depending on the initial structure of patterns cut out from the graphene. ... calculations but most they could reach a cage like structure with many defects.
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Chapter 2
Self Organizing Carbon Structures: Tight Binding Molecular Dynamics Calculations
István László Budapest University of Technology and Economics, Hungary Ibolya Zsoldos Széchenyi István University, Hungary Dávid Fülep Széchenyi István University, Hungary
ABSTRACT Graphene is a two-dimensional building material for the zero-dimensional fullerenes and the onedimensional nanotubes. Using mathematical constructions and identifying some atoms, these materials can be rolled up from appropriate patterns cut out from the hexagonal lattice of carbon atoms. The question arises if there is a realistic formation process behind this idealized construction. Although the first time the C60 and C70 fullerenes were produced by laser irradiated graphite, the fullerene formation theories are based on various fragments of carbon chains, and networks of pentagonal and hexagonal rings. The first successful results concerning fullerene formations in a priori molecular dynamics simulations based on a true quantum chemical potential was published twenty-one years after discovering the buckminsterfullerene. The greater application of fullerenes and nanotube faces the lack of selective growth and assembly processes. Here we review quantum chemical molecular dynamics calculations which selectively produce the buckminsterfullerene C60, the C70, the armchair and the zigzag nanotubes depending on the initial structure of patterns cut out from the graphene.
DOI: 10.4018/978-1-5225-0492-4.ch002
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Self Organizing Carbon Structures
INTRODUCTION Self organization has a vast literature (Glansdorff & Prigogine, 1971; Feltz et al., 2006) containing several topics from physics, chemistry, and biology. It can be applied for producing supercapacitor electrodes (Kim et al. 2015) and sub-10 nm nanostructures (Otsuka et al., 2015). In the present chapter we shall focus on the formation of carbon nanostructures as fullerenes and nanotubes. Till now the formation of fullerenes and nanotubes is still a mystery. The most important procedures in which fullerenes can be produced are the laser evaporation (Kroto et al., 1985), and the arc deposition (Krätscmer et al., 1990). In all of the other experimental conditions it looked that the fullerenes and nanotubes were produced in some kind of self organizing way. Any traditional chemical synthesis was unsuccessful (Scott et al., 2002; Kabdulov et al., 2013). Many authors tried to produce the C60 fullerene in molecular dynamics calculations but most they could reach a cage like structure with many defects. They also were using some kind of artificial conditions. Ballone and Milani (Ballone & Milani, 1990) kept the carbon atoms on the surface of a sphere for T > 4000 K, Chelikowsky (Chelikowsky, 1991) removed and randomly replaced the energetically unfavourable atoms and Wang et al. (Wang et al., 1992) confined the carbon atoms into a sphere. Irle et al. (Irle et al., 2006) developed the “shrinking hot giant” road that leads to the formation of buckminsterfullerene C60, C70, and larger fullerenes. In the present chapter we present two kind of self organizing processes for the formation of carbon nanostructures. First we present our results obtained for C80 fullerene formation in molecular dynamics simulation at helium atmosphere. In the second part of our work we present our results where carbon nanostructures are formed from graphene patterns containing the code of the final structure. The usual routes to graphene are the top-down approaches (Geim & Novoselov, 2007) but there are successful bottom-up approaches as well (Cataldo et al., 2011).
FORMATION IN HELIUM ATMOSPHERE Formation of Cage-Like C60 Clusters In these calculations we wanted to simulate the original laser evaporation experiment (Kroto et al., 1985) by “exploding” four different initial arrangements of carbon atoms (Laszlo, 1998, 1999). First we started the simulation with Kroto’s four-deck sandwich model 6:24:24:6 (Kroto, 1992). In this model there are 6 24, 24 and 6 carbon atoms in four layers of a graphite structure. Our unit cell of side 25.0 Å contained initially these 60 carbon atoms and 1372 randomly distributed helium atoms. The carbon-carbon interaction was calculated width the help of the tight-binding potential of Xu et al. (Xu et al. 1992) and the carbon-helium and helium-helium interaction was given by the Girifalco potential (Girifalco & Lad, 1956; Girifalco, 1992). In the calculations periodic boundary condition was used and the helium gas temperature Tgas was controlled with the help of Nosé-Hoover thermostat (Nosé, 1984; Hoover, 1985). In Figure 1 the Tgas = 4000K run is presented for this four-deck initial structure and for the other initial structure as well. We began the simulation process by giving an initial temperature of T = 13000K to the carbon atoms. The temperature of the helium gas fluctuated around the given Tgas temperature value and the temperature of the carbon atoms reached also this value due to the helium-carbon interactions.
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