Session Y29: Focus Session: Carbon Nanotubes and Related Materials XVI: Mechanical and Thermal Properties

Anisotropic Casimir interactions between a one-dimensional object (nanotube) and a polar substrate

The energy of Casimir interaction of a polarizable one-dimensional object (1DO), e.g. a nanotube, and a polar substrate was estimated. Within our model the energy of the dipole moment induced in the 1DO by the external electric field of the fluctuations of the quantized surface optical phonon modes is evaluated. Such polariton modes are known to exist in polar insulators and have the electric field with an exponentially decreasing wing in vacuum. If the polarization tensor of the 1DO is not isotropic, an orientation dependent Casimir force may arise. To the best of our knowledge, such anisotropic Casimir interaction has not been considered before and may lead to an orientation of long flexible objects, like nanotubes, at polar substrates. The interaction energy is derived analytically for the case of a single-wall nanotube on the ST-cut quartz. Besides a material dependent energy constant, it is proportional to the ratio of the volume of interacting segment of the nanotube and cube of the distance to the substrate.   

Dynamics and energy dissipation of nano-graphite mechanical devices.

Controllable mechanical motion of nano-structures holds great interests because of their applications in the nano-electromechanical systems (NEMS). One of the novel models proposed was the nano-graphitic materials based devices, where planar or cylindrical graphene layers act as moving parts and the motion is managed by the van der Waals force between them. Comparing with the multi-walled carbon nanotubes, nano-graphite flakes have an accessible scale for current techniques. Recent experiments using nano-mechanical manipulator have shown self-retraction motion of micrometer graphite layers after mechanical extrusion (Zheng et al. submitted to PRL). However, persistent oscillation as expected was not observed. The short lifetime implies severe energy dissipation. Analysis based on MD simulation show that the coupling with rotation and lattice vibration contribute significantly. Furthermore we have discussed the effects of edge instabilities, surface contamination and non-planar deformation, which also introduce complexities into the dynamics as approved by the experimental observation.   

Large Negative Thermal Expansion of an Individual Carbon Nanotube

It is of fundamental value to understand the thermo-mechanical properties of individual carbon nanotubes (CNTs). The coefficient of thermal expansion (CTE) of CNTs has been a subject of considerable debate in the literature with more recent works predicting thermal contraction. Because of the small size, experimental measurement of individual CNTs is very difficult; So far only limited data was reported by X-ray diffraction that measured the average CTE of many tubes. Here, we use nanoarea electron diffraction to measure the CTE of an individual Multi-walled carbon nanotube (MWCNT) and correlate the CTE with the tube atomic structure. All the 4 walls of this individual MWCNT show apparent radial diameter thermal contraction from 297 to 827k, and thermal expansion from 827 to 1027k. The radial CTE has strong diameter dependence between 297 and 827k; It changes from (-6.48$\pm$0.46) E-5 (1/K) for the wall with the theoretical diameter 16.4 A to (-2.37$\pm$0.77) E-5 (1/K) for the wall with the theoretical diameter 37.3 A, which means smaller diameter wall contracts more. On the other hand, all the 4 walls of this individual MWCNT show apparent axial thermal contraction from 297 to 1073k. The axial CTE is independent of the diameter, and the average axial CTE for different walls is (-1.30$\pm$0.07) E-5 (1/K).   

Optical Measurement of Thermal Contact Resistance in Suspended Carbon Nanotubes

We observe the local temperature increase profile $\Delta T(x)$ along suspended carbon nanotubes (CNTs) by converting the shifts in the $G$-band Raman mode to temperature. By deconvolving the temperature profile using the Fourier heat transport equation, we determine the thermal contact resistance ($R_{c})$ relative to the intrinsic thermal resistance of the nanotube itself ($R_{NT})$. The curvature of the temperature profile is found to be dominated by the ratio of $R_{NT }$to $R_{c}$. Moreover, the difference between the left and right thermal contact resistances can also be differentiated via the offset of the temperature increase at the ends of the suspended CNT. The results show the ratio of the contact thermal resistance to the nanotube thermal resistance to range from 0.02 to 17. The measurement is also able to distinguish between ballistic and diffusive thermal transport. We find diffusive thermal transport to dominate the heat transport in all nanotubes measured in this study. The authors would like to acknowledge support from DOE Award Nos. DE-FG02-07ER46376 and DE-FG02-07ER46377. I.K. Hsu \textit{et al.}, Applied Physics Letters (in press).   

