Radial elasticity of multiwalled carbon nanotubes

We report an experimental and a theoretical study of the radial elasticity of multiwalled carbon nanotubes as a function of external radius. We use atomic force microscopy and apply small indentation amplitudes in order to stay in the linear elasticity regime. The number of layers for a given tube radius is inferred from transmission electron microscopy, revealing constant ratios of external to internal radii. This enables a comparison with molecular dynamics results, which also shed some light onto the applicability of Hertz theory in this context. Using this theory, we find a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30+/-10 GPa.     

Measurement of the elastic moduli of dense layers of oriented carbon nanotubes by a scanning force microscope

A technique is developed for measuring the modulus of elasticity of a material with a Nanoscan scanning force microscope on the basis of measuring the dependence of probe vibration frequency on the penetration depth of the needle into the specimen. This technique makes it possible to study materials with elastic moduli from 50 to 1000 GPa. The Young moduli of dense films of carbon nanotubes oriented at angles of 45° and 90° to the quartz substrate are measured. From their ratio, the Young modulus in the direction perpendicular to the tubes and the anisotropy of the elastic moduli are determined. A comparison of these values with the corresponding values obtained for a nanotube film deposited on a silicon substrate is carried out. On the basis of this comparison, a conclusion is made concerning the interaction between single-layer nanotubes and between nanotubes in a mixture of single-layer and multilayer ones.     

Rheological Behaviors of Poly(Vinylidene Fluoride)/“Bud-Branched” Nanotubes Nanocomposites

Bud-branched nanotubes, fabricated by growing metal particles on the surfaces of multiwall carbon nanotubes (MWCNTs), were used to prepare poly(vinylidene fluoride) (PVDF)-based nanocomposites. The melt viscoelastic behaviors of PVDF and its nanocomposites were characterized. The results showed that the introduction of both the MWCNTs and bud-branched nanotubes (MWCNTs-B) increased the storage modulus, loss modulus, and complex viscosity of the nanocomposites. However, the bud-branched nanotubes were more efficient to increase the elasticity than the MWCNTs that have relatively smooth surfaces. In particular, it was observed that the bud-branched nanotubes caused an increase of normal force and crossover modulus, while for MWCNTs, no variation in the normal force and a decrease of the crossover modulus were observed.     

Elastic modulus of polypyrrole nanotubes

The first measurements of the tensile elastic modulus of polypyrrole nanotubes are presented. The nanotubes were mechanically tested in three points bending using atomic force microscopy. The elastic tensile modulus was deduced from force-curve measurements on different nanotubes with outer diameter ranging between 35 and 160 nm. It is shown that the elastic modulus strongly increases when the thickness or outer diameter of polypyrrole nanotubes decreases.     

Nonlinear mechanical response and rippling of thick multiwalled carbon nanotubes

The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum method. The previous hypothesis that this reduction is due to a rippling mode is confirmed by the calculations. The observed ripples result from a complex three-dimensional deformation similar to the Yoshimura buckling pattern. It is found that thick MWCNTs exhibit a well-defined nonlinear moment-curvature relation, even for small deformations, governed by the interplay of strain energy relaxation and intertube interactions. Rippling deformations are also predicted for MWCNTs subject to torsion, resulting in an effective torsional modulus much smaller than that predicted by linear elasticity.     

Mechanical and microwave absorbing properties of carbon-filled polyurethane

Polyurethane (PU) matrix composites were prepared with various carbon fillers at different filler contents in order to investigate their structure, mechanical and microwave absorbing properties. As fillers, flat carbon microparticles, carbon microfibers and multiwalled carbon nanotubes (MWNT) were used. The microstructure of the composite was examined by scanning electron microscopy and transmission electron microscopy. Mechanical properties, namely universal hardness, plastic hardness, elastic modulus and creep were assessed by means of depth sensing indentation test. Mechanical properties of PU composite filled with different fillers were investigated and the composite always exhibited higher hardness, elastic modulus and creep resistance than un-filled PU. Influence of filler shape, content and dispersion was also investigated.     

