshold, the electrochemical impedance response of this electrode is associated with an equivalent circuit of resistance Ru in series with a constant phase element (CPE). An insulator material + conducting filler model is proposed in which the electroactive surface is considered as the intersection of the percolation cluster through the solid and the cluster associated with the interfacial region. CPE is analyzed assuming a distribution of microcapacitors of the graphite particles in contact with the dielectric solution and inside the dielectric polymeric phase.

Tailoring microstructure in a soft-magnetic Fe-based amorphous-nanocrystalline alloy for high resistivity according to electrical percolation threshold

Superior soft-magnetic materials are necessary for the development of modern magnetic devices with energy-saving and high-power density requirements. However, improving the magnetism by nanocrystallization always brings about the sacrifice of resistivity, presenting a common trade-off in Fe-based amorphous-nanocrystalline alloys. Here, the comprehensive merits of both superior soft-magnetic properties (high saturation magnetization of 1.81 T and low coercivity of 3.8 A/m) and high resistivity of 117.2 μΩ·cm were obtained by precisely tailoring amorphous-nanocrystalline microstructure close to electrical percolation threshold for a Fe82.5B12P2C1Cu0.5Co2 amorphous alloy. The soft-magnetic properties are attributed to the low magnetic anisotropy stemming from high nuclei number density and ultrafine nanocrystalline grains of 9.2 nm. The high resistivity is associated with the electrical percolation behavior with a nanocrystalline volume threshold of 14.8 % in the composite alloy. The results provide an effective strategy to overcome the trade-off in traditional amorphous-nanocrystalline alloys, significant for applications in high-frequency, high-power, and energy-saving devices.

PLA/CB and HDPE/CB conductive polymer composites: Effect of polymer matrix structure on the rheological and electrical percolation threshold

AbstractIn this study, the effect of the polymer matrix structure on the rheological and electrical percolation threshold of polymer/carbon black (CB) conductive polymer composites (CPCs) was investigated. Poly(lactic acid) (PLA) and high‐density polyethylene (HDPE) were used as polymer matrices. Through rheological analyses, an increase in complex viscosity was observed with increasing CB concentration, accompanied by a reduction in the Newtonian plateau. Additionally, an increase in the solid‐like behavior was observed, suggesting the formation of a percolated network. The rheological percolation threshold was found to be 5.13% CB mass fraction for the PLA/CB composite and 10.72% for the HDPE/CB composite. Electrical conductivity results were fitted to the sigmoidal Boltzmann model, and its derivative was used to identify the electrical percolation threshold. For PLA/CB, this threshold was reached at 5.39% CB mass fraction, while for HDPE/CB, it occurred at 5.75%. Morphology analysis by scanning electron microscopy and atomic force microscopy indicated that the polymer matrix structure affected the distribution/dispersion of the CB particles within the polymer matrix.Highlights The effect of polymer matrix structure on polymer/CB CPCs was investigated. The crystallinity of the polymer matrix affected the percolation threshold. PLA/CB showed higher conductivity than HDPE/CB CPCs.

A Review of the Establishment of Effective Conductive Pathways of Conductive Polymer Composites and Advances in Electromagnetic Shielding.

The enhancement of the electromagnetic interference shielding efficiency (EMI SE) for conductive polymer composites (CPCs) has garnered increasing attention. The shielding performance is influenced by conductivity, which is dependent on the establishment of effective conductive pathways. In this review, Schelkunoff's theory on outlining the mechanism of electromagnetic interference shielding was briefly described. Based on the mechanism, factors that influenced the electrical percolation threshold of CPCs were presented and three main kinds of efficient methods were discussed for establishing conductive pathways. Furthermore, examples were explored that highlighted the critical importance of such conductive pathways in attaining optimal shielding performance. Finally, we outlined the prospects for the future direction for advancing CPCs towards a balance of enhanced EMI SE and cost-performance.

Electrofluids with Tailored Rheoelectrical Properties: Liquid Composites with Tunable Network Structures as Stretchable Conductors.

