Stiffness threshold of randomly distributed carbon nanotube networks

For carbon nanotube (CNT) networks, with increasing network density, there may be sudden changes in the properties, such as the sudden change in electrical conductivity at the electrical percolation threshold. In this paper, the change in stiffness of the CNT networks is studied and especially the existence of stiffness threshold is revealed. Two critical network densities are found to divide the stiffness behavior into three stages: zero stiffness, bending dominated and stretching dominated stages. The first critical network density is a criterion to judge whether or not the network is capable of carrying load, defined as the stiffness threshold. The second critical network density is a criterion to measure whether or not most of the CNTs in network are utilized effectively to carry load, defined as bending–stretching transitional threshold. Based on the geometric probability analysis, a theoretical methodology is set up to predict the two thresholds and explain their underlying mechanisms. The stiffness threshold is revealed to be determined by the statical determinacy of CNTs in the network, and can be estimated quantitatively by the stabilization fraction of network, a newly proposed parameter in this paper. The other threshold, bending–stretching transitional threshold, which signs the conversion of dominant deformation mode, is verified to be well evaluated by the proposed defect fraction of network. According to the theoretical analysis as well as the numerical simulation, the average intersection number on each CNT is revealed as the only dominant factor for the electrical percolation and the stiffness thresholds, it is approximately 3.7 for electrical percolation threshold, and 5.2 for the stiffness threshold of 2D networks. For 3D networks, they are 1.4 and 4.4. And it also affects the bending–stretching transitional threshold, together with the CNT aspect ratio. The average intersection number divided by the fourth root of CNT aspect ratio is found to be an invariant at the bending–stretching transitional threshold, which is 6.7 and 6.3 for 2D and 3D networks, respectively. Based on this study, a simple piecewise expression is summarized to describe the relative stiffness of CNT networks, in which the relative stiffness of networks depends on the relative network density as well as the CNT aspect ratio. This formula provides a solid theoretical foundation for the design optimization and property prediction of CNT networks.     

A molecular based anisotropic shell model for single-walled carbon nanotubes

Single-walled carbon nanotubes (SWCNTs) are frequently modeled as isotropic elastic shells. However, there are obvious evidences showing that SWCNTs exhibit remarkable chirality induced anisotropy that should not be neglected in some cases. In this paper, we derive the closed-form expressions for the anisotropic elastic properties of SWCNTs using a molecular mechanics model. Based on these anisotropic elastic properties, we develop a molecular based anisotropic shell model (MBASM) for predicting the mechanical behavior of SWCNTs. The explicit expressions for the coupling of axial, circumferential, and torsional strains, the radial breathing mode frequency, and the longitudinal and torsional wave speeds are obtained. We show that the MBASM is capable of predicting the effects of size and chirality on these quantities. The efficiency and accuracy of the MBASM are validated by comparisons of the present results with the existing results.     

A theory of plasticity for carbon nanotube reinforced composites

Carbon nanotubes (CNTs) possess exceptional mechanical properties, and when introduced into a metal matrix, it could significantly improve the elastic stiffness and plastic strength of the nanocomposite. But current processing techniques often lead to an agglomerated state for the CNTs, and the pristine CNT surface may not be able to fully transfer the load at the interface. These two conditions could have a significant impact on its strengthening capability. In this article we develop a two-scale micromechanical model to analyze the effect of CNT agglomeration and interface condition on the plastic strength of CNT/metal composites. The large scale involves the CNT-free matrix and the clustered CNT/matrix inclusions, and the small scale addresses the property of these clustered inclusions, each containing the randomly oriented, transversely isotropic CNTs and the matrix. In this development the concept of secant moduli and a field fluctuation technique have been adopted. The outcome is an explicit set of formulae that allows one to calculate the overall stress-strain relations of the CNT nanocomposite. It is shown that CNTs are indeed a very effective strengthening agent, but CNT agglomeration and imperfect interface condition can seriously reduce the effective stiffness and elastoplastic strength. The developed theory has also been applied to examine the size (diameter) effect of CNTs on the elastic and elastoplastic response of the composites, and it was found that, with a perfect interface contact, decreasing the CNT radius would enhance the overall stiffness and plastic strength, but with an imperfect interface the size effect is reversed. A comparison of the theory with some experiments on the CNT/Cu nanocomposite serves to verify the applicability of the theory, and it also points to the urgent need of eliminating all CNT agglomeration and improving the interface condition if the full potential of CNT reinforcement is to be realized.     

