Multiscale modeling of carbon nanotube reinforced polymer composites

This article examines the effect of interfacial load transfer on the stress distribution in carbon nanotube/polymer composites through a stress analysis of the nanotube/matrix system. Both isostrain and isostress loading conditions are investigated. The nanotube is modeled by the molecular structural mechanics method at the atomistic level. The matrix is modeled by the finite element method, and the nanotube/matrix interface is assumed to be bonded either perfectly or by van der Waals interactions. The fundamental issues examined include the interfacial shear stress distribution, stress concentration in the matrix in the vicinity of nanotube ends, axial stress profile in the nanotube, and the effect of nanotube aspect ratio on load transfer.     

Controlled electrostatic gating of carbon nanotube FET devices

Carbon nanotube transistors are a promising platform for the next generation of nonoptical biosensors. However, the exact nature of the biomolecule interactions with nanotubes in these devices remains unknown, creating one of the major obstacles to their practical use. We assembled alternating layers of oppositely charged polyelectrolytes on the carbon nanotube transistors to mimic gating of these devices by charged molecules. The devices showed reproducible oscillations of the transistor threshold voltage depending on the polarity of the outer polymer layer in the multilayer film. This behavior shows excellent agreement with the predictions of a simple electrostatic model. Finally, we demonstrate that complex interactions of adsorbed species with the device substrate and the surrounding electrolyte can produce significant and sometimes unexpected effects on the device characteristics.     

Vibration analysis of multi-walled carbon nanotubes using a spring–mass based finite element model

We report a study of the vibrational characteristics of multi-walled carbon nanotubes modeled exclusively using springs and lumped masses. Based on the atomic microstructure of the nanotube, three-dimensional nanoscale spring elements are utilized to simulate the dynamic behavior of each layer of the multi-walled carbon nanotubes. Appropriate spring elements are also developed to model the interlayer interactions and describe the van der Waals potentials between carbon atoms on different layers. Direct application of the physical variables of molecular mechanics theory to the springs is used to simulate the relative translations and rotations between atoms as well as the masses of the carbon atoms. The stiffness and mass matrices of the problem are used to construct the dynamic equilibrium equation. The natural modes of vibration and the corresponding natural frequencies are derived by solving the eigenvalue problem for different support conditions. The present method suggests novel basic modes of vibration, beyond those reported in the literature pertaining to multi-walled carbon nanotubes. The effects on the basic modes and natural frequencies created by van der Waals interactions and geometric parameters such as number of layers and aspect ratio are investigated in the context of elastic support conditions. Comparisons with other theoretical studies reveal very good correlations in terms of fundamental modes and frequencies.     

Tensile failure prediction of single wall carbon nanotube

Carbon nanotubes (CNT) possess remarkable mechanical, thermal and electrical properties, which combined with their low density and high aspect ratio, make them a very attractive candidate as reinforcing materials for the development of an entirely new class of composites. However, to determine CNTs mechanical properties in a direct experimental way is a challenging and not economical task, because of the technical difficulties and the costs involved in the manipulation of nanoscale objects. Moreover, there is still a lack of the fundamental knowledge regarding the strength and failure behaviour of carbon nanotubes.Due to nanoscale, most of the continuum based classical fracture mechanics are not really suitable to describe the failure evolution. Failure of nanotubes has been mainly investigated using molecular dynamics theory. In this paper, we present an innovative method for modelling the failure of carbon nanotubes under uniaxial tensile loading.CNT can be thought as structural systems, where the primary bond between two nearest-neighbouring atoms forms the axially loaded-bearing components member and the individual atom acts as joints of the related load-bearing members.A Finite Element Model, based on the molecular mechanics theory, is proposed in this paper in order to investigate the fracture progress in Zig-Zag and Armchair carbon nanotube with defects under uniaxial tensile stress. The novelty of the proposed approach lies in the use of nonlinear axial and torsional springs to model the local interaction and breakage of bonds of CNT atoms under axial loads. The complete load-displacement relationship of Force/Displacement curve for a (5, 5) and a (9, 0) nanotube up to the complete fracture was obtained. Further, with a continuum assumption, it was possible to define a Stress/Strain curve with ultimate strength and strain. The results show that the effect of chirality on the mechanical properties and failure mode of CNTs was quite significant and cannot be neglected. Moreover, the results are in good agreement with experimental data and classical molecular dynamics simulation validating, therefore, the proposed modelling approach.     