Flexible and stretchable electronics require both sensing elements and stretching-insensitive electrical connections. Conductive polymer composites and liquid metals are highly deformable but change their conductivity upon elongation and/or contain rare metals. Solid conductive composites are limited in mechanoelectrical properties and are often combined with macroscopic Kirigami structures, but their use is limited by geometrical restraints. Here, we introduce "Electrofluids", concentrated conductive particle suspensions with transient particle contacts that flow under shear that bridge the gap between classic solid composites and liquid metals. We show how Carbon Black (CB) forms large agglomerates when using incompatible solvents that reduce the electrical percolation threshold by 1 order of magnitude compared to more compatible solvents, where CB is well-dispersed. We analyze the correlation between stiffness and electrical conductivity to create a figure of merit of first electrofluids. Sealed elastomeric tubes containing different types of electrofluids were characterized under uniaxial tensile strain, and their electrical resistance was monitored. We found a dependency of the piezoresistivity with the solvent compatibility. Electrofluids enable the rational design of sustainable soft electronics components by simple solvent choice and can be used both as sensor and electrode materials, as we demonstrate.

(Invited) Reversible Electrical Percolation in a Stretchable and Self-Healable Silver-Gradient Nanocomposite Bilayer

The reversibly stable formation and rupture processes of electrical percolative conducting path in organic and inorganic insulating materials are prerequisites for operating non-volatile resistive memory devices. However, it has been one of challenging tasks for such resistive switching in dynamically cross-linked polymers capable of intrinsic stretchability and self-healing. This is attributed to the uncontrollable interplay between the conducting filler and the self-healing polymer. In this talk, the development of the self-healing, stretchable, and reconfigurable resistive random-access memory will be presented. The device was fabricated via the self-assembly of a silver-gradient nanocomposite bilayer which is capable of easily forming the metal-insulator-metal structure. To realize stable resistive switching in dynamic molecular networks, our device features the following two properties. First, self-reconstruction of nanoscale conducting fillers in dynamic hydrogen bonding for self-healing and reconfiguration. Second, stronger interaction among the conducting fillers than with polymers for the formation of robust percolation paths. Based on these unique features, we successfully demonstrated stable data storage of cardiac signals, damage-reliable memory triggering system using a triboelectric energy-harvesting device, and touch sensing via pressure-induced resistive switching.

High-Performance Yet Sustainable Triboelectric Nanogenerator Based on Sulfur-Rich Polymer Composite with MXene Segregated Structure.

State-of-the-art triboelectric nanogenerators (TENGs) typically employ fluoropolymers, highly negative chargeable materials in triboelectric series. However, many researchers nowadays are concerned about environmental pollution caused by poly-and per-fluoroalkyl substances (PFAS) due to their critical immunotoxicity as fluoropolymers are likely to release PFAS into the ecosystem during their life cycle. Herein, a sulfur-rich polymer (SRP)/MXene composite, offering high-performance yet sustainable TENG is developed. Value-addition of sulfur into SRP-based TENG has huge advantages since sulfur is abundant waste from petroleum refining and possesses the highest electron affinity (-200kJmol-1) among polymerizable atoms. MXene segregated structure is introduced into SRP to achieve homogeneous distribution without electrical percolation by utilizing below 0.5wt% of MXene, resulting in a significantly enhanced dielectric constant without a drastic increase of dielectric loss. Due to homogeneous MXene distribution, SRP/MXene composite-based TENG demonstrates 2.9 times and 19.5 times enhances peak voltage and peak current compared to previous SRP-based TENGs. Additionally, it exhibits reusability without critical reduction of modulus and TENG performance due to dynamically exchangeable disulfide bonds. Finally, after the corona discharging and scaling-up process to a 4-inch wafer size, SRP/MXene composite-based TENG exhibits an 8.4 times improvement in peak power density, reaching 3.80Wm-2 compared to previous SRP-based TENGs.

Integration of inter-ply electrical percolation phenomena in the multiphysics modelling of laminated composite materials

PurposeThis study aims to introduce a predictive homogenization model incorporating electrical percolation considerations to forecast the electrical characteristics of unidirectional carbon-epoxy laminate composites.Design/methodology/approachThis study presents a method for calculating the electrical conductivity tensor for various ply arrangement patterns to elucidate phenomena occurring around the interfaces between plies. These interface models are then integrated into a three-dimensional (3D) magneto-thermal model using the finite element method. A comparative study is conducted between different approaches, emphasizing the advantages of the new model through experimental measurements.FindingsThis research facilitates the innovative integration of electrical percolation considerations, resulting in substantial improvement in the prediction of electrical properties of composites. The validity of this improvement is established through comprehensive validation against existing approaches and experimentation.Research limitations/implicationsThe study primarily focuses on unidirectional carbon-epoxy laminate composites. Further research is needed to extend the model's applicability to other composite materials and configurations.Originality/valueThe proposed model offers a significant improvement in predicting the electrical properties of composite materials by incorporating electrical percolation considerations at inter-ply interfaces, which have not been addressed in previous studies. This research provides valuable information to improve the accuracy of predictions of the electrical properties of composites and offers a methodology for accounting for these properties in 3D magneto-thermal simulations.

