Thermal Science & Engineering Vol.3 No.3 (1995) A Molecular Dynamics Simulation for the Formation Mechanism of Fullerene * Shigeo MARUYAMA † and Yasutaka YAMAGUCHI † Abstract The formation mechanism of fullerene, a new type of carbon molecule with a hollow caged structure, was studied using a molecular dynamics method. In order to simulate the basic reaction process observed in the arc-discharge or the laser vaporization fullerene generation, we have calculated the clustering process starting from randomly located isolated carbon atoms. Here, an empirical many- body carbon potential proposed by Brenner (1990) was employed. Under a certain condition of the initial density and the temperature control, the simulation yielded the hollow caged carbon network which could be regarded as an imperfect fullerene. Intermediate clusters observed in the clustering process were dimers, trimers, linear chains up to C10, mono-cyclic rings in C10-C15, poly-cyclic rings of about C20, fragments of 2 dimensional network, and the imperfect fullerene. One of the remarkable reactions was a linear chain wrapping a poly-cyclic ring to form a larger fragment of network structure. KEYWORDS: Fullerene, Molecular Dynamics Method, C60, Cluster, Condensation, Precursor * Received: March 17, 1995, Editor Susumu KOTAKE † Dept. of Mechanical Engineering, The University of Tokyo (Hongo, Bunkyo-ku, Tokyo 113, Japan Tel. 81-3-5800-6983) 1 Introduction Existence of soccer ball structured C 60 shown in Figure 1(a) was demonstrated by Kroto et al. (1985) through their time-of- flight mass spectra of carbon clusters generated by the laser- vaporization supersonic-nozzle technique. They observed a prominent C 60 + signal and the complete lack of odd numbered clusters. They named the cluster C 60 of truncated icosahedron as Buckminsterfullerene since the beautiful network structure resembled the famous geodesic dome designed by Buckminster Fuller. According to the Euler’s rule of geometry, a polyhedron with only pentagonal and hexagonal faces (5/6 polyhedron) must have 12 pentagons and n hexagons (n = 0, 2, 3, 4, ...). Then, the number of vertices (number of atoms) is 2n + 20. Truncated icosahedron is the case of n = 20. Since mass spectra of positive carbon clusters exhibited only even numbered clusters in the range of C 30 to at least C 600 [Rohlfing et al. (1984) and Maruyama et al. (1991)], we could speculate that all of those clusters had 5/6 polyhedral structure. Carbon clusters with such hollow close- caged structure are called fullerene [Figure 1]. In 1990 discoveries of simple techniques for macroscale generation and isolation of fullerene by Kra "tschmer et al. (1990), Haufler et al. (1991) and Taylor et al. (1990) made this new material ready for wide areas of applications. The observation of the superconductivity by Hebard et al. (1991) at T c = 19 K of potassium-doped C 60 crystal further accelerated the research field. Within a few years, macroscale amount of metal containing fullerene [Chai et al. (1991), Shinohara et al. (1992) and Kikuchi et al. (1993)], higher fullerenes [Kikuchi et al. (1992) and Achiba & Wakabayashi (1993)] and bucky tube in Figure 1(c) [Iijima (1991) and Ebbesen & Ajayan (1992)] were available. A common technique of the macroscale generation of fullerene is the arc-discharge method which is simply an arc- discharge of graphite electrodes under certain pressure of helium buffer gas proposed by Haufler et al. (1991). The amount of extracted fullerene compared to the collected soot can yield up to about 15% under the optimum condition as in Maruyama et al. (1994). Usually the generated fullerene consists of 80% of C 60 , 15% of C 70 and a small amount of higher fullerene like C 76 ,C 78 , C 82 ,C 84 , ..., quite interesting magic numbers. It is also surprising that once vaporized carbon atoms automatically form such highly symmetric structures like C 60 in the clustering process. Besides these theoretical interests, it is required to clarify the generation mechanism in order to find a more efficient generation method of the higher fullerene or the metal doped fullerene. Since the macroscale generation technique was found accidentally, the formation mechanism of fullerene is not clear. Several models have been proposed based on experimental insights. Haufler et al. (1991) described that a growth of a hexagonal network by successive additions of dimers and trimers eventually left pentagons as the defect. They claimed that the pentagons was essential to give the curvature and to decrease the number of dangling bonds. On the other hand, two neighboring pentagons should result too much strain to the network system, so the Isolated Pentagon Rule (IPR) was assumed. It is interesting to (a) C 60 (b) C 70 (c) Bucky tube Figure 1 Typical structures of fullerene