Collision-induced fusion of two ${\text{C}}_{60}$ fullerenes: Quantum chemical molecular dynamics simulations

Collision-induced fusion of two $C_{60}$ fullerenes: Quantum chemical molecular dynamics simulations

Jacek Jakowski, Stephan Irle, and Keiji Morokuma

Phys. Rev. B 82, 125443 – Published 24 September 2010

Abstract

We characterize the collision-induced fusion reaction of buckminsterfullerenes by means of direct self-consistent-charge density-functional tight-binding molecular dynamics simulations. In agreement with experimental data, we find that the highest probability of fusion is for collisions with incident energy range of 120–140 eV. In this energy region, fusion occurs by way of the formation of hot, vibrationally excited peanut-shaped structures within 1 ps. These nanopeanuts further undergo relaxation to short carbon nanotubes and are cooling by evaporation of short carbon chains during the next 200 ps. The size of the fusion product after the evaporation agrees well with the average size of carbon clusters experimentally detected after collisions on the microsecond time scale. The average number of $s p^{3}$ carbons in our simulations is in an excellent correlation with experimental cross sections.

Received 27 April 2010

DOI:https://doi.org/10.1103/PhysRevB.82.125443

Authors & Affiliations

Jacek Jakowski^*

National Institute for Computational Sciences, JICS-ORNL, One Bethel Valley Road, Bldg 5100 ms 6173, Oak Ridge, Tennessee 37831, USA and Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, 1515 Dickey Drive, Atlanta, Georgia 30322, USA

Stephan Irle^†

Institute for Advanced Research and Department of Chemistry, Nagoya University, Nagoya 464-8602, Japan

Keiji Morokuma^‡

Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, 1515 Dickey Drive, Atlanta, Georgisa 30322, USA and Fukui Institute for Fundamental Chemistry, Kyoto University, Sakyo, Kyoto 6006-8103, Japan

^*jacek@euch4e.chem.emory.edu
^†sirle@iar.nagoya-u.ac.jp
^‡morokuma@euch4e.chem.emory.edu

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Vol. 82, Iss. 12 — 15 September 2010

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Figure 1
(Color online) Schematic outcomes of collision between fullerenelike (denoted as circle or oval) structures: (a) nonreactive elastic scattering, (b) dimerization/polymerization, (c) collision-induced internal reorganization/inelastic scattering, (d) partial coalescence, (e) full coalescence, (f) fragmentation. Black arrows on panels (a) and (c) and on left panel represent velocity vector of corresponding unit.Reuse & Permissions
Figure 2
(Color online) Time dependence of kinetic and potential energy during collision MD between two $C_{60}$ with $T_{e l} = 2000 K$ . Top left: elastic collision (route A) with CM kinetic energy $E_{k i n} = 3.6 eV$ . Top right: inelastic collision without significant structure deformation (route A) at $E_{k i n} = 42 eV$ . Bottom left: collision-induced partial fusion (route D) at $E_{k i n} = 102 eV$ . Bottom right: collision induced disintegration of carbon skeleton (route F) at $E_{k i n} = 141 eV$ . The difference between total kinetic energy (green) and collision kinetic energy (purple) is a heat energy (1500 K). At time =0 fs the ordering of plots (from top to bottom) is Ekin( $coll + heat$ ), Ekin (CM), Etot (dotted line), Epot (solid line).Reuse & Permissions
Figure 3
(Color online) Collision-induced symmetry change for incident kinetic energy equals 79 eV. The initial symmetry of both fullerenes before collision was $I_{h}$ . The coloring of carbon atoms is chosen to emphasize the symmetry of fullerenes.Reuse & Permissions
Figure 4
(Color online) Left: experimental fusion cross section from Ref. 5 for collision between $C_{60}^{+}$ and $C_{60}$ . Right: theoretical average number of $s p^{3}$ -type carbon atoms from current SCC-DFTB MD collisions between two $C_{60}$ calculated as average over 50 trajectories at any given value of collision energy. Structure beneath is an MD frame from 127.3 eV, $T_{e l} = 2000 K$ trajectory at time 2 ps (see also Table ). $s p$ -, $s p^{2}$ -, and $s p^{3}$ -type carbons are marked by purple, yellow, and cyan, respectively.Reuse & Permissions
Figure 5
(Color online) Post collision transformation of a peanutlike structure to a short CNT structure within 200 ps. The collision energy was 127 eV. During relaxation, 20 carbon atoms evaporated from $C_{120}$ fusion product as short chains, leading to the $C_{100}$ structure at 120 ps. Estimated theoretical temperature of two fused fullerenes after collision at 2 ps was 4000 K.Reuse & Permissions
Figure 6
(Color online) Maximum (open squares), minimum (full squares), and average (full circles) carbon cluster mass observed experimentally as the product of a fusion reaction as a function of collision energy from Ref. 27. The full line is an estimate of the cluster from the statistical thermal evaporation model (Ref. 34). The open circle (red) is result from the current post collision relaxation simulation. For collision energy 127 eV, we observed that 20 carbons evaporated from the hot $C_{120}$ fusion product within 0.2 ns SCC-DFTB dynamics.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Collision-induced fusion of two $C_{60}$ fullerenes: Quantum chemical molecular dynamics simulations

Jacek Jakowski, Stephan Irle, and Keiji Morokuma

Phys. Rev. B 82, 125443 – Published 24 September 2010

Abstract

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Physical Review B

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Collision-induced fusion of two C60 fullerenes: Quantum chemical molecular dynamics simulations

Jacek Jakowski, Stephan Irle, and Keiji Morokuma

Phys. Rev. B 82, 125443 – Published 24 September 2010

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Collision-induced fusion of two $C_{60}$ fullerenes: Quantum chemical molecular dynamics simulations