Evaluation of multi-walled carbon nanotubes alignment during 3D printing of poly(acrylonitrile-butadiene-styrene) nanocomposite filaments

Nanocomposites incorporated with one-dimensional electrical conductive materials such as carbon nanotubes have been used in many applications in various industries. In this research, the filaments made of poly (acrylonitrile-butadiene-styrene) (ABS) containing 1, 3, and 5 wt% multi-walled carbon nanotubes (MWCNT) were first prepared and then printed in three directions and two printing speeds. The rheological and electrical percolation thresholds were found to take place at 0.32 and 0.96 wt% MWCNT, respectively. Using the Casson plot, it was revealed that the yield stress of the nanocomposites containing 5 wt% MWCNT was 70 times higher than that of the pristine ABS. The results also indicated that the electrical resistance decreased from 17.4 to 6.8 Ω with the increase in printing speed from 4 to 20 mm/s, respectively. The alignment of the nanofillers was examined using X-ray diffraction method. It was found from the azimuth angle that the materials printed at higher printing speed had more orientation, with respect to the director, in comparison with that of printed at lower speed.

Thermo-Mechanical and Thermo-Electric Properties of a Carbon-Based Epoxy Resin: An Experimental, Statistical, and Numerical Investigation.

Due to their remarkable intrinsic physical properties, carbon nanotubes (CNTs) can enhance mechanical properties and confer electrical and thermal conductivity to polymers currently being investigated for use in advanced applications based on thermal management. An epoxy resin filled with varying concentrations of CNTs (up to 3 wt%) was produced and experimentally characterized. The electrical percolation curve identified the following two critical filler concentrations: 0.5 wt%, which is near the electrical percolation threshold (EPT) and suitable for exploring mechanical and piezoresistive properties, and 3 wt% for investigating thermo-electric properties due to the Joule effect with applied voltages ranging from 70 V to 200 V. Near the electrical percolation threshold (EPT), the CNT concentration in epoxy composites forms a sparse, sensitive network ideal for deformation sensing due to significant changes in electrical resistance under strain. Above the EPT, a denser CNT network enhances electrical and thermal conductivity, making it suitable for Joule heating applications. Numerical models were developed using multiphysics simulation software. Once the models have been validated with experimental data, as a perfect agreement is found between numerical and experimental results, a simulation study is performed to investigate additional physical properties of the composites. Furthermore, a statistical approach based on the design of experiments (DoE) was employed to examine the influence of certain thermal parameters on the final performance of the materials. The purpose of this research is to promote the use of contemporary statistical and computational techniques alongside experimental methods to enhance understanding of materials science. New materials can be identified through these integrated approaches, or existing ones can be more thoroughly examined.

Polyolefin elastomer/cyclic olefin copolymer/multi‐walled carbon nanotubes nanocomposites: Rheological, morphological, electrical and mechanical study

AbstractThe subject of this research is a relatively detailed investigation of the rheological, morphological and electrical properties of nanocomposites based on polyolefin elastomer (POE), cyclic olefin copolymer (COC) and multi‐walled carbon nanotubes (MWCNTs). To formulate a mixture of two polymers (COC and POE), the melt mixing method was used and their morphology was studied by SEM technique and it was found that the morphology is of co‐continuous type. When the weight percentage ratio of COC was between 40 and 60, the desired morphology (co‐continuous) appeared. Interfacial tension calculations and TEM images proved that the nanotube particles were stabilized both within the phase of POE as well as at the interface of the two polymer phases. The rheological behavior was analyzed for composite samples containing 0–3 wt % MWCNT. The electrical and rheological percolation thresholds appeared at 1 and a 0.5 percent by weight of nanotube particles, respectively, which may be better to consider as related to the phenomenon of dual percolation. The highest conductivity was obtained for the nanocomposite containing 3% MWCNT. The results of mechanical tests also showed a strong upward trend of properties due to the addition of nanotube.Highlights The effect of COC content on the morphology of POE/COC blend was investigated. The Morphology for the POE/COC blend at low COC content was droplet‐matrix type. MWCNT has a greater tendency to be in the POE phase than COC. Rheological behavior strongly depended on the amount of nanotube particles. The highest conductivity was obtained for the sample containing 3% MWCNT.