Young’s moduli of functionalized single-wall carbon nanotubes under tensile loading

This paper quantitatively investigates the effect of chemical functionalization on the axial Young’s moduli of single-walled carbon nanotubes (SWCNTs) based on molecular mechanics (MM) simulation, in which the COMPASS force field is used to model the interatomic interactions in a nonfunctionalized nanotube or a functionalized nanotube grafted with vinyl groups. We obtain the axial Young’s moduli of both functionalized and nonfunctionalized SWCNTs. The influences of the number and distribution density of the sp³-hybridized carbon atoms and the radius and chirality of the SWCNTs on Young’s moduli are studied. The results indicate that Young’s moduli depend strongly on the chirality of the SWCNTs and the distribution density of the sp³-hybridized carbon atoms. A 37.50% content of sp³-hybridized carbon atoms may degrade Young’s modulus by up to 33.36%. In addition, MM simulations show that the functionalization of SWCNTs results in a decrease of Young’s moduli of the corresponding SWCNT/polyethylene composites.     

Consideration of critical axial properties of pristine and defected carbon nanotubes under compression

Carbon nanotubes are hexagonally configured carbon atoms in cylindrical structures. Exceptionally high mechanical strength, electrical conductivity, surface area, thermal stability and optical transparency of carbon nanotubes outperformed other known materials in numerous advanced applications. However, their mechanical behaviors under practical loading conditions remain to be demonstrated. This study investigates the critical axial properties of pristine and defected single- and multi-walled carbon nanotubes under axial compression. Molecular dynamics simulation method has been employed to consider the destructive effects of Stone-Wales and atom vacancy defects on mechanical properties of armchair and zigzag carbon nanotubes under compressive loading condition. Armchair carbon nanotube shows higher axial stability than zigzag type. Increase in wall number leads to less susceptibility of multi-walled carbon nanotubes to defects and higher stability of them under axial compression. Atom vacancy defect reveals higher destructive effect than Stone-Wales defect on mechanical properties of carbon nanotubes. Critical axial strain of single-walled carbon nanotube declines by 67% and 26% due to atom vacancy and Stone-Wales defects.     

Nonlinear free vibration of embedded double-walled carbon nanotubes with layerwise boundary conditions

This paper investigates the large-amplitude free vibration of a double-walled carbon nanotube (DWCNT) surrounded by an elastic medium in the presence of temperature change. Based on continuum mechanics, a nonlocal elastic beam model is employed in which nanotubes are coupled together via the van der Waals (vdW) interlayer interactions. The Pasternak foundation model and a nonlinear vdW model are utilized to describe the surrounding elastic medium effect and the vdW interlayer interactions, respectively. DWCNTs with different boundary conditions are analyzed utilizing the Timoshenko beam theory that considers the shear deformation and rotary inertia effects. The governing equations are derived from Hamilton’s principle; the Galerkin method is utilized to discretize the governing equations. The influences of the nonlocal parameter, spring constant, carbon nanotube aspect ratio, and temperature change on the nonlinear free vibration characteristics of a double-walled carbon nanotube with different boundary conditions are thoroughly investigated. It is deduced that the nonlocal parameter, spring constant, and the aspect ratio play significant roles for the value of the nonlinear frequency. Also, the temperature change and the type of boundary conditions have an effect on the nonlinear frequency.     

Electromechanical actuation of single-walled carbon nanotubes: an ab initio study

The mechanical actuation of a (5, 5) single-walled carbon nanotube as a result of added charge is simulated using first-principles calculations. It is observed that while both positive and negative charging tend to expand the nanotube in the axial direction for most levels of charge, radial actuation is less even and symmetric with respect to charge. The spin distribution of the additional charges is investigated, and it is predicted that in some cases unpaired spin configurations are energetically favourable, significantly affecting actuation strains.     

Elastic Vibration Behaviors Oof Carbon Nanotubes Based on Micropolar Mechanics

The concept of the micropolar theory is employed to investigate vibration behaviors of carbon nanotubes. The constitutive relation has been deduced from the two-dimensional analysis of the microstructure of the carbon nanotube. Van der Waals interactions are simulated by a weak spring model. Hamilton's principle is employed to obtain dynamics equations of the multi-walled carbon nanotube. Numerical examples for both single-walled and double-walled carbon nanotubes are presented and the significant difference in vibration behaviors between them has been distinguished. Numerical results show that fundamental frequencies for the cantilever single-walled carbon nanotube decreases with increase of the aspect ratio of them, and the fundamental frequencies of the double-walled carbon nanotube are lower than those of the single-walled carbon nanotube with the same inner diameter and length. The first four natural frequencies for the double-walled carbon are coaxial.     

