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Multi-Scale Modeling of Processing of Carbon Nanotubes

H.S. Choi, K.H. Kim, K-H Hong, J. Kim, H.S. Lee, J.K. Shin, A.V. Vasenkov, A.I. Fedoseyev and V. Kolobov
Samsung Advanced Institute of Technology, KR

multiscale simulation, carbon nanotube, molecular dynamics, kinetic monte-carlo, plasma, coarse time stepper, gap-tooth method

The current rapid development of nanotechnology has created a significant interest to predict the behavior of materials from the atomic to the engineering scales. However, it was found that such prediction is a very challenging problem since existing atomistic models are too slow, while mesoscopic and/or continuum codes are not capable of capturing nanoscale effects. This paper addresses this problem by introducing a Multi Scale Computational Framework (MSCF) which couples a reactor-scale module for gas/plasma-phase and surface processes, a Kinetic Monte Carlo (KMC) – FILM module for the growth of molecular structures, Molecular Dynamics (MD) NAMD module for the self-assembly of atoms into molecular structures, a “Gap-tooth” module for bridging reactor-scale and atomistic KMC simulations, and a “Coarse timestepper” module for coupling KMC and MD modeling. This framework works on length and time scales that are a million times disparate as shown in Fig. 1. The high efficiency was achieved due to the use of continuum model in large gaps where details of atomic motion are unimportant, while atomistic KMