Modeling electrical conductivities of nanocomposites with aligned carbon nanotubes

Advances in Monte Carlo Method for Simulating the Electrical Percolation Behavior of Conductive Polymer Composites with a Carbon-Based Filling

Conductive polymer composites (CPCs) filled with carbon-based materials are widely used in the fields of antistatic, electromagnetic interference shielding, and wearable electronic devices. The conductivity of CPCs with a carbon-based filling is reflected by their electrical percolation behavior and is the focus of research in this field. Compared to experimental methods, Monte Carlo simulations can predict the conductivity and analyze the factors affecting the conductivity from a microscopic perspective, which greatly reduces the number of experiments and provides a basis for structural design of conductive polymers. This review focuses on Monte Carlo models of CPCs with a carbon-based filling. First, the theoretical basis of the model's construction is introduced, and a Monte Carlo simulation of the electrical percolation behaviors of spherical-, rod-, disk-, and hybridfilled polymers and the analysis of the factors influencing the electrical percolation behavior from a microscopic point of view are summarized. In addition, the paper summarizes the progress of polymer piezoresistive models and polymer foaming structure models that are more relevant to practical applications; finally, we discuss the shortcomings and future research trends of existing Monte Carlo models of CPCs with carbon-based fillings.

Stochastic model for the transfer of gaseous particles in polymer-carbon-nanotube nanocomposites with interfacial regions

In this work, a stochastic model of gaseous transfer in polymer-carbon-nanotube (CNT) nanocomposites is presented. The model takes into account interfacial areas, i.e., polymer depletion regions. The local regime of transport is controlled by the density of the polymer. In a dense polymer, this regime corresponds to the ordinary diffusion, while in free volume regions, it corresponds to the ballistic transport. The introduction of a free volume and/or a depleted polymer layer near to a CNT wall leads to the emergence of anomalous diffusion. We have demonstrated how the anomalous diffusion regime changes in the presence of nanotubes for different distributions of polymer density. The presented approach allows us to describe the threshold effect in the diffusion coefficient as a function of CNTs density in polymer-CNT nanocomposites.

Green's functions for random resistor networks

We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation to compute ensemble-averaged nodal voltages and bond currents in a hierarchical fashion. We verify the validity of this expansion with direct numerical simulations of a square lattice with resistances at each bond exponentially distributed. Additionally, we construct a formalism to recursively obtain the exact Green's functions for finitely many disordered bonds. We provide explicit expressions for lattices with up to four disordered bonds, which can be used to predict nodal voltage distributions for arbitrarily large disorder strengths. Finally, we introduce a novel order parameter that measures the overlap between the bond current and the optimal path (the path of least resistance), for a given resistance configuration, which helps to characterize the weak and strong disorder regimes of the system.

Printable Carbon Nanotube-Liquid Elastomer-Based Multifunctional Adhesive Sensors for Monitoring Physiological Parameters

Developing a printed elastomeric wearable sensor with good conformity and proper adhesion to skin, coupled with the capability of monitoring various physiological parameters, is very crucial for the development of point-of-care sensing devices with high precision and sensitivity. While there have been previous reports on the fabrication of elastomeric multifunctional sensors, research on the printable elastomeric multifunctional adhesive sensor is not very well explored. Herein, we report the development of a stencil printable multifunctional adhesive sensor fabricated in a solvent-free condition, which demonstrated the capability of having good contact with skin and its ability to function as a temperature and strain sensor. Functionalized liquid isoprene rubber was selected as the matrix while carboxylated multiwalled carbon nanotubes (c-CNTs) were used as the nanofiller. The selection of the above model compounds facilitated the printability and also helped the same composition to demonstrate stretchability and adhesiveness. A realistic three-dimensional microstructure (representative volume element model) was generated through a computational framework for the current c-CNT-liquid elastomer. Further computational simulations were performed to test and validate the correlation between electrical responses to that of experimental studies. Various physiological parameters like motion sensing, pulse, respiratory rate, and phonetics detection were detected by leveraging the electrically resistive nature of the sensor. This development route can be extended toward developing different innovative adhesives for point-of-care sensing applications.

