Elastic Modulus Of Carbon Nanotubes Research Articles

THE ESTIMATION OF REINFORCEMENT DEGREE OF NANOCOMPOSITES POLYMER/CARBON NANOTUBE WITHIN THE FRAMEWORKS OF MICROMECHANICAL AND PERCOLATION MODELS

It has been shown that any theoretical model describes correctly reinforcement degree of nanocomposites polymer/carbon nanotube at right choice of included in they characteristics only, i.e. real but nominal ones. The elastic modulus of interfacial regions exceeds the corresponding parameter for bulk polymer matrix. This circumstance assumes that interfacial regions are the same reinforcing element of polymer nanocomposites as actually nanofiller. In this case both mixtures rule and percolation model shown good correspondence with experimental data. It has been shown that the real (effective) elastic modulus of carbon nanotubes (their aggregates) is function of stiffness of polymer matrix.

Raman spectroscopy used for estimating the effective elastic modulus of carbon nanotubes in aligned multi-walled carbon nanotubes/ epoxy composites under tensile loading

Raman spectroscopy used for estimating the effective elastic modulus of carbon nanotubes in aligned multi-walled carbon nanotubes/ epoxy composites under tensile loading

Modified couple stress flexure mechanics of nanobeams

In view of numerous contributions accessible in the literature associated with the modified couple stress theory, its deficiency in precise description of the material response of continua with nano-structural features is investigated. The flexure mechanics of nano-scale beams in the framework of the modified couple stress theory is reassessed applying a consistent variational scheme. The physically motivated constitutive laws of the stress resultant fields, flexural moment and shear force, associated with the modified couple stress beam are introduced. The well-established differential conditions of equilibrium equipped with the proper mathematical form of the higher-order boundary conditions are reinstated. The exact analytical solutions of the kinematic fields of the nano-sized beam are derived by direct solving of the governing coupled differential equations. The flexure response of the modified couple stress beam is numerically illustrated wherein the effects of the symmetric rotation gradients along with the transverse shear deformation are examined. Closed-form analytical formulae of the elastic modulus of Carbon Nanotubes are detected and thoroughly discussed. Serious suspicions on the applicability of the modified couple stress beam model in accurately capturing the size-effects in nano-materials are emerged as evinced by rigorous examination of the elastic modulus of CNTs.

Prediction of the elastic modulus of LLDPE/CNT nanocomposites by analytical modeling and finite element analysis

In the present work, the effective elastic modulus of carbon nanotube (CNT) polymer nanocomposites has been evaluated through micromechanics modeling and finite element analysis (FEA). In the micromechanics model, the inherent trend of CNTs to aggregate is taken into account, considering a two-phase material system, that of the matrix with the finely dispersed CNTs and the inclusions, involving agglomerated CNTs and matrix material. A new model is proposed for the elastic stiffness evaluation of the two phases and the elastic stiffness of the nanocomposite, introducing two aggregation parameters. It was proved that this analysis was rational and operative. The same aggregation concept has been investigated using FEA, and a comparative study between the two procedures was performed. Furthermore, an additional treatment with FEA was performed, based on a three-phase model, including the matrix, the CNTs and the interphase. A parametric analysis has been executed and a comparison with experimental data of linear low density polyethylene (LLDPE)/CNT nanocomposites has been performed.

Reinforcement of Carbon Nanotube/Polydimethylsiloxane True Nanocomposite

The paper shows that the elastic modulus of carbon nanotubes in a polymer matrix nanocomposite is lower not only than its nominal value, but also the elastic modulus of the interfacial regions. Therefore, a degree of reinforcing carbon nanotube/polydimethylsiloxane nanocomposites is completely determined by the amount of the interfacial regions, whereas the effectiveness of the nanofiller is determined by its ability to generate such regions.

Simulation of static and dynamic mechanical characteristics of carbon nanotubes and carbon nano-peapods with defects

