Percolation Threshold Of Carbon Nanotubes Research Articles

Double Percolation of Poly(lactic acid)/Low-Density Polyethylene/Carbon Nanotube (PLA/LDPE/CNT) Composites for Force-Sensor Application: Impact of Preferential Localization and Mixing Sequence.

This study explores the enhancement of electrical conductivity in polymer composites by incorporating carbon nanotubes (CNTs) into a co-continuous poly(lactic acid)/low-density polyethylene (PLA/LDPE) blend, creating a double percolation structure. Theoretical thermodynamic predictions indicate that CNTs preferentially localize in the LDPE phase. The percolation threshold of CNTs in the PLA/LDPE/CNT composites was 0.208 vol% (5.56 wt%), an 80% reduction compared to the LDPE/CNT composite, due to the double percolation structure. This thermodynamic migration of CNTs from PLA to LDPE significantly enhanced conductivity, achieving a 13.8-fold increase at a 7.5 wt% CNT loading compared to the LDPE/CNT composite. The localization of CNTs was driven by thermodynamic, kinetic, and rheological factors, with viscosity differences between PLA and LDPE causing dense CNT aggregation in LDPE. Initial contact of CNTs with PLA reduced aggregation, allowing PLA to infiltrate CNT aggregates during melt-mixing, which influenced the final morphology and electrical conductivity. These findings provide new insights into the fabrication of conductive polymer composites for force sensor applications.

Copolymer composition tailored carbon nanotube network breakdown and piezoresistivity of ethylene-vinyl acetate electroconductive composites

Herein, the development of carbon nanotube-based electromechanical sensors with excellent sensing range and gauge factor is reported. Electroconductive composites (EPCs) of ethylene–vinyl acetate random copolymer (EVAc) with different ethylene (E) and vinyl acetate (VAc) segment ratios and different volume fractions of carbon nanotube (CNT) were prepared. The E/VAc ratio was found to significantly impact the AC impedance, electron tunneling, CNT-CNT structural breakdown, effective aspect ratio, and electromechanical behavior. The percolation threshold of CNT was lowest in EPCs with VAc 12%; interestingly, though, the effective aspect ratio, as determined from the micromechanical modeling, was considerably increased in EPC with VAc 40%. With an increase in VAc content, the electrical conductivity decreased; however, the electromechanical response improved significantly. Crystalline content, interfacial wetting, critical strain for the shear strain-induced structural breakdown of percolated CNT network, and effective aspect ratio were found to correlate with the superior electromechanics of EVAc/CNT EPC.

Increasing self-sensing capability of carbon nanotubes cement-based materials by simultaneous addition of Ni nanofibers with low content

This paper aims to increase self-sensing capability of carbon nanotubes cement-based materials by simultaneous addition of Ni nanofibers with low content. The carbon nanotubes cement-based composites with a low content of Ni nanofibers and without Ni nanofibers were fabricated. The microstructures of as-fabricated cement-based composites were observed with transmission electron microscopy (TEM), scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS). Besides, the conductivity and pressure sensitivity of as-fabricated cement-based composites were studied by four electrode voltammetry. The results show that the Ni nanofibers and carbon nanotubes were well dispersed in the as-fabricated cement-based composites. The resistivities of as-fabricated cement-based composites show typical percolation phenomenon with the increases of carbon nanotube contents. The addition of Ni nanofibers with a low content induces the increase in the conductivity of cement-based composites, but not change the percolation threshold of carbon nanotubes. Moreover, the addition of Ni nanofibers with a low content increases the sensitivity, linearity and repeatability of cement-based composite with carbon nanotubes.

Enhanced field-dependent conductivity of magnetorheological gels with low-doped carbon nanotubes

Magnetorheological gels (MRG) exhibit field-dependent conductivity and controllable mechanical properties. In order to extend their application field, filling a large number of traditional conductive materials is the most common means to enhance the poor conductivity of MRG. In this study, the conductivity of MRG is improved by low-doped carbon nanotubes (CNTs). The influence of CNTs on the magnetoresistance of MRG is discussed from two aspects—the improvement in electrical conductivity and the magnetic sensitivity of conductivity variation. The percolation threshold of CNTs in MRG should be between 1 wt% and 2 wt%. The conductivity of a 4 wt% CNT-doped sample increases more than 28 000 times compared with pure MRG. However, there is a cliff-like drop for the range and rate of conductivity variation when the doping amount of CNTs is between 3 wt% and 4 wt%. Therefore, it is concluded that the optimal mass fraction of CNTs is 3%, which can maintain a suitable variation range and a strong conductivity. Compared with pure MRG, its conductivity increases by at least two orders of magnitude. Finally, a sketch of particle motion simulation is developed to understand the improving mechanism and the effect of CNTs.