Explicit solution of the radial breathing mode frequency of single-walled carbon nanotubes

On the basis of a molecular mechanics model, an analytical solution of the radial breathing mode (RBM) frequency of single-walled carbon nanotubes (SWCNTs) is obtained. The effects of tube chirality and tube diameter on the RBM frequency are investigated and good agreement between the present results and existing data is found. The present analytical formula indicates that the chirality and size dependent elastic properties are responsible for the effects of the chirality and small size on the RBM frequency of an SWCNT. The project supported by the National Natural Science Foundation of China (10402019), Shanghai Rising-Star Program (05QMX1421), Shanghai Leading Academic Discipline Project (Y0103), and Key Project of Shanghai Committee of Science and Technology (04JC14034).     

Creep and recovery of polypropylene/carbon nanotube composites

The creep and recovery of polypropylene/multi-walled carbon nanotube composites were studied. It was found for thermoplastics in general that the creep strain reduces with decreased temperature, and with enhanced content of carbon nanotubes. The incorporation of nanotubes improved the recovery property remarkably, especially at high temperature. The unrecovered creep strain of nanocomposites with content of 1 and 2.8 vol.% carbon nanotubes decreased by 53% and 73% compared to that of polymer matrix. To understand the mechanisms, the Burger’s model and Weibull distribution function were employed since the variations in the simulating parameters illustrated the influence of nano-fillers on the creep and recovery performance of the bulk matrix. To further study the recovery properties, the particular contribution of each Burger’s element to the total deformation was obtained and the recovery percentage was calculated. The time-temperature-superposition-principle was applied to predict the long-term creep behavior.     

Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model

An analytical model based on a molecular mechanics approach is presented to relate the elastic properties of a single-walled carbon nanotube to its atomic structure. We derive closed-form expressions for elastic modulus and Poisson's ratio as a function of the nanotube diameter. Properties at different length scales are directly connected via these expressions. The analytically calculated elastic properties for achiral nanotubes using force constants obtained from experimental data of graphite are compared to those based on tight binding numerical calculations. This study represents a preliminary effort to develop analytical methods of molecular mechanics for applications in nanostructure modeling.     

Coarse-grained potentials of single-walled carbon nanotubes

We develop the coarse-grained (CG) potentials of single-walled carbon nanotubes (SWCNTs) in CNT bundles and buckypaper for the study of the static and dynamic behaviors. The explicit expressions of the CG stretching, bending and torsion potentials for the nanotubes are obtained by the stick-spiral and the beam models, respectively. The non-bonded CG potentials between two different CG beads are derived from analytical results based on the cohesive energy between two parallel and crossing SWCNTs from the van der Waals interactions. We show that the CG model is applicable to large deformations of complex CNT systems by combining the bonded potentials with non-bonded potentials. Checking against full atom molecular dynamics calculations and our analytical results shows that the present CG potentials have high accuracy. The established CG potentials are used to study the mechanical properties of the CNT bundles and buckypaper efficiently at minor computational cost, which shows great potential for the design of micro- and nanomechanical devices and systems.     

Filament stretching of carbon nanotube suspensions

This paper reports the application of a recently developed filament stretching protocol for the study of the extensional rheology of both treated and untreated carbon nanotubes (CNT) suspended within an epoxy resin. It was experimentally observed that filaments formed by treated and untreated CNT suspensions behaved differently after initial stretching. The filament thinning process of the base epoxy was consistent with a simple Newtonian fluid, whilst the filament of treated CNT suspensions also thinned in a Newtonian way but with an enhanced extensional viscosity. Filaments formed with untreated CNT suspensions behaved in a non-uniform way with local fluctuation in filament diameter, and it was not possible to obtain reliable extensional viscosity data. Irregularity of the untreated CNT filaments was consistent with coupled optical images, where spatial variation in CNT aggregate concentration was observed. In the case of treated CNT suspensions, the enhanced extensional viscosity was modelled in terms of the alignment of CNTs in the stretching direction, and the degree of alignment was subsequently estimated using a simple orientation model.     

Analysis of the entanglements in carbon nanotube fibers using a self-folded nanotube model

Carbon nanotube (CNT) fibers have shown superb mechanical properties, and have high potential to be used as reinforcements in multifunctional composites. CNT entanglements always exist in CNT fibers and play a crucial role in affecting their mechanical properties. In this study, the CNT entanglement is modeled as two connecting self-folded CNTs (SFCNTs). At large aspect ratios, a CNT is energetically favorable to be self-folded due to the van der Waals interactions between different parts of the CNT. The geometrical characteristics of the SFCNTs, such as the critical length for self-folding as well as the critical effective width and length, are investigated by using both an exact theoretical model and an approximate theoretical model. The tensile properties of the SFCNTs have been examined by using both the approximate theoretical model and atomistic simulations. Good agreements are achieved in the results of these two approaches.     