The static and dynamic mechanical characteristics of carbon nanotubes with double and multiple vacancy defects are simulated by the molecular dynamics method. Firstly, the effects of diatomic and polyatomic vacancy defects on the quasi-static mechanical properties of carbon nanotubes are discussed. Then, the effects of defects and axial pre-stress on the dynamics of C60 molecular oscillation in carbon nano-peapods are discussed. The results show that the ultimate stress, ultimate strain and elastic modulus of carbon nanotube containing different types of diatomic vacancies are significantly reduced as compared with those of non-defective carbon nanotubes. When the carbon nanotubes have many defective atoms and the defects are connected together to form a crack, the axial compressive properties of the carbon nanotubes are greatly reduced. Compared with the circumferential development of cracks, the cracks along the axis greatly reduce the compressive capacity of carbon nanotubes, which is similar to that of shell models with cracks. The oscillation frequency of C60 molecular in defective carbon nano-peapods is affected by the number of missing atoms. The single vacancy defect increases the oscillation frequency of C60 molecule, while with the further increase of vacancy number, the oscillation frequency of C60 molecule decreases gradually. When the defective carbon nano-peapod has axial tensile or compressive pre-stress, the oscillation of the C60 molecule is affected not only by the defects, but also by the axial pre-stress, which makes the oscillation of C60 molecule more complicated.

Measurement of the elastic modulus of nanowires based on resonant frequency and boundary condition effects

The elastic modulus of nanowires can be measured by resonant frequency method, in which the elastic modulus is determined using the classical theory of beam deflection. However, the measurement accuracy of the elastic modulus obtained from the resonant frequency can be largely affected by theoretical models and boundary conditions. In the present paper, a theoretical model is developed by considering nonlocal interactions and boundary condition effects of cantilever support. Based on the proposed model, we investigate the influence of nonlocal parameter and elastic foundation on the elastic modulus of carbon nanotubes (CNTs). The results show that the resonant frequency of CNTs is affected by the clamped cantilever condition. Support stiffness and clamped length of CNTS cannot be ignored in determining the elastic modulus of CNTs, especially for CNTs with low stiffness support. After considering the boundary conditions, the influence of cantilever support on the frequency is effectively removed, and the elastic modulus can be precisely determined by measuring the resonant frequency.

Finite element investigation of temperature dependence of elastic properties of carbon nanotube reinforced polypropylene

This paper aims to investigate the elastic modulus of the polypropylene matrix reinforced by carbon nanotubes at different temperatures. To this end, the finite element approach is employed. The nanotubes with different volume fractions and aspect ratios (the ratio of length to diameter) are embedded in the polymer matrix. Besides, random and regular algorithms are utilized to disperse carbon nanotubes in the matrix. It is seen that as the pure polypropylene, the elastic modulus of carbon nanotube reinforced polypropylene decreases by increasing the temperature. It is also observed that when the carbon nanotubes are dispersed parallelly and the load is applied along the nanotube directions, the largest improvement in the elastic modulus of the nanotube/polypropylene nanocomposites is obtained.

A new micromechanics model and effective elastic modulus of nanotube reinforced composites

In the present study, a new model, in which the wavy carbon nanotubes are replaced with effective fibers, has been developed. The analytical expressions are derived based on the micromechanics method, then the effective elastic modulus of carbon nanotube (CNT)/polymer composites can be predicted. This paper mainly investigates the effects of waviness and agglomeration on the effective elastic modulus of curved carbon nanotube reinforced composites. It is found that both of those factors can significantly affect the stiffening of composites. The stiffness of carbon nanotubes can be reduced significantly due to the effects of waviness and agglomeration. Moreover, the effects of waviness and agglomeration on the effective elastic modulus are also discussed. It is noted that the effective elastic modulus of CNT reinforced composites is very sensitive to the waviness and the agglomeration.

English

Owing to the superior mechanical properties of Carbon Nanotubes (CNTs), research has been initiated to use this nanomaterial in construction industry. The elastic modulus of CNT is of great importance in order to use CNTs in construction industry. For judicious and effective application of CNT in construction industry where mass scale utilization is inevitable, it is important to accurately assess the properties of CNTs since these nano fiber materials are extremely cost sensitive. There is no well established tool or method available for the engineers to determine the properties of CNT, other than to accept the manufacturer’s data. Nanoscale continuum theory uses a representative volume to determine the elastic modulus which does not include the effect of radius and aspect ratio. In the present study, numerical model is developed and the validated one is used to study the effects of geometrical variability’s on the properties of CNT. Further, a methodology has been proposed to determine the mechanical properties, such as tensile stiffness, of the Carbon nanotube with a given structural arrangement (chirality and radius) if the same for the basic configuration, graphene, is known. The procedure discussed in this study will be helpful to the engineers to easily estimate the properties such as elastic modulus or tensile stiffness of CNTs before incorporating into conventional materials for developing new materials with enhanced properties.