The Effect of Agglomeration on the Electrical and Mechanical Properties of Polymer Matrix Nanocomposites Reinforced with Carbon Nanotubes

In this work, we investigated the effect of carbon nanotubes addition and agglomeration formation on the mechanical and electrical properties of CNT–polymer-based nanocomposites. Six specimens with carbon nanotubes (CNTs) fractions of 0%, 0.5%, 1%, 2%, 4% and 5% were manufactured and characterized by dynamic mechanical analysis (DMA) and four-probe method. The stress–strain curves and electrical conductivity properties were obtained. Scanning electron microscopy (SEM) was used to characterize both agglomeration and porosity formation. By employing micromechanics, through representative volume element (RVE), finite element analysis (FEA) and resistor network model (RNM), the Young’s modulus and electrical conductivity values were calculated. The samples’ elastic moduli showed an increment, reaching the maximum value at a CNTs fraction of 2%, thereafter an adverse effect was caused in the high CNT percentage samples. The final electrical conductivity seemed greatly altered with the addition of CNTs, reaching the percolation threshold at 2%. The unavoidable formation of CNT agglomerates appeared to influence the final physical properties. The CNT agglomerates adversely affect the mechanical performance of high-CNT-percentage samples. Conversely, an exponential increment in the electrical conductivity was presented as the agglomerates formed networks allowing the transport of electrons through the tunnelling effect. These phenomena were experimentally and numerically confirmed, showing a good correlation.

Electrical Properties and Strain Sensing Mechanisms in Hybrid Graphene Nanoplatelet/Carbon Nanotube Nanocomposites

Electrical and electromechanical properties of hybrid graphene nanoplatelet (GNP)/carbon nanotube (CNT)-reinforced composites were analyzed under two different sonication conditions. The electrical conductivity increases with increasing nanofiller content, while the optimum sonication time decreases in a low viscosity media. Therefore, for samples with a higher concentration of GNPs, an increase of sonication time of the hybrid GNP/CNT mixture generally leads to an enhancement of the electrical conductivity, up to values of 3 S/m. This means that the optimum sonication process to achieve the best performances is reached in the longest times. Strain sensing tests show a higher prevalence of GNPs at samples with a high GNP/CNT ratio, reaching gauge factors of around 10, with an exponential behavior of electrical resistance with applied strain, whereas samples with lower GNP/CNT ratio have a more linear response owing to a higher prevalence of CNT tunneling transport mechanisms, with gauge factors of around 3-4.

Synergistic effect in improving the electrical conductivity in polymer nanocomposites by mixing spherical and rod-shaped fillers

In this work, coarse-grained molecular dynamics simulation is adopted to investigate the effect of hybrid fillers [nanospheres (NSs) and nanorods (NRs)] on the conductive probability of polymer nanocomposites (PNCs) in the quiescent state and under the shear field. The percolation threshold gradually rises as the volume fraction ratio (α) of NSs to all the fillers increases in the quiescent state. Compared to the NSs, the greater number of beads in the NRs help them connect to other NRs to form the conductive network. Meanwhile, compared to NSs, more NRs participate in building the conductive network. A transition from the synergistic effect to the antagonistic effect occurs as the NS-NR tunneling distance is reduced. Furthermore, the shear field induces a more direct aggregation structure of NSs, which act as linkers between fillers to protect the conductive network. This result is confirmed by the fact that more NSs occupy the conductive network under the shear field. As a result, the percolation threshold declines with increasing shear rate. Finally, compared to in the quiescent state, the percolation threshold increases at α = 0.0 and remains nearly unchanged for α = 0.25 under the shear field, while it gradually decreases for α≥ 0.5. In total, the results further our understanding of how to realize the synergistic effect between NSs and NRs when forming a conductive network of PNCs.

Development of Nanocomposite-Based Strain Sensor with Piezoelectric and Piezoresistive Properties