Transition of electrical conductivity in carbon nanotube/silver particle composite buckypapers

The electrical conductivity of carbon nanotube buckypapers can be dramatically increased by incorporation of silver particles contained in a commercial silver paste.Two methods,co-dispersion during the production of buckypaper and surface coating on a preformed buckypaper,were used to prepare composite buckypapers.The two types of composite buckypapers exhibited very different electrical conductivity profiles.The composite buckypapers prepared by the surface coating method showed a distinct step transition in electrical conductivity at 3 vol%silver content,leading to a 15-fold improvement at 6%silver content.The composite buckypapers prepared by the co-dispersion method showed a gradual change in electrical conductivity with increasing silver particle content,resulting in a five-fold improvement at12%silver content.Surface and sectional morphologies of the two types of composite buckypapers were examined and related to their electrical conductivity profiles.     

A single degree of freedom ‘lollipop’ model for carbon nanotube bundle formation

Current carbon nanotube (CNT) synthesis methods include the production of ordered, free-standing vertically aligned arrays, the properties of which are partially governed by interactions between adjacent tubes. Using material parameters determined by atomistic methods, here we represent individual CNTs by a simple single degree of freedom ‘lollipop’ model to investigate the formation, mechanics, and self-organization of CNT bundles driven by weak van der Waals interactions. The computationally efficient simple single degree of freedom model enables us to study arrays consisting of hundreds of thousands of nanotubes. The effects of nanotube parameters such as aspect ratio, bending stiffness, and surface energy, on formation and bundle size, as well as the intentional manipulation of bundle pattern formation, are investigated. We report studies with both single wall carbon nanotubes (SWCNTs) and double wall carbon nanotubes (DWCNTs) with varying aspect ratios (that is, varying height). We calculate the local density distributions of the nanotube bundles and show that there exists a maximum attainable bundle density regardless of an increase in surface energy for nanotubes with given spacing and stiffness. In addition to applications to CNTs, our model can also be applied to other types of nanotube arrays (e.g. protein nanotubes, polymer nanofilaments).     

Modulational instability of gap solitons in single-walled carbon nanotube lattices

Modulational instability and nonlinear localized excitations are addressed, in the framework of a one-dimensional diatomic carbon nanotube (CNT) model, using the quasi-discrete approximation. Gap soliton solutions, based on the modulational instability criterion, are studied, where one considers the solutions arising in the upper and lower optical frequency cutoff regimes, and in the upper acoustic frequency cutoff mode. Solutions are found as breathers and double breathers, and their response to interatomic interaction parameters is discussed. Vibrations of the CNTs from the two modes are compared based on their capability of carrying the amount of energy required for specific purposes, either in Microelectronics or in Nano-devices.     

A molecular mechanics study on size-dependent elastic properties of single-walled boron nitride nanotubes

We present an analytical study for the elastic properties of single-walled boron nitride nanotubes via a molecular mechanics model. Closed-form expressions for Young's modulus, Poisson's ratio and surface shear modulus are derived as functions of the nanotube diameter. The results are helix angle sensitive and comparable to those from ab initio calculations. This work is a first effort to establish analytical model of molecular mechanics for composite nanotubes and reveals the dissimilarities between size-dependent elastic properties of carbon and boron nitride nanotubes.     

镍涂层对碳纳米管/镁复合材料界面结合强度影响的分子动力学模拟

使用分子动力学模拟方法研究了镍涂覆单壁碳纳米管(SWCNTs)增强镁基复合材料的力学行为.结果表明,镍涂覆SWCNT/Mg复合材料的杨氏模量显著大于未涂覆SWCNT/Mg复合材料的杨氏模量,在碳纳米管表面修饰的Ni涂层可有效传递碳纳米管和Mg基体之间的载荷.此外,还研究了Ni涂层数对SWCNT/Mg复合材料界面结合强度的影响.对于不同Ni涂层数,即无Ni涂层、1层Ni涂层和2层Ni涂层,涂覆1层Ni和2层Ni的SWCNT从Mg基体中完全拔出后的界面结合强度分别约为无Ni涂层SWCNT/Mg复合材料界面结合强度的3.9和11.9倍.     