Numerical evaluation of effective elastic properties of CNT-reinforced polymers for interphase effects

This paper presents the stiffening effect of carbon nanotubes dispersed in polymer composites using micromechanics models and finite element analysis. The effective elastic modulus of carbon nanotube (CNT)-reinforced composites is predicted by assuming that all the CNTs are either aligned or randomly oriented in the polymer matrix. An extended three-phase rule of mixture is implemented to analyze the effect of interphase properties on the effective elastic modulus. Homogenized representative volume element with multiple CNTs embedded inside the matrix with an interface layer is employed. The analysis is performed using a 3D finite element model of the representative volume element. Effects of interface stiffness, its thickness and dispersion of CNTs within the polymer matrix are studied. Results reveal the extent these factors influencing the elastic modulus of the composite.

Research on the Elastic Modulus of Single-Walled Carbon Nanotubes

The calculation of elastic modulus of carbon nanotubes is an essential prerequisite for future Micro-nano devices fabrication that based on carbon nanotubes. The interaction potential of C-C covalent bond in single-walled carbon nanotubes (SWCNTs) is described by Terrsoff-Brenner potential in this paper. The elastic modulus of SWCNTs is ranged from 1.1078TPa to 1.23789TPa with the diameter increases from 0.3176nm to 2.0626nm by molecular dynamics (MD) simulation. The critical diameters of armchair and zigzag nanotubes are 1nm and 0.6nm.The elastic modulus changes with the diameter of nanotubes increasing clearly when the diameter smaller than the critical diameter, but the value of elastic modules tends to convergence when the diameter of nanotubes larger than the critical diameter.

Predictive model for carbon nanotube–reinforced nanocomposite modulus driven by micromechanical modeling and physical experiments

This article proposes an improved surrogate model for the prediction of the elastic modulus of carbon nanotube–reinforced-nanocomposites. By statistically combining micromechanical modeling results with limited amounts of experimental data, a better predictive surrogate model is constructed using a two-stage sequential modeling approach. A set of data for multi-walled carbon nanotube–bismaleimide nanocomposites is used in a case study to demonstrate the effectiveness of the proposed surrogate modeling procedure. In the case study, the theoretical composite modulus is computed with micromechanical models, and the experimental modulus is measured through tensile tests. Both theoretical and experimental composite moduli are integrated by using a statistical adjustment method to construct the surrogate model. The results demonstrate an improved predictive ability compared to the original micromechanical model.

Analysis of the vibration characteristics of double-walled carbon nanotubes

The induced electric-field has been applied to measure the elastic modulus of carbon nanotubes. However, the vibrational modes of the multi-walled carbon nanotubes are quite different from those of the single-walled carbon nanotubes. Analysis of the vibration characteristics of double-walled carbon nanotubes (DWCNTs) with simply supported boundary condition are carried out based on Euler–Bernoulli beam theory. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. It is found that the vibrational modes of DWCNTs are noncoaxial intertube vibrations, and the deflections of the inner and outer nanotubes can occur in the same or in opposite deflections. In the same vibrational mode, the resonant frequencies of DWCNTs with deflections between the inner and outer nanotubes in the same direction are smaller than those of DWCNTs with the opposite deflections.

Development of novel single-wall carbon nanotube–epoxy composite ply actuators

This paper describes a carbon nanotube epoxy ply material that has electrochemicalactuation properties. The material was formed by dispersing single-wall carbon nanotubesin a solvent and then solution casting a thin paper using a mold and vacuum oven. In orderto take advantage of the high elastic modulus of carbon nanotubes for actuation, epoxy asa chemically inert polymer is considered. An epoxy layer was cast on the surface of thenanotube paper to make a two-layer ply. A wet electrochemical actuator was formed byplacing the nanotube epoxy ply in a 2 M NaCl electrolyte solution. Electrochemicalimpedance spectroscopy and cyclic voltammetry were carried out to characterize theelectrochemical properties of the actuator. The voltage–current relationship andpower to drive the actuator material were also determined. Compared to previoussingle-wall carbon nanotube buckypaper tape actuators, which had poor adhesionbetween the nanotubes and tape, and other nanotube–thermal plastic polymeractuators, which could not provide high strength, the epoxy based actuator has ahigher elastic modulus and strength, which will be useful for future structuralapplications. This demonstrates that a polymer layer can reinforce nanotube paper,which is an important step in building a new structural material that actuates.Further work is under way to develop a solid electrolyte to allow dry actuation.Finally, these actuator plies will be laminated to build a carbon nanocompositematerial. This smart structural material will have potential applications thatrange from use in robotic surgical tools to use as structures that change shape.