Thermal Conductance Measurement of Metal-CNT Composites using Micro-Sized Suspended Structure

As CNTs have a unique structure and remarkable physical properties, CNT composites have attracted much attention from many researchers. Especially the thermal properties of CNTs and their composite materials have been studied intensively, because CNT has very good thermal transport properties [1-5]. For example, thermal conductivity of CNT is known to be much larger than that of metals such as Ag, Au, Cu and Al. To study the thermal conductance of metal-CNT composites, we have fabricated the micro-sized suspended structures. By using e-beam lithography and metallization, two thermometers have been patterned on the GaAs substrates. Thermal links made of metal or metal-CNT composite also have been patterned between the two thermometers. Then GaAs substrate has been under-etched to form suspended structures. We will show the fabrication methods and measurement scheme using these microstructures. $^{*}$ parkyd@phya.snu.ac.kr [1] J.A. Eastman \textit{et al.}, Appl. Phys. Lett. \textbf{78}, 718 (2001). [2] S.U.S. Choi \textit{et al.}, Appl. Phys. Lett. \textbf{79}, 2252 (2001). [3] M.J. Biercuk \textit{et al.}, Appl. Phys. Lett. \textbf{80}, 2767 (2002). [4] R. Ramasubramaniam \textit{et al.}, Appl. Phys. Lett. \textbf{80}, 4647 (2003). [5] H.Q. Xia \textit{et al.}, Appl. Phys. Lett. \textbf{94}, 4967 (2003).   

Thermal conductivity of isolated and interacting carbon nanotubes

We have investigated the thermal conductivity of single wall carbon nanotubes (SWCNT) either isolated or in contact with external media, by using equilibrium molecular dynamics and the Boltzmann transport equation\footnote{Chantrenne {\sl et al.} J. Appl. Phys. \textbf{97}, 104318 (2005).}. We show that, contrary to existing controversies, both methods yield a finite value of the thermal conductivity for infinitely long tubes, as opposed to the case of 1D momentum conserving systems\footnote{O. Narayan and S. Ramaswamy, Phys. Rev. Lett. \textbf{89}, 200601 (2002).}. Acoustic and flexure modes with mean free paths of the order of a few micron, as observed also in experiments\footnote{C.~Yu, {\sl et al.} Nano Lett. \textbf{5}, 1842 (2005).}, are identified as major contributors to the high value of SWCNT conductivity. We also find that the interaction with an external medium may substantially decrease the lifetime of the low frequency vibrations, reducing the thermal conductivity by up to two orders of magnitude.   

Determination of carbon nanotube wall thickness and elasticity by atomic force micrsocopy.

To understand the operation of carbon nanotube (CNT) devices it is important to determine whether nanotubes are single-walled or multi-walled. Transmission electron microscopy of CNTs has previously been the only tool available to count the number of graphene sheets forming the wall of a CNT. We show that atomic force microscopy can measure CNT wall thickness by squeezing individual nanotubes between a tip and a hard surface. Full compression of single-walled and double-walled CNTs can be achieved either by a static force or by ac-mode imaging, allowing clear determination of wall number. Direct measurements of compression forces are used to determine the elastic properties of the wall, yielding the bending modulus of graphene.   

Pressure Induced Changes in the Atomic and Electronic Structure of Carbon Nanotubes

We present first principle density functional calculations on small diameter single walled carbon nanotubes to explore the changes in their electronic structure and atomic arrangement under hydrostatic compression. Simulations on zigzag (n, 0) SWCNT 6$\le $n$\le $9 using the full potential projector augmented wave and ultra-soft pseudo potentials were conducted. Large structure-related changes are found in the density of states at the Fermi energy. The cross sections of small tubes exhibits deformations not predicted by classical models. The structural cross sections of large diameter tubes$^{1}$ (10, 0) calculated under moderate pressure are consistent with the reported results. The details of calculations and other results will be presented. This work is supported in part by NSF DMR-0512196. \begin{enumerate} \item Paul Tangney, Rodrigo B. Capaz, Catalin D. Spataru, Marvin L. Cohen and Steven G. Louie, Nano Lett. 5, 2268 (2005). \end{enumerate}   

Nanomechanical energy transfer in carbon nanotubes: fundamental insights from molecular dynamics simulations

Single wall carbon nanotubes have been employed as oscillating elements in nanoeletromechanical resonators (NEMS), attaining very high frequencies but disappointingly low quality factors. Despite the amount of work regarding internal friction, intrinsic dissipation within such nanoscale systems is still poorly understood. In this work we employ molecular dynamics simulations to gain insight into how energy is dissipated in a plucked CNT. It is found that dissipation exhibits two regimes depending on the background temperature. At high temperature, the energy decay is exponential, resembling the behavior of a classical damped oscillator, while at low temperatures an initial transient region is observed during which there is little damping. Increasing the duration of this transient region could be a route for engineering higher Q factors NEMS resonators.   

A Failure Criterion for Single-Walled Carbon Nanotubes Based on Molecular Mechanics

Single-walled carbon nanotubes (SWNT) are the natural choice for high performance materials. The problem, however, rises when the experimental data are compared against each other. The large variability of experimental data lead to development of a new set of numerical simulations called molecular mechanics, which is a ``symbiotic'' association of molecular dynamics and solid mechanics. This papers deals with a molecular mechanics simulations of single-walled carbon nanotubes. Three SWNT configurations and its combinations were simulated, i.e. armchair, zigzag and chiral. The failure criterion introduced is based on modified Morse's potential with dissociation energy of 124 Kcal/mol and an inflection point considered is around 13{\%} of strain. The numerical data are in good agreement with data from Belytschko et al. (2002) where the failure occurred at 10.6{\%} strain at 65.2 GPa of stress. To be able to identify the highest stress concentration region, one end of the SWNT all degrees-of-freedom were fixed and a prescribed axial displacement was applied at the opposite end. The Sadoc (chiral-chiral) configuration had the highest stress at the smallest chiral SWNT. For the Dunlap configuration (chiral-zigzag) the highest stress occurred at chiral part close to the pentagon location.   