N-doped carbon nanotube encapsulated nZVI as a high-performance bifunctional catalyst for oxidative desulfurization

Great efforts have been made to remove sulfur from fossil fuels to protect the environment. We proposed synthesis of high efficiency oxidation desulfurization (ODS) catalysts by encapsulating nano zero valent iron (nZVI) in self-catalyzed carbon nanotubes. The synthetic strategy features facile hydrothermal and pyrolysis process. The specific surface area, pore structure, and microstructure of the catalysts were characterized by series techniques, and the catalytic ability was evaluated by the reduction of sulfur after oxidation and reflux-extraction. The optimized nZVI@CNT catalyst exhibits outstanding catalytic performance (within 120 min, the oxidative removal rate of DBT reached 96%) and enhanced stability (a 80% retention of initial performance after six cycles.), revealing the effective optimization and modulation between carbon nanotubes and iron particles. This excellent ODS activity originated from the defects of N-doped nanotubes as well as excellent particle dispersion and material transport capacity, which excites highly active free radicals with the assistance of H₂O₂. In addition, the unique two-dimensional tube channel and mesoporous structure promoted the diffusion and transfer of reactants and electrons, leading to high density of active sites. The different experimental conditions confirmed that the material is a bifunctional catalyst integrating adsorption and catalysis. This work provides an creative ideas for the rational design and synthesis of advanced ODS catalysts for fuel oil.     

Measuring elastic property of single-walled carbon nanotubes by nanoindentation: A theoretical framework

Nanoindentation is an effective technique for deducing the elastic property of single-walled carbon nanotubes (SWCNTs). Following an atomistic study of the nanoindentation mechanism, reverse analysis algorithms are proposed by utilizing the indentation force-depth data measured from the initial uniaxial compression and post-buckling regimes, respectively, which lead to stretching stiffness of 382 Pa m and 429 Pa m, that are very close to those in the literature. Parallel finite element simulations incorporating atomic interactions are also carried out, which closely duplicates the indentation response of SWCNTs in atomistic simulations. The numerical studies carried out in this paper may be used to guide the nanoindentation experiments, explain and extract useful data from the test, as well as stimulate new experiments.     

Influence of interphase and filler distribution on the elastic properties of nanoparticle filled polymers

The present work presents a preliminary study on the effect of the filler distribution on the elastic modulus of a nanoparticle filled polymer. To this end, two different theoretical approaches are implemented and compared. Both of them account for an interphase layer embedding the nanoparticle, with mechanical properties different from those of the matrix. Conversely, only one of them accounts for the variation of the interparticle distance. The comparison between these models allows to draw some conclusions on the effect of the filler distribution.     

Rheological characterization of carbon nanotubes/poly(ethylene oxide) composites

Rheological properties of poly(ethylene oxide) nanocomposites embedded with carbon nanotubes (CNTs) were investigated in the present study. It was found that the CNT nanocomposites had a higher effective filler volume fraction than the real filler volume fraction, which yielded a drastic enhancement of shear viscosity. As the CNT loading in the nancomposites increases, non-Newtonian behavior was observed at the low-shear-rate region in the steady shear experiments. Oscillatory dynamic shear experiments showed that more addition of the CNTs led to stronger solidlike and nonterminal behaviors. To identify a dispersion state of the CNTs, field emission scanning electron spectroscopy and transmission electron microscopy were adopted and thermal analysis was also performed by using differential scanning calorimetry. The existence of percolated network structures of the CNTs even at a low CNT loading was verified by rheological properties and electrical conductivities.     

Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites

The load transfer mechanisms and effective moduli of single-walled nanotube (SWNT) reinforced composites are studied using a continuum model. A “critical” fiber length is defined for full load transfer by numerically evaluating the strain-energy-changes for different fiber lengths. The effective longitudinal Young’s modulus and bulk modulus of the composite are derived. The effect of the interphase is also discussed. The results indicate the fiber length is critical both to the load transfer efficiency and effective moduli of the composite. The SWNT-matrix interphase plays an important role in load transfer efficiency but affects the effective moduli only slightly.     

A statistical mechanics model of carbon nanotube macro-films

Carbon nanotube macro-films are two-dimensional films with micrometer thickness and centimeter by centimeter in-plane dimension. These carbon nanotube macroscopic assemblies have attracted significant attention from the material and mechanics communities recently because they can be easily handled and tailored to meet specific engineering needs. This paper reports the experimental methods on the preparation and characterization of single-walled carbon nanotube macro-films, and a statistical mechanics model on the deformation behavior of this material. This model provides a capability to optimize the synthesis process by comparing with the experiments.