C. J. Brabec

Structural flexibility of carbon nanotubes

We report high resolution electron microscope (HREM) observations and atomistic simulations of the bending of single and multi‐walled carbon nanotubes under mechanical duress. Single and multiple kinks are observed at high bending angles. Their occurrence is quantitatively explained by the simulations, which use a realistic many‐body potential for the carbon atoms. We show that the bending is fully reversible up to very large bending angles, despite the occurrence of kinks and highly strained tube regions. This is due to the remarkable flexibility of the hexagonal network, which resists bond breaking and bond switching up to very high strain values.

High strain rate fracture and C-chain unraveling in carbon nanotubes

Abstract Nanotube behavior at high rate tensile strain (~ 1 MHz) is studied by molecular dynamics using a realistic many-body interatomic potential. The simulatins performed for single- and double-walled nanotubes of different helicities, and at different temperatures, show that nanotubes have an extremely large breaking strain. It decreases somewhat with increasing temperature and smaller strain rate, while the influence of helicity is very weak. At later stages of fracture, the nanotube fragments are connected by a set of unraveling monoatomic chains. The chains ‘compete’ with each other for carbon atoms popping out of the original tube segments. The interaction between chains eventually leads to a single chain, which grows up to hundreds of atoms in length before its breakage.

GROWTH OF CARBON NANOTUBES : A MOLECULAR DYNAMICS STUDY

Abstract Molecular dynamics with realistic many-body atomic potentials was used to study the growth of carbon nanotubes. Analysis of the bond switching and ring migration processes has led to an identification of tube growth mechanisms. Wide tubes, initially open, were found to grow straight maintaining an all-hexagonal structure, while narrow tubes were found to develop permanent pentagonal rings that lead to tube closure upon further deposition. Continued deposition on the top of a closed tube yields a disordered cap structure, implying that open tubes are critical for defect-free growth.

Structural defects and the shape of large fullerenes

Abstract Motivated by the recent experimental observation of nearly spherical multi-layer fullerenes, we investigate theoretically the role of thermally generated structural defects on the shape and stability of large fullerenes by equilibrium statistical mechanics methods. Low energy defects are generated via atom insertions and bond rotations and the resulting structures are relaxed using realistic atomic potentials. The lowest defect formation energies are about 1 eV. A free energy analysis shows that large fullerenes will contain a substantial number of such defects at high temperatures. The presence of these defects effectively spreads out the sharp “kinks” associated with the faceted ground state structure, leading to a more spherical cage of a uniform curvature.

Structural mechanics of carbon nanotubes: From continuum elasticity to atomistic fracture

SummaryMotivated by recent observations of bent, collapsed and twisted carbon nanotubes, we investigate their behavior at large deformations. These hollow molecules behave remarkably similar to their macroscopic homologs. They reversibly switch into different morphological patterns, and each shape change corresponds to an abrupt release of energy and a singularity in the stress-strain curve. These transformations, simulated using a realistic many-body potential, are accurately described by a continuum-shell model. In contrast, a response to axial tension proceeds smoothly up to a fracture threshold, beyond which a monoatomic carbon chain unravels between the tube fragments.

Theoretical Investigations of Carbon Nanotube Growth

Abstract The growth of carbon nanotubes was investigated using a variety of complementary simulation techniques. Currently, a number of experimental methods are used to synthesize carbon nanotubes suggesting that different mechanisms play a role in their formation. However, it has been shown that growth of nanotubes takes place primarily at the open-ended tips of nanotubes. Ab initio simulations show that the high electric fields present at the nanotube tips in carbon arc discharges cannot be responsible for keeping the tubes open. Rather, the opening and closing of tubes is controlled by the formation of curvature-inducing defects such as adjacent pentagon pairs. On narrow tubes, the formation of such defects is favored leading to the rapid closure of the tubes. By contrast, the formation of hexagons, which lead to straight open-ended growth is favored on large-diameter tubes, with an estimated crossover radius of about 3 nm. Large-scale molecular dynamics and kinetic Monte Carle simulations have been used to verify these ideas. We have also explored the role of the so-called lip–lip interactions during growth. Such an interaction is important in producing multiwalled nanotubes, where the interaction between two open nanotube tips leads to the formation of a network of bonds. Simulations show that such an interaction is indeed significant, but does not provide the additional stabilization required for straight, open-ended, multiwalled nanotube growth. Finally, we consider the formation of nanotubes in the presence of large and small catalytic particles. In the former case, growth is believed to take place via a root-growth mechanism, while the direct adsorption and extrusion of carbon from the vapor dominates the latter. Both mechanisms lead to the formation of small-diameter, single-wall nanotubes.