Heat exchange and damage of carbon black‐filled styrene‐butadiene rubber under uniaxial cyclic loading

AbstractIn this paper, we present an original experimental approach combining infrared thermography, analysis of voiding, and swelling tests to investigate damage mechanisms in carbon black (CB)‐filled styrene‐butadiene rubber (SBR). Heat exchange and voiding under uniaxial cyclic loading have been observed. A mechanical and electrical percolating filler network was identified by atomic force microscopy and electrical conductivity for the SBR with highest content of fillers (60 phr). SBR materials with a non percolating filler network show a reversible thermal energy dissipation during a series of cyclic loading, concomitant with reversible voiding mechanisms, through the successive formation and closing of voids. The SBR with the percolating network undergoes, during the series of cyclic loading, a high dissipation of energy under the form of heat, concomitantly with irreversible voiding mechanisms. Such mechanisms are shown to be due primarily to (i) the alteration of the filler network and/or filler/rubber interface and to a lower extent to (ii) the rubber matrix alteration (chains scission and/or crosslink breakage) as demonstrated by ex‐situ swelling.

Developing an efficient analytical model for predicting the electrical conductivity of polymeric nanocomposites containing hybrid carbon nanotube/carbon black nanofillers

Inter-cluster bridging of carbon nanotubes (CNTs) and carbon black (CB) nanoparticles conjoins inactive branches of carbonaceous nanofillers within the matrix and reduces the electron tunneling distance. This mechanism moderately overcomes quantum tunneling and provides percolative polymer networks exhibiting favorable electrical responses. This study focuses on devising an analytical procedure to scrutinize the electrical conductivity and percolation threshold of CNT/CB/polymer nanocomposites. To involve the physics of electrical processes, the modeling approach considers cylindrical CNTs and spherical CB nanoparticles surrounded by a continuum interphase, which serves as an electron hopping duct. This model is extended in a bottom-up micromechanics generalization to a level where it is capable of predicting the effects of a wide range of microstructural properties. The comparison of predictions with those obtained via experimental examinations, while affirming the infrastructure for investigating the electrical behavior of binary systems, convincingly captures the electrical conductivity/percolation threshold of ternary nanocomposites containing CNT/CB nanofillers.

Assessment of effective electrical conductivity in spherocylindrical carbon nanotube composites incorporating intrinsic properties of CNTs and interphase layer

This study introduces an analytical model using mean-field theory to estimate the effective electrical conductivity in composites of spherocylindrical carbon nanotubes (CNTs). The model adjusts the interphase layer's thickness and conductivity based on CNT concentration, affecting the electrical tunneling effect, and incorporates the properties of both CNTs and the interphase layer. Validated through detailed comparisons with experimental data, the model accurately predicts the electrical conductivities of polymer-CNT composites (PCNTs). Mean Squared Error analysis highlights its enhanced precision and superiority over traditional cylindrical CNT models. The model also explores how CNT dimensions, intrinsic conductivity, tunneling distance, potential barrier height, and variations in interphase thickness and conductivity influence electrical conductivity and percolation thresholds. This analytical model improves accuracy in predicting PCNT electrical conductivity and provides critical insights for designing and optimizing conductive polymer nanocomposites.

Design of interconnected graphene loaded thermoplastic elastomeric blend composite films for minimizing electromagnetic radiation and efficient heat management

AbstractIn this work, electrically conductive thermoplastic elastomeric blend composite films based on polystyrene (PS)/ethylene‐co‐methyl acrylate (EMA) filled with functionalized graphene were developed via the solution mixing technique. Morphological analysis revealed that selective localization of amine‐functionalized reduced graphene oxide (G‐ODA) sheets in the EMA phase of co‐continuous binary blend formed a well‐connected dense conductive pathway by graphene sheets ultimately facilitating the double percolation phenomenon. The electrical percolation threshold was achieved at ~2 wt% of G‐ODA loading which was much lower than that for both single polymer composites. An electrical conductivity of 0.9 S/cm was obtained for blend composite film with 10 wt% of graphene concentration whereas for the same filler loading, PS and EMA composites exhibited electrical conductivity of 1.9 × 10−1 and 2.3 × 10−1 S/cm, respectively. The obtained thermal conductivity of the blend composite with 10 wt% of G‐ODA loading was 0.95 W/m K with 400% enhancement compared to the neat blend system. The same composite exhibited increased real and imaginary permittivity of 92 and 83, respectively. The electrical percolation threshold is well‐correlated with the percolation concentration found from storage modulus and thermal conductivity data. The fabricated PS/EMA blend composite film exhibited absorption‐dominant electromagnetic interference SE of −25 and − 35 dB in X‐band frequency (8.2–12.4 GHz) for 10 wt% of graphene loading with a sample thickness of 0.5 and 1 mm, respectively.