Synergistic effects and piezoresistive characteristics of carbon nanofillers/silicone rubber composites

Silicone rubber (SR) filled with different concentrations of carbon nanotubes (CNTs), carbon black (CB) and (CNTs/CB) hybrid fillers was fabricated by melt blending. The effects of filler type on the electrical properties and piezoresistive properties (in the region of the percolation) of the conductive SR composites were studied. Percolation threshold of CNTs, CB and (CNTs/CB) based composites was found to be 0.20, 0.255 and 0.22 volume fraction respectively. The piezoresistive sensitivity GR of these conductive SR composites, dependent on different filler types, was 0.8549, 0.7267 and 0.9361 respectively. Compared to CB/SR and CNTs/SR, CNTs/CB/SR revealed an unexpectedly high GR, which indicated that the synergistic effects have formed in CNTs/CB network. In addition, microscopic analysis (SEM) can also explain the existence of synergies. A model describing the electrical percolation of mixed carbon fillers CNTs and CB is proposed. The experimental value (0.22) of hybrid filler systems is smaller than the theoretical value (0.23), which can prove the existence of synergies once again.

Site-percolation threshold of carbon nanotube fibers—Fast inspection of percolation with Markov stochastic theory

We present a site-percolation model based on a modified FCC lattice, as well as an efficient algorithm of inspecting percolation which takes advantage of the Markov stochastic theory, in order to study the percolation threshold of carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the inspection of percolation by performing repeated sparse matrix–vector multiplications, which allows parallelized computation to accelerate the inspection for a given configuration. With this approach, we determine that the site-percolation transition of CNT fibers occurs at pc=0.1533±0.0013, and analyze the dependence of the effective percolation threshold (corresponding to 0.5 percolation probability) on the length and the aspect ratio of a CNT fiber on a finite-size-scaling basis. We also discuss the aspect ratio dependence of percolation probability with various values of p (not restricted to pc).

Effects of the dispersion state and aspect ratio of carbon nanotubes on their electrical percolation threshold in a polymer

AbstractThe electrical percolation threshold of carbon nanotubes (CNTs) is correlated with their dispersion state and aspect ratio through modeling. An analytical percolation model based on excluded volume theory and developed for systems containing two types of fillers is used. CNTs are modeled as two types of fillers: single CNT and m‐CNT bundle, and a variable P representing the dispersion state of CNTs is introduced. An equation showing the effects of the dispersion state and aspect ratio on the electrical percolation threshold of CNTs is established and verified with some of the published experimental data. It is useful for predicting the conductive behavior of polymer/CNT composites and for the design of their processing conditions. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

An Innovative Method to Reduce Percolation Threshold of Carbon Nanotubes Filled Nylon6/Polystyrene Blends

Selective localization of carbon nanotubes (CNTs) at the interface of immiscible polymer blend was achieved by the method that poly(styrene-co-maleic anhydride) (SMA) was first reacted with CNTs, and then blended with nylon6/polystyrene (PA6/PS). In the PA6/PS blends, CNTs was localized in PA6 phase and the percolation threshold was 2wt%. However, for the PA6/PS/(SMA- CNTs) composites, TEM results showed that most of CNTs were selectively localized in matrix, but some of tubes were induced by SMA to disperse at the interface. The localization of CNTs at the interface caused the percolation threshold of PA6/PS/(SMA- CNTs) was only 0.33 wt%, which is much lower than that of PA6/PS/ CNTs.

Comparative study on electrical properties of orientated carbon nanotubes/epoxy composites

AbstractThe percolation threshold of carbon nanotubes (CNTs)/epoxy resin composites was simulated in the Bruggeman' Effective‐Medium Theory based on experiment. Both distinct percolation effect and low percolation threshold in the aligned CNTs/epoxy composites were predicted. With the CNTs loading larger than the percolation threshold, the critical exponent of CNTs/epoxy composites rises rapidly with the increase of aspect ratio of CNTs. It is shown that the electrical conductivity of composites presents distinct aeolotropism, the percolation threshold is sensitive relative to the tiny change of the orientation factor, the aspect ratio, and the structure of CNTs in the composites matrix. The simulated results are consistent with the experimental results basically, and the discrepancy between simulated results and experimental results has been interpreted reasonably. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Percolation threshold of carbon nanotubes filled unsaturated polyesters

This paper reports on the development of electrically conductive nanocomposites containing multi-walled carbon nanotubes in an unsaturated polyester matrix. The resistivity of the liquid suspension during processing is used to evaluate the quality of the filler dispersion, which is also studied using optical microscopy. The electrical properties of the cured composites are analysed by AC impedance spectroscopy and DC conductivity measurements. The conductivity of the cured nanocomposite follows a statistical percolation model, with percolation threshold at 0.026 wt.% loading of nanotubes. The results obtained show that unsaturated polyesters are a matrix suitable for the preparation of electrically conductive thermosetting nanocomposites at low nanotube concentrations. The effect of carbon nanotubes reaggregation on the electrical properties of the spatial structure generated is discussed.