Excitons in Single-Walled Carbon Nanotubes in Different Local Environments: Effects of Strain and Disorder on Magnetic Brightening

Recent experiments on single-walled carbon nanotubes (SWNTs) have shown that in the presence of a high magnetic field the two lowest-energy spin-singlet exciton states become bright [1]. Furthermore, this ``magnetic brightening'', or increase in photoluminescence (PL) intensity as a function of magnetic flux through each SWNT, increases as the temperature decreases. Here, we report results of temperature-dependent magneto-PL from 2 to 200 K and up to 45 T on SWNTs of the same stock solution suspended in four different local environments. We compared both the brightening and temperature dependence of tubes stretch aligned and unaligned in poly-acrylic acid matrices. As expected, the tubes aligned at high magnetic field exhibited more brightening than those unaligned. We also investigated the behavior of SWNTs in two other matrices, iota-Carrageenan and gelatin. Along with the expected peak shifting and broadening from the effects of strain, we found that the temperature dependence changes with local environment. [1] S. Zaric \textit{et al}., PRL \textbf{96}, 016406 (2006); J. Shaver \textit{et al}., Nano Lett. \textbf{7}, 1851 (2007); I. B. Mortimer and R. J. Nicholas, PRL \textbf{98}, 027404 (2007).   

Carbon nanotube nanomechanical mass sensors

Single-walled carbon nanotubes are arguably the lightest and smallest wires in the world, and have recently been shown to act as nanomechanical resonators [1]. As a result, single-wall carbon nanotubes are excellent candidates for highly sensitive mass sensing [2]. We observed the down shift of the resonant frequency of a suspended double-clamped carbon nanotube resonator at cryogenic temperatures upon helium mass loading. Using a straightforward estimate of the nanotube mass, the observed frequency shift corresponds to the mass of $\sim $1000 helium atoms, which is the zeptogram range. This is considerably smaller than found previously with nanotube resonators, and comparable to that found using nanowire resonators [3]. Our noise floor is currently $\sim $1 Xenon atom per root Hz, which may enable single-atom detection in future experiments. [1] Vera Sazonova, et al., Nature \textbf{431}, 284 (2004). [2] H. B. Peng, et al. Phys. Rev. Lett. \textbf{97}, 087203 (2006) [3] Y. T. Yang, et al. Nano Lett. \textbf{6}, 583 (2006).   

Anharmonic phonon lifetimes in carbon nanotubes, graphene and graphite

In this work we present a first-principles study of the anharmonic phonon lifetimes of the key vibrational modes that most strongly interact with electrons in carbon nanotubes, graphene and graphite. The calculations of both harmonic and anharmonic properties are performed using density-functional theory and density-functional perturbation theory. Our results---in excellent agreement with the available experimental data---provide a microscopic characterization of the energy relaxation mechanisms and of the relative importance of the individual decay channels. We will discuss the relevance of these results to elucidate the role of non-equilibrium phonon populations in high-field electronic transport.   

Measurement of mechanical properties of graphene using nanoindentation

Mechanical properties of graphene have been measured using AFM nanoindentation. Mono-, bi-, and tri-layer graphene sheets are suspended over micron-sized circular hole arrays. Force-displacement curves obtained by AFM nanoindentation allow the extraction of mechanical properties such as Young's modulus and fracture strength using equations for thin circular membranes. In order to verify the validity of the equations, the experimental and analytical results were compared with finite element simulation. The analytical equations fitted to the measurements show that Young's modulus is 0.9-1.2 TPa and the fracture strength is 90-150 GPa for up to 3 layers.   

Electrical conductivity of individual, thermally reduced graphene oxide sheets

Electrical properties of individual graphene oxide sheets were investigated. Graphene oxide itself is insulating, but its conductivity is finite and measureable following heat treatment in vacuum. The dependence on temperature and time for reduction of graphene oxide were fit to a standard chemical kinetics rate law and from this an activation energy of 30 kcal/mole was found. I-V curves, obtained at several stages of the chemical reduction achieved by heating, are non-linear and slightly asymmetric. The effect of applying an electric field via a back gate and the resulting change in resistance was measured at different temperatures and at different stages of reduction. The maximum conductivity by thermal annealing graphene oxide sheets was 85 S/m at room temperature and zero gate potential. This value was determined based on 4-probe pseudo Van der Pauw measurements and numerical modeling and using 1.0 nm as the sheet thickness.