Sensors provide aninterface between mechanical systems and the physical world. With the move towardsIndustry 4.0 and cyber-physical systems, demands for cost-effective sensors are rapidly increasing. Conventional sensors used for monitoring manufacturing processes are often bulky and need complex processes. In this study, a novel high-sensitive nanocomposite-based sensor is developed for measuring strain. The developed sensor is comprised of polyvinylidene fluoride (PVDF) as a piezoelectric polymer matrix, and embedded carbon nanotube (CNT) nanoparticles creating a conductive network. Exhibiting both piezoelectric and piezoresistive properties, the developed sensors are capable of strain measurement over a wide frequency band, including static and dynamic measurements. The piezoresistive and piezoelectric properties are fused to improve the overall sensitivity and frequency bandwidth of the sensor. To simulate the sensor, a 3D random walk model and a 2D finite element (FE) model are used to predict the electrical resistivity and the piezoelectric characteristics of the sensor, respectively. The developed models are verified with the experimental results. The developed nanocomposite sensors were employed for strain measurement of a cantilever beam under static load, impulse excitation, free and forced vibrations, collecting both piezoelectric and piezoresistive properties measurements. The obtained signals were fused and compared with those of a reference sensor. The results show that the sensor is capable of strain measurement in the range of 0⁻10 kHz, indicating its effectiveness at measuring both static and high frequency signals which is an important feature of the sensor.

Thermoplastic Elastomer Systems Containing Carbon Nanofibers as Soft Piezoresistive Sensors

Soft, wearable or printable strain sensors derived from conductive polymer nanocomposites (CPNs) are becoming increasingly ubiquitous in personal-care applications. Common elastomers employed in the fabrication of such piezoresistive CPNs frequently rely on chemically cross-linked polydiene or polysiloxane chemistry, thereby generating relatively inexpensive and reliable sensors that become solid waste upon application termination. Moreover, the shape anisotropy of the incorporated conductive nanoparticles can produce interesting electrical effects due to strain-induced spatial rearrangement. In this study, we investigate the morphological, mechanical, electrical, and electromechanical properties of CPNs generated from thermoplastic elastomer (TPE) triblock copolymer systems containing vapor-grown carbon nanofiber (CNF). Modulus-tunable TPE gels imbibed with a midblock-selective aliphatic oil exhibit well-behaved properties with increasing CNF content, but generally display nonlinear negative piezoresistance at different strain amplitudes and stretch rates due to nanofiber mobility upon CPN strain-cycling. In contrast, a neat TPE possessing low hard-block content yields a distinctive strain-reversible piezoresistive response, as well as low electrical hysteresis, upon cyclic deformation. Unlike their chemically cross-linked analogs, these physically cross-linked and thus environmentally benign CPNs are fully reprocessable by thermal and/or solvent means.

Multifunctional Polymer Nanocomposites Reinforced by Aligned Carbon Nanomaterials

Carbon nanomaterials such as carbon black (CB), carbon nanotubes (CNTs), and graphene have demonstrated significant potential as fillers to improve the electrical, thermal, and mechanical properties of polymers and their fiber-reinforced polymer composites. The level of improvement has been found to depend significantly on the degree of alignment of carbon nanomaterials. Due to the very small scale and complex interactions of carbon nanomaterials with polymers and structural fibers, alignment in a given direction has been a major challenge. Over the past decade, considerable effort has been devoted to developing effective strategies to align carbon nanomaterials in polymer matrices. However, significant technological challenges remain, and there is still a lack of understanding of the alignment mechanisms and their effects on the properties of polymers and composites. This paper reviews in situ alignment techniques including shear deformation, mechanical stretching, electrospinning, and application of an external magnetic or electric field, and ex situ techniques including using vertically grown CNTs or graphene. This review particularly focuses on physical mechanisms underpinning the magnetic or electric field-induced alignment and theoretical analyses that describe the different motions occurring and the major parameters controlling alignment. Moreover, this review highlights the recent research findings of the effects of alignment on the properties of polymer nanocomposites. The outlook towards the challenges and opportunities in this field are also discussed in this review.

Eliminating common biases in modelling the electrical conductivity of carbon nanotube-polymer nanocomposites

Modelling carbon nanotube-polymer nanocomposites to predict their electrical conductivity demands high computational power. Past research has led to the assumption that conductive networks follow a periodic pattern; however, the impact of the underlying biases had never been investigated. This work provides insights into evaluating such biases and eliminating them to improve simulation accuracy.