Controlling bubble density in MWNT/polymer nanocomposite foams by MWNT surface modification

Polymer nanocomposite foams are promising substitutes for polymeric foams. Carbon nanotube/polymer nanocomposite foams possess high strength, low density, and can be made conductive. Creating polymer foams with controlled foam morphology is of great importance for controlling foam properties. The foam morphology is influenced by the foaming conditions and filler properties. For carbon nanotube/polymer composite foams, dispersion state and aspect ratio of the carbon nanotubes have been shown to influence the bubble density and bubble size. In the current study, the influence of carbon nanotube surface chemistry on the bubble density of multi-walled carbon nanotube/poly(methyl methacrylate), MWNT/PMMA, nanocomposite foams was investigated. The surface of the MWNTs with controlled aspect ratio was covalently modified with glycidyl phenyl ether (GPE). Surface modified MWNT/PMMA nanocomposite foams were produced using a supercritical carbon dioxide foaming process. At constant MWNT concentration, the bubble density of polymer nanocomposite foams filled with GPE surface modified MWNT was found to be several times higher than that of polymer nanocomposite foams filled with nitric acid treated MWNT. After the MWNTs were modified with GPE, the surface chemistry of the MWNT became the dominant factor in determining the bubble density while the MWNT aspect ratio became less influential.     

Deformation of single-walled carbon nanotubes under large axial strains

The deformations of single-walled carbon nanotubes (SWCNTs) under large axial strains are investigated. The Tersoff-Brenner potential is adopted to describe the interactions between carbon atoms. Results show that the changes of strain energies are dependent on chirality but independent of the tubes' radii. Under large axial tension, abrupt changes of the configurations of SWCNTs may occur when the strains exceed 0.382 for armchair patterns and 0.43 for zigzag patterns. The reason is that the changes of bond lengths and angles lead to corresponding changes of many-body coupling interactions between atoms. Then the tubes reach new equilibrium states. Such abrupt changes of configurations must trigger fracture of CNTs in a dynamic deformation.     

Ultrasharp and high aspect ratio carbon nanotube atomic force microscopy probes for enhanced surface potential imaging

The resolution of scanning surface potential microscopy (SSPM) is mainly limited by non-local electrostatic interactions due to the finite probe size. Here we present high resolution surface potential imaging with ultrasharp and high aspect ratio carbon nanotube (CNT) atomic force microscopy (AFM) probes fabricated via dielectrophoresis. Enhancement of surface potential contrast by several factors is reported for integrated circuit structures and purple membrane fragments for these CNT AFM probes as compared to conventional probes. In particular, ultrahigh lateral resolution (～2?nm) surface potential images of self-assembled bacteriorhodopsin proteins are reported at ambient conditions, with the implication of label-free protein detection by SSPM techniques.     

Portable Free-Fall Electrostatic Separator for Beneficiation of Charged Particulate Materials

A portable free-fall electrostatic separator capable of analyzing gram quantities of charged powders is presented. Unlike a Faraday pail, in which only the net average charge-to-mass (Q/M) ratio of the particles sampled by the instrument is measured, an electrostatic separator is capable of separately measuring the charge-to-mass ratios of positively and negatively charged sampled powders. Thus, with an electrostatic separator it is possible to measure the mass fractions of powders that are charged with different polarities and the respective charge-to-mass ratios, along with the mass fraction of particles that are uncharged or charged below a threshold level. We describe a method of measuring the total charge of the collected particles in real time by incorporating an electrometer to integrate the current flowing through the collecting electrode to the high voltage power supply. In this manner, both the total charge and total mass of powder deposited on the two electrodes are measured in near real time, providing information on charge-to-mass ratio of the aerosol cloud sampled. Such real time measurements are often needed to analyze the electrostatic charging properties of small quantities of dispersed powder, particularly in such applications where the charge characteristics are of high importance.     

Lipid/polydiacetylene films for colorimetric protein surface-charge analysis

The distribution and organization of charges on a protein surface are fundamental properties which affect protein functions and interactions. We demonstrate a new approach for protein surface-charge analysis through modulating protein interactions with chromatic lipid/polydiacetylene (PDA) films. We show that visible and easily quantifiable blue-red transitions, induced on the film surface through electrostatic interactions between the negatively charged PDA and positive soluble species, constitute an effective means for characterizing protein surface charge. Specifically, protein-film interactions can be significantly modulated by complexation between the tested macromolecules and lipid-embedded multivalent calixarene ligands displaying charged residues, making possible protein discrimination based upon the abundance and organization of surface charge. The lipid/PDA film system, in conjunction with the calixarene-derived ligands, facilitates characterization of protein surface charges and identification of anomalous protein electrostatic properties.     