Influence of the molecular weight distribution on the percolation threshold of carbon nanotube – polystyrene composites

AbstractCarbon nanotubes were introduced into insulating polystyrene (PS) and poly(methyl methacrylate) (PMMA) by means of a latex-based technique. A systematic study of the effect of the polydispersity index, more particularly the presence of different amounts of low molar mass polymer, on the final composite conductivity was performed. Six latexes with varying molecular weight distributions were prepared by means of conventional free radical emulsion polymerization in the presence of different amounts of chain transfer agent, namely n-dodecyl mercaptan. Composites were prepared with both multi-walled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs). Shifts in the percolation threshold from 0.9 to 0.6 wt% for MWCNTs and from 0.7 to 0.4 wt% for SWCNTs were observed for PS matrix material, whereas for PMMA matrix material the percolation thresholds shifted from 0.6 to 0.3 wt% for MWCNTs and 0.35 to 0.2 wt% for SWCNTs upon increasing the amount of low molecular weight polymer in the polymer matrix.

A Novel Concept for Highly Oriented Carbon Nanotube Composite Tapes or Fibres with High Strength and Electrical Conductivity

AbstractA new concept is described for the creation of multifunctional polymer nanocomposite tapes (or fibres) that combines high stiffness and strength with good electrical properties and a low percolation threshold of carbon nanotubes (CNTs). The concept is based on a bicomponent tape (or fibre) construction consisting of a highly oriented polymer core and a conductive polymer composite (CPC) skin based on a polymer with a lower melting temperature than the core, enabling thermal annealing of these skins to improve conductivity through a dynamic percolation process while retaining the properties of the core and hence those of the tape (or fibre). The percolation threshold in the CPC skins of the highly drawn conductive bicomponent tapes could be decreased from 5.3 to 1.1 wt.‐% after annealing.magnified image

Anomalous electrical conductivity and percolation in carbon nanotube composites

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

Continuum percolation of carbon nanotubes in polymeric and colloidal media

We apply continuum connectedness percolation theory to realistic carbon nanotube systems and predict how bending flexibility, length polydispersity, and attractive interactions between them influence the percolation threshold, demonstrating that it can be used as a predictive tool for designing nanotube-based composite materials. We argue that the host matrix in which the nanotubes are dispersed controls this threshold through the interactions it induces between them during processing and through the degree of connectedness that must be set by the tunneling distance of electrons, at least in the context of conductivity percolation. This provides routes to manipulate the percolation threshold and the level of conductivity in the final product. We find that the percolation threshold of carbon nanotubes is very sensitive to the degree of connectedness, to the presence of small quantities of longer rods, and to very weak attractive interactions between them. Bending flexibility or tortuosity, on the other hand, has only a fairly weak impact on the percolation threshold.

Correlations between Percolation Threshold, Dispersion State, and Aspect Ratio of Carbon Nanotubes

AbstractCritical factors that determine the percolation threshold of carbon nanotube (CNT)‐reinforced polymer nanocomposites are studied. An improved analytical model is developed based on an interparticle distance concept. Two dispersion parameters are introduced in the model to correctly reflect the different dispersion states of CNTs in the matrix—entangled bundles and well‐dispersed individual CNTs. CNT–epoxy nanocomposites with different dispersion states are fabricated from the same constituent materials by employing different processing conditions. The corresponding percolation thresholds of the nanocomposites vary over a wide range, from 0.1 to greater than 1.0 wt %, and these variations are explained in terms of dispersion parameters and aspect ratios of CNTs. Important factors that control the percolation threshold of nanocomposites are identified based on the comparison between modeling data and experimental results.

Study in the Dispersion of Carbon Nanotubes

AbstractIn the past, the dispersion of carbon nanotubes (CNTs) in both liquids and solids has been difficult due to the high surface interactions between the tubes. Dispersion of polymer CNT composites is important for such benefits as structural reinforcement of composites, the percolation threshold of CNT based conducting materials, and the thermal properties with the exploitation of the high surface area of CNTs. Here we discuss two approaches towards addressing dispersion of multiwalled nanotubes (MWNTs). One approach is the use of surfactant chemicals selected on the basis that they interact with CNT chemical groups. The second approach is the functionalization through covalent bonding of the CNTs with various polymers including polyethylenimine (PEI), and poly(methyl methacrylate) (PMMA). The two approaches were evaluated to determine whether covalent functionalization was more beneficial than the use of surfactants. Characterization of the dispersion was performed using various microscopy techniques.