Kinks, rings, and rackets in filamentous structures

Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and "tennis racket" shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important determinant of the morphology than any molecular details. Our mesoscopic continuum theory is capable of quantifying observations of these structures, and is suggestive of their occurrence in other filamentous assemblies as well.Comment: This paper was originally published in PNAS 100: 12141-12146 (2003). The present version has corrected Eq. 3, A1, and A2, and some minor typo

Multi-shell gold nanowires under compression

Deformation properties of multi-wall gold nanowires under compressive loading are studied. Nanowires are simulated using a realistic many-body potential. Simulations start from cylindrical fcc(111) structures at T=0 K. After annealing cycles axial compression is applied on multi-shell nanowires for a number of radii and lengths at T=300 K. Several types of deformation are found, such as large buckling distortions and progressive crushing. Compressed nanowires are found to recover their initial lengths and radii even after severe structural deformations. However, in contrast to carbon nanotubes irreversible local atomic rearrangements occur even under small compressions.Comment: 1 gif figure, 5 ps figure

Structural stability and energetics of single-walled carbon nanotubes under uniaxial strain

A (10x10) single-walled carbon nanotube consisting of 400 atoms with 20 layers is simulated under tensile loading using our developed O(N) parallel tight-binding molecular-dynamics algorithms. It is observed that the simulated carbon nanotube is able to carry the strain up to 122% of the relaxed tube length in elongation and up to 93% for compression. Young s modulus, tensile strength, and the Poisson ratio are calculated and the values found are 0.311 TPa, 4.92 GPa, and 0.287, respectively. The stress-strain curve is obtained. The elastic limit is observed at a strain rate of 0.09 while the breaking point is at 0.23. The frequency of vibration for the pristine (10x10) carbon nanotube in the radial direction is 4.71x10^3 GHz and it is sensitive to the strain rate.Comment: 11 pages, 8 figure

Single- and multi-walled carbon nanotubes viewed as elastic tubes with Young's moduli dependent on layer number

The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky {\it et al.} \lbrack Nature (London) {\bf 355}, 333 (1992)\rbrack and shows to be content with the classic shell theory by which the Young's modulus, the Poisson ratio and the effective wall thickness of SWNTs are obtained as $Y=4.70$TPa, $\nu=0.34$, $h=0.75{\rm \AA}$, respectively. The elasticity of a multi-walled carbon nanotube (MWNT) is investigated as the combination of the above SWNTs of layer distance $d=3.4 {\rm \AA}$ and the Young's modulus of the MWNT is found to be an apparent function of the number of layers, $N$, varying from 4.70TPa to 1.04TPa for N=1 to $\infty$.Comment: 4 pages, 1 figur

Extreme structure and spontaneous lift of spin degeneracy in doped perforated bilayer graphenes

Extreme structure and spin states of doped and undoped perforated bigraphenes was studied using DFT simulations. It was found that folded nanopores possess extremely high curvature of 0.34 Å−1. Dramatic structural deformation causes severe changes of the chemical properties of carbon atoms localized at the nanopores converting the folded edges to local oxidative fragments. It was found that asymmetrical coordination of either Li, Ca, or Al to the nanopores is coupled with electron transfer from metal to edge carbon atoms and breakdown of local inversion symmetry. Li-, Ca-, and Al-doped perforated AA bigraphene revealed ferromagnetic spin ordering with magnetic moments of 0.38, 0.14, and 0.32μB/unit cell, respectively, and spin polarization energy gain of 0.037eV for Ca-doped superlattice. It was shown that ferromagnetic spin ordering of bigraphene nanopores contradicts to the Nagaoka's theorem, which excludes strong electron correlations as a reason of spin polarization. Spontaneous lift of spin degeneracy was interpreted in terms of perturbing intense local electrostatic fields from extra electron charges localized at the nanopore edges, coupled with breakdown of space inversion and local translation invariances. It was shown that spin energy splitting is proportional to the matrix elements calculated on Bloch states with opposite wavevectors and perturbing electrostatic fields

Atomistic Simulations of Nanotube Fracture

The fracture of carbon nanotubes is studied by atomistic simulations. The fracture behavior is found to be almost independent of the separation energy and to depend primarily on the inflection point in the interatomic potential. The rangle of fracture strians compares well with experimental results, but predicted range of fracture stresses is marketly higher than observed. Various plausible small-scale defects do not suffice to bring the failure stresses into agreement with available experimental results. As in the experiments, the fracture of carbon nanotubes is predicted to be brittle. The results show moderate dependence of fracture strength on chirality.Comment: 12 pages, PDF, submitted to Phy. Rev.

Nonlinear resonance in a three-terminal carbon nanotube resonator

The RF-response of a three-terminal carbon nanotube resonator coupled to RF-transmission lines is studied by means of perturbation theory and direct numerical integration. We find three distinct oscillatory regimes, including one regime capable of exhibiting very large hysteresis loops in the frequency response. Considering a purely capacitive transduction, we derive a set of algebraic equations which can be used to find the output power (S-parameters) for a device connected to transmission lines with characteristic impedance $Z_0$.Comment: 16 pages, 8 figure

Coil Formation in Multishell Carbon Nanotubes: Competition between Curvature Elasticity and Interlayer Adhesion

To study the shape formation process of carbon nanotubes, a string equation describing the possible existing shapes of the axis-curve of multishell carbon tubes (MCTs) is obtained in the continuum limit by minimizing the shape energy, that is the difference between the MCT energy and the energy of the carbonaceous mesophase (CM). It is shown that there exists a threshold relation of the outmost and inmost radii, that gives a parameter regime in which a straight MCT will be bent or twisted. Among the deformed shapes, the regular coiled MCTs are shown being one of the solutions of the string equation. In particular,the optimal ratio of pitch $p$ and radius $r_0$ for such a coil is found to be equal to $2\pi$, which is in good agreement with recent observation of coil formation in MCTs by Zhang et al.Comment: RevTeX, no figure, 12 pages, to appear in Phys. Rev. Let

In-situ observation of graphene sublimation and edge reconstructions

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