Nanomechanical analysis of Clostridium tyrobutyricum spores

In this work we report on the measurement of the Young modulus of the external surface of Clostridium tyrobutyricum spores in air with an atomic force microscope. The Young modulus can be reliably measured despite the strong tip-spore adhesion forces and the need to immobilize the spores due to their slipping on most substrates. Moreover, we investigate the disturbing factors and consider some practical aspects that influence the measurements of elastic properties of biological objects with the atomic force microscopy indentation techniques.     

游标卡尺在测定金属杨氏模量中的应用

根据拉伸法测量金属杨氏模量的原理,利用现有的杨氏模量仪,设计了一套应用游标卡尺测定金属杨氏模量的方法。     

Theoretical study of the dependences of the young’s and torsion moduli of thin single-layer carbon zigzag and armchair nanotubes on the geometric parameters

The Young’s and torsion moduli of single-layer carbon (m, 0) and (m, m) nanotubes are studied. It is demonstrated that both moduli depend on the chirality, diameter, and length of the nanotube. It is found for the first time that the torsion modulus increases with the nanotube diameter and diminishes with an increase in its length. By considering nanotubes with various values of the diameter-to-length ratio, it is shown that the Young’s and torsion moduli of the nanotubes saturate at a diameter-to-length ratio of ～0.3. The values of the torsion modulus as calculated from the Young’s modulus we obtained and from the deformation energy do not coincide, which can be attributed to the effect of dangling bonds at the open ends of the nanotubes. Energy calculations are performed using the Goodwin modification of the semiempirical Harrison tight-binding method.     

Elastic properties of dense nanotube layers

The Young modulus of a thin layer consisting of densely packed carbon nanotubes oriented normally to a substrate is measured using a scanning probe atomic force microscope. It is found that the adhesion of the film and the silicon substrate is not very strong, and, at certain conditions, this may lead to an intense energy dissipation in an oscillatory system loaded by the film.     

Elastic properties of polyelectrolyte capsules studied by atomic-force microscopy and RICM

Mechanical properties of polyelectrolyte multilayer capsules were studied using a new method combining atomic-force microscopy and reflection interference contrast microscopy. By measuring the force vs. deformation for poly(styrene sulfonate)/poly(allylamine) capsules the existence of different deformation regimes depending on the applied deformation was shown. The present paper focuses on the small-deformation regime. The elastic response of the deformed capsule was studied as a function of the wall thickness and the capsule size, and showed the theoretically expected variations. The Young modulus obtained from the experiments ranges between 1.3 and 1.9 GPa.Received: 5 August 2003, Published online: 28 October 2003PACS: 46.25.-y Static elasticity - 46.70.De Beams, plates and shells - 82.35.Rs Polyelectrolytes     

Atomic force microscopy of bamboo-shaped multiwalled carbon nanotube structures

Atomic force microscopy (AFM) was employed for the morphology measurements of bamboo-shaped multiwalled carbon nanotubes (BS-MWNTs) grown by thermal chemical vapor deposition on Fe catalyst deposited SiO₂/Ti substrates. Greater diameters and compartment distances of the bamboo structures were observed for the BS-MWNTs grown at 950 °C than for those grown at 850 °C.     

Investigation of the radial deformability of individual carbon nanotubes under controlled indentation force

Tapping-mode atomic force microscopy was used to study the radial deformability of a multiwalled carbon nanotube (MWCNT). By imaging the MWCNT under different tapping forces, we were able to demonstrate its remarkable reversible radial deformability (up to approximately 40%) and reveal internal discontinuities along its length. The values of the effective elastic modulus of several sections of the MWCNT in the radial direction were estimated with the Hertz model.     

