Vibrational modes of graphitic fragments and the nucleation of carbon nanotubes
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Vibrational modes of graphitic fragments and the nucleation of carbon nanotubes Manuela Volpe1, Fabrizio Cleri2 and Gregorio D’Agostino Ente Nuove Tecnologie, Energia e Ambiente, Divisione Materiali Centro Ricerche Casaccia, CP 2400, I-00100 Roma, Italy Vittorio Rosato2 Ente Nuove Tecnologie, Energia e Ambiente, High-Performance Computing Project Centro Ricerche Casaccia, CP 2400, I-00100 Roma, Italy 1also with Dipartimento Scienze e Tecnologie Chimiche, Università Tor Vergata, Roma, Italy 2also with Istituto Nazionale per la Fisica della Materia, Roma, Italy ABSTRACT We studied the nucleation mechanism of carbon nanotubes based on the hypothesis that the starting nanotube seed can be nucleated by rolling a small fragment of a graphite sheet (graphene) under thermal fluctuations. The energy barriers for rolling a graphene along different crystallographic directions are calculated from a tight-binding model,. We then estimate the relative weight of the large-amplitude fluctuations corresponding to low-frequency vibrational modes of graphene sheets of increasing size. Direct molecular dynamics simulation of the hightemperature fluctuation of a pair of parallel graphenes demonstrates that a nanotube closed at one end can spontaneously form. We discuss the combined effects due to: (a) the decrease of the energy barriers against rolling with increasing nanotube radius, and (b) the increase of random fluctuations with increasing size of the graphene sheet. The superposition of such effects may lead to a preferential range of nanotube diameters which could nucleate more abundantly than others.
INTRODUCTION The detailed atomic-scale mechanism by which a carbon nanotube can be formed from graphite under high-energy processing, such as arc discharge [1-3] or laser evaporation [4] is still far from known. Extensive experimental studies of the growth of carbon nanotubes under different conditions have provided useful insights into the microscopic growth mechanisms. Time-resolved experiments in which the high-temperature reaction zone is monitored give evidence that most of the free carbon is either atomic or aggregated in dimers and trimers. From these studies it is becoming clear that nanotube growth must occur by addition of C, C2 or C3 to a pristine seed with cylindrical shape, eventually attached to a catalyst particle. Different theoretical models have addressed specific aspects of the growth of both singlewall (SWNT) and multi-wall nanotubes (MWNT). For SWNT growth in presence of metal catalysts the scooter model [5] and the root-growth mechanism [6] have been proposed, while for MWNTs the role of lip-lip interaction in limiting the growth rate has been investigated [7]. Molecular dynamics simulations have been very useful in establishing several details of the growth mechanism [8-10] as, for example, the cap formation process [11] and the incorporation of C2 dimers in SWNT [12]. The role of pentagonal and heptagonal defects in inducing local curvature in the perfect hexagonal network of sp2 bonds has been repeatedly str
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