ZERO AND FINITE TEMPERATURE STUDY OF SINGLE FULLERENE CAGES AND CARBON “ONIONS” — GEOMETRY AND SHAPE

Scaling arguments are used to show that above a critical size of several thousand atoms, there is a stability crossover from single to multilayer cages. Conjugate gradient minimization using a classical three-body interatomic potential, as well as tight-binding electronic structure calculations yield ground-state configurations for large fullerene shells that are polyhedral with clearly faceted geometry. The structure, energetics and configurational entropy associated with low-energy defects are calculated and the number of defects estimated as a function of temperature. The role of these thermally generated defects on the shape of large fullerenes is investigated in order to explain the nearly spherical shapes of the newly discovered carbon “onions”.

Structural transformations, reactions, and electronic properties of fullerenes, onions, and buckytubes

Abstract We describe the results of extensive quantum molecular dynamics calculations of the properties of fullerenes and microtubules. The topics to be discussed include: (i) stability of C 60 isomers and barriers to isomerization; (ii) reactivity of C 60 and C 58 with C 2 and C 3 , and its implications on the formation and growth of fullerenes; and (iii) atomic and electronic structure and doping of semiconducting microtubules. We also discuss the structures, stabilities and atomic transformations of large multishell fullerenes and offer an explanation for the formation of spheroidal “onions” under high fluence electron irradiation conditions. The last results, which involved calculations for up to ∼ 15 000 atoms, were obtained using classical three-body potentials.

QUANTUM MOLECULAR DYNAMICS OF CLUSTERS

Recent quantum molecular dynamics studies of Al and carbon clusters are described. For Al, we focused on the 13- and 55-atom clusters, which can assume perfect icosahedral and cubic structures. However, the distortions from these ideal structures are substantial. For the 55-atom cluster, several inequivalent but nearly energetically degenerate structures are found, due to the short range of the screened interatomic interactions. For solid C60, it is found that the soccerball structure is well-preserved in the solid. The intermolecular interactions are so weak that the individual C60 can rotate at relatively low temperatures. At high temperatures vibrations cause large distortions, but the cage structure is still preserved. The C60 isomer containing two pairs of adjacent five-fold rings has a binding energy only 1.6 eV smaller than that of perfect C60, but the transformation between these two structures is hindered by a 5.5 eV barrier. It thus requires high temperatures and long annealing times. High temperatures are also needed for the transformation of the lowest energy C20 isomer, a dodecahedron, to a corannulene structure, which can be thought of as a fragment of C60. The corannulene structure is a natural precursor for the formation of C60. These results are consistent with the experimental findings that high temperatures are necessary for the formation of substantial quantities of C60. A formulation and the first applications of a new, real space quantum molecular dynamics method, particularly suitable for cluster calculations, are also described.

STRUCTURE, DYNAMICS, AND FORMATION OF CARBON AND ALUMINUM CLUSTERS

The results of recent ab initio molecular dynamics studies of C and Al clusters are presented. The simulations have shown that C60 molecular structure is well preserved in the solid and that the individual C60 molecules start to rotate at relatively low temperatures. Our results are in very good agreement with NMR, photoemission, and neutron scattering data. At high temperatures C60 undergoes large amplitude soccerball-rugbyball oscillations, but the cage structure is still preserved. The C60 isomer containing two pairs of adjacent pentagons has a binding energy only 1.6 eV smaller than that of perfect C60, but high temperatures and long annealing times are required for the transformation between these two structures. Its activation energy is 5.4 eV. We have also studied the various isomers of C20, since it could form the smallest possible fullerene. At T=0, the lowest energy isomer is indeed a dodecohedral structure. However, high temperatures favor the corannulene structure, which is a perfect precursor...