Advancing anti-corrosion performance of composite coating: Self-aligned fluorinated graphene for multifunctional electronic packaging

Fluorinated graphene (FG) is considered an ideal filler for polymer nanocomposites to enhance anti-corrosion performance due to its hydrophobicity and electrical insulation properties. A key objective in advanced anti-corrosion design is to create a structure where FG sheets are stacked and aligned, forming an ultra-long, circuitous path to impede the diffusion of active corrosion species. Additionally, integrating aligned FG sheets with polymers prevents the formation of electrical percolation paths, making the coating suitable for electronic passivation. However, achieving a high degree of alignment of FG within the polymer matrix has been a challenge. In this study, we employ a straightforward electrophoretic deposition method to align FG sheets in a polyurethane (PU) matrix for anti-corrosion coatings on copper. The optimized coating exhibits outstanding corrosion resistance for copper, with a stable corrosion rate of 4.0 × 10−3 μm/year in a 3.5 wt% NaCl solution. Moreover, the FG composite coating significantly enhances thermal conductivity, increasing it by 97 % compared to pristine PU, while also providing high electrical resistance. This results in a high breakdown electric field of 28 kV/cm and an extremely low current density of 1.32 × 10−8 A/cm2, which is advantageous for electronic packaging. This multifunctional coating meets industrial standards for large-scale production, uniformity, and controllable thickness, offering a promising approach to improving anti-corrosion protective coatings.

Effect of TiC addition on microstructure and properties of network structured TiC–ZrO2 composite conductive ceramics

Zirconia (ZrO2) ceramics have excellent mechanical properties and high-temperature conductivities. However, ZrO2 ceramics do not possess room-temperature conductivity, which significantly limits their application as functional components in smart communication devices and wearable smart products. To achieve room-temperature conductivity in ZrO2 ceramics, this study prepared a network-structured TiC–ZrO2 composite conductive ceramic with a low titanium carbide (TiC) addition using pressureless sintering. The influence of the TiC addition on the microstructure, mechanical properties, and electrical properties of the TiC–ZrO2 composite material was investigated. The results showed that the composite material consists of cubic zirconia (c-ZrO2), tetragonal zirconia (t-ZrO2), and titanium carbide (TiC) phases. When the TiC content was 11 vol %, the relative density, open porosity, flexural strength, and fracture toughness of the sample were 98.6 ± 0.1 %, 0.16 ± 0.06 %, 383 ± 38 MPa, and 4.66 ± 0.26 MPa m1/2, respectively. The electrical percolation threshold of the TiC–ZrO2 composite was between 8.0 and 11.0 vol %. When the TiC content is 18.8 vol %, the sample exhibited the lowest room-temperature resistivity of 3.00 × 10−5 Ω m. The electrical resistance of the TiC–ZrO2 composite material is mainly attributed to the grain boundary effect. With increasing TiC content, the resistivity of the composite material decreased, exhibiting linear conductivity and achieving conductive percolation characteristics.

Surface Modification of Copper-Based Flakes for Conductive Polymer Composites.

The physical properties as well as thermal and electrical stability of copper particles can be improved by surface protection, which mainly depends on the coating material. Our study was, therefore, focused on the rheological, thermal, mechanical and electrical characterization of polymer composites by comparing uncoated (Cu), silver-coated (Cu@Ag) and silica-coated (Cu@Si) copper flakes in low-density polyethylene at various volume concentrations (up to 40%). Interactions among particles were investigated by rheological properties, as these indicate network formation (geometrical entanglement), which is important for mechanical reinforcement as well as establishing an electric pathway (electrical percolation). The results showed that geometrical and electrical percolation were the same for Cu and Cu@Si, ~15%, while, surprisingly, Cu@Ag exhibited much lower percolation, ~7.5%, indicating the fusion of the Ag coating material, which also decreased crystal growth (degree of crystallinity). Furthermore, the magnitude of the rheological and mechanical response remained the same for all investigated materials, indicating that the coating materials do not provide any load transfer capabilities. However, they profoundly affect electron transfer, in that, Cu@Ag exhibited superior conductivity (74.4 S/m) compared to Cu (1.7 × 10-4 S/m) and Cu@Si (1.5 × 10-10 S/m). The results obtained are important for the design of advanced polymer composites for various applications, particularly in electronics where enhanced electrical conductivity is desired.