Synergistic Effects in Thermoplastic Polyurethanes Incorporating Hybrid Carbon Nanofillers

In this study thermoplastic polyurethane (TPUs) nanocomposites incorporating carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) were prepared via melt blending and compression molding and CNT dispersion was optimized by using non-covalent surface modification (surfactant). Filler dispersion was further improved by combining two fillers with different geometric shape and aspect ratio in hybrid filler nanocomposites. Synergistic effects were observed in the TPU-GNP-CNT hybrid composites, especially when combining GNP and CNT at a ratio of 6 : 4, showing higher tensile modulus and strength with respect to the systems incorporating individual CNTs and GNPs at the same overall filler concentration. This improvement was attributed to the interaction between CNTs and GNPs limiting GNP aggregation and bridging adjacent graphene platelets thus forming a more efficient network. Hybrid systems also exhibited improved creep resistance and recovery ability. Morphological analysis carried out by scanning electron microscopy (SEM) indicated that the hybrid nanocomposite presented slightly smaller and more homogeneous filler aggregates. The well-dispersed nanofillers also favored higher phase separation in TPU, as indicated by atomic force microscopy (AFM), resulting in a better microstructure able to enhance the load transfer and maximize the mechanical and viscoelastic properties.

Novel approach to percolation threshold on electrical conductivity of carbon nanotube reinforced nanocomposites

An analytical model to correlate dispersion state given by waviness, aspect ratio and agglomerate size to the electrical conductivity of CNT nanocomposites is developed.

Chemical control of graphene architecture: tailoring shape and properties

Single layer graphene and graphene oxide feature useful and occasionally unique properties by virtue of their two-dimensional structure. Given that there is a strong correlation between graphene architecture and its conductive, mechanical, chemical, and sorptive properties, which lead to useful technologies, the ability to systematically deform graphene into three-dimensional structures, therefore, provides a controllable, scalable route toward tailoring such properties in the final system. However, the advent of chemical methods to control graphene architecture is still coming to fruition and requires focused attention. The flexibility of the graphene system and the direct and indirect methods available to induce morphology changes of graphene sheets are first discussed in this review. Focus is then given toward chemical reactions that influence the shape of presynthesized graphene and graphene oxide sheets, from which a toolbox can be extrapolated and used in controlling the spatial arrangement of graphene sheets within composite materials and ultimately tailoring graphene-based device performance. Finally, the properties of three-dimensionally controlled graphene-based systems are highlighted for their use as batteries, strengthening additives, gas or liquid sorbents, chemical reactor platforms, and supercapacitors.

New insights into the analysis of the electrode kinetics of flavin adenine dinucleotide redox center of glucose oxidase immobilized on carbon electrodes

New insights into electrochemical kinetics of the flavin adenine dinucleotide (FAD) redox center of glucose-oxidase (GlcOx) immobilized on reduced graphene oxide (rGO), single- and multiwalled carbon nanotubes (SW and MWCNT), and combinations of rGO and CNTs have been gained by application of Fourier transformed AC voltammetry (FTACV) and simulations based on a range of models. A satisfactory level of agreement between experiment and theory, and hence establishment of the best model to describe the redox chemistry of FAD, was achieved with the aid of automated e-science tools. Although still not perfect, use of Marcus theory with a very low reorganization energy (≤0.3 eV) best mimics the experimental FTACV data, which suggests that the process is gated as also deduced from analysis of FTACV data obtained at different frequencies. Failure of the simplest models to fully describe the electrode kinetics of the redox center of GlcOx, including those based on the widely employed Laviron theory is demonstrated, as is substantial kinetic heterogeneity of FAD species. Use of a SWCNT support amplifies the kinetic heterogeneity, while a combination of rGO and MWCNT provides a more favorable environment for fast communication between FAD and the electrode.

Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation

This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites. For the determination of the effective stress-strain curve and thermal conductivity of the composite material, finite-element analysis (FEA), in conjunction with the embedded fibre method (EFM), is used. Variable nanotube geometry, alignment and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the EFM. Next, incremental and iterative FEA approaches are used for the determination of the nonlinear properties of the nanocomposite. For the determination of the electrical properties, a spanning network identification algorithm is used. First, a realistic nanotube morphology is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in a representative volume element. Then, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's current law is used in conjunction with FEA to solve for the voltages and currents in the system and thus calculate the effective electrical conductivity of the nanocomposite. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone and determines the effective conductivity. Monte Carlo analysis of 500 random microstructures is performed to capture the stochastic nature of the fibre generation and to derive statistically reliable results. The models are validated by comparison with various experimental datasets reported in the recent literature.