Application of scanning force microscopy in nanotube science

Recent developments in the application of scanning force microscopy in nanotube science are reviewed. The non-destructive character of this technique allows the structural characterisation of (chemically modified) single- and multi-wall nanotubes deposited on substrates for further investigations such as electrical transport measurements. Furthermore, SFM is now an established tool for manipulation of nanotubes, which allows position control and determination of elastic constants such as the Young’s modulus. Finally it is shown that very sharp and stable probes for scanning force microscopy can be made from nanotubes due to their excellent stability and aspect ratio. Received: 17 May 1999 / Accepted: 18 May 1999 / Published online: 29 July 1999     

Structural Analysis of Collapsed, and Twisted and Collapsed, Multiwalled Carbon Nanotubes by Atomic Force Microscopy

A fully collapsed multiwalled carbon nanotube (MWCNT1) section and a different twisted and fully collapsed MWCNT were observed with tapping-mode atomic force microscopy. The collapsed section of MWCNT1 was significantly more flexible than the uncollapsed sections, and advanced 120 nm within 1 month. The collapse of MWCNT1 was most likely initiated by its interaction with the surface, and possibly a water meniscus. The ability of carbon nanotubes to radially deform under the influence of surface interactions is in striking contrast with their extremely high axial rigidity.     

Study of the Microstructure of the Aluminum-Based Composite Material with the Addition of Carbon Nanotubes after Spark Plasma Sintering

Technical Physics - Electron microscopy is used to study samples of an aluminum matrix composite material with multiwalled carbon nanotubes (MWCNTs). The features of microstructure changes...     

Scaling law in carbon nanotube electromechanical devices

We report a method for probing electromechanical properties of multiwalled carbon nanotubes (CNTs). This method is based on atomic force microscopy measurements on a doubly clamped suspended CNT electrostatically deflected by a gate electrode. We measure the maximum deflection as a function of the applied gate voltage. Data from different CNTs scale into an universal curve within the experimental accuracy, in agreement with a continuum model prediction. This method and the general validity of the scaling law constitute a very useful tool for designing actuators and in general conducting nanowire-based nanoelectromechanical systems.     

Investigation of the radial compression of carbon nanotubes with a scanning probe microscope

Efforts have been made to characterize the mechanical properties of carbon nanotubes. Previous work has concentrated on the tubes' longitudinal properties, and studies of their radial properties have lagged behind. We have used a scanning probe microscope with an indentation/scratch function to investigate the radial compression of multiwalled carbon nanotubes under an asymmetric stress. In particular, we have determined the radial compressive elastic modulus at different compression levels and have estimated the compressive strength to be well beyond 5.3 GPa.     

Growth of multiwalled carbon nanotube arrays by chemical vapour deposition over iron catalyst and the effect of growth parameters

Multiwalled carbon nanotube (CNT) arrays were grown by catalytic thermal decomposition of acetylene, over Fe-catalyst deposited on Si-wafer in the temperature range 700-750 °C. The growth parameters were optimized to obtain dense arrays of multiwalled CNTs of uniform diameter. The vertical cross-section of the grown nanotube arrays reveals a quasi-vertical alignment of the nanotubes. The effect of varying the thickness of the catalyst layer and the effect of increasing the growth duration on the morphology and distribution of the grown nanotubes were studied. A scotch-tape test to check the strength of adhesion of the grown CNTs to the Si-substrate surface reveals a strong adhesion between the grown nanotubes and the substrate surface. Transmission electron microscopy analysis of the grown CNTs shows that the grown CNTs are multiwalled nanotubes with a bamboo structure, and follow the base-growth mechanism.     

Structure and properties of BeO nanotubes

The structure of a new non-carbon (beryllium oxide BeO) nanotube consisting of a rolled-up graphene sheet is proposed, and its physical properties are described. Ab initio calculations of the binding energy, the electronic band structure, the density of states, the dependence of the strain energy of the nanotube on the nanotube diameter D, and the Young’s modulus Y for BeO nanotubes of different diameters are performed in the framework of the density functional theory (DFT). From a comparison of the binding energies calculated for BeO nanotubes and crystalline BeO with a wurtzite structure, it is inferred that BeO nanotubes can be synthesized by a plasma-chemical reaction or through chemical vapor deposition. It is established that BeO nanotubes are polar dielectrics with a band gap of ～5.0 eV and a stiffness comparable to that of the carbon nanotubes (the Young’s modulus of the BeO nanotubes Y _BeO is approximately equal to 0.7Y _C, where Y _C is the Young’s modulus of the carbon nanotubes). It is shown that, for a nanotube diameter D > 1 nm, the (n, n) armchair nanotubes are energetically more favorable than the (n, 0) zigzag nanotubes.