Charge transfer in single-walled carbon nanotubes filled with cadmium halogenides

In this work the internal channels of the single-walled carbon nanotubes (SWCNTs) were filled with cadmium chloride, cadmium bromide, and cadmium iodide by a capillary method using melts of these salts. The influence of incorporated chemical compounds on the electronic properties of the carbon nanotubes was investigated by optical absorption spectroscopy, Raman spectroscopy, near edge X-ray absorption fine structure spectroscopy, and X-ray photoelectron spectroscopy. It was found that there is the chemical bonding between carbon atoms of nanotube walls and metal atoms of encapsulated CdX₂ nanocrystals. The obtained data testify acceptor doping effect of cadmium halogenides incorporated into the SWCNT channels, which is accompanied by the charge transfer from nanotube walls to introduced substances.     

Energy dissipation in carbon nanotube composites: a review

In this article we discuss the energy dissipation that occurs when the interfacial slip of nanoscale fillers is activated in a host matrix material. We consider both polymer (such as polycarbonate, PEO, PEG) and epoxy matrices. The nanoscale fillers considered are carbon nanotubes (both singlewalled and multiwalled) as well as fullerenes. The nano-composites are fabricated by using a solution mixing technique with tetra-hydro-furan as the solvent. The interfacial friction damping is quantified by performing uniaxial dynamic load tests and measuring the material storage and loss modulus. We study various effects such as impact of nanotube weight fraction, nanotube surface treatment (oxidation, epoxidation etc.), test frequency, strain amplitude, operating temperature, as well as effect of pre-strain or biased strain. The effect of geometry (i.e., aspect ratio) is also considered by comparing the damping response of fullerene-composites with that of nanotube-composites.     

Density functional calculations of response of single-walled armchair carbon nanotubes to axial tension

The response of single-walled armchair carbon nanotubes (SWACNTs) to axial tension was studied using density functional calculations. A new response causing an abrupt change in nanotube structure at specific strains was detected. Atom rearrangement results in a lower energy than expected. The geometry of armchair nanotube plays an important role in the observed response, with the effect of curvature being important. There is a meaningful relationship between rearrangement strain and nanotube diameter. Rearrangement can be explained using the Poisson effect, which increases with the lateral displacement and is inversely proportional to nanotube index number.     

Self‐Assembly Behavior of Oppositely Charged Inverse Bipatchy Microcolloids

A directed attractive interaction between predefined “patchy” sites on the surfaces of anisotropic microcolloids can provide them with the ability to self‐assemble in a controlled manner to build target structures of increased complexity. An important step toward the controlled formation of a desired superstructure is to identify reversible electrostatic interactions between patches which allow them to align with one another. The formation of bipatchy particles with two oppositely charged patches fabricated using sandwich microcontact printing is reported. These particles spontaneously self‐aggregate in solution, where a diversity of short and long chains of bipatchy particles with different shapes, such as branched, bent, and linear, are formed. Calculations show that chain formation is driven by a combination of attractive electrostatic interactions between oppositely charged patches and the charge‐induced polarization of interacting particles.     

On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region

The longitudinal behavior of a carbon nanotube in a polymeric matrix is studied using a non-linear analysis on a full 3D multi-scale finite element model consisting of carbon nanotube, non-bonded interphase region and surrounding polymer. The bonding between carbon nanotube and its surrounding polymer is treated as van der Waals interactions. The results of simulation of carbon nanotube reinforced polymer implies on a non-linear stress–strain behavior. A comparison between finite element analysis results and the rule of mixture for conventional composites shows that the rule of mixture overestimates the result and cannot capture the scale difference between micro- and nano-scale. An equivalent fiber is developed to overcome this difficulty and corresponding longitudinal, transverse and shear moduli are calculated. The results reveal that the length of CNT affects the efficiency of reinforcement phenomenon.     

Electrochemical organization of monolayer protected gold nanoclusters on single-walled carbon nanotubes: significantly enhanced double layer capacitance

This paper reports a novel electrochemical route for anchoring monolayer protected gold nanoclusters (size 8 +/- 0.2 nm) on single-walled carbon nanotube bundles, resulting in the formation of hybrid materials. Monolayer protected gold nanoclusters prepared by modified Brust synthesis route were organized on SWNT bundles by cycling the potential in dichloromethane between -1 to +1 V at a scan rate of 50 mV/s. Monolayer protected nanoclusters in electrolyte solutions possess ionic space charge around them (double layer charging), making them suitable for organization on nanotube bundles, by tuning the electrostatic interactions. More significantly, analysis of the double layer capacitance of these hybrid materials shows almost ten times increase in capacitance compared to that of bare SWNT bundles. We believe that these hybrid materials are potentially useful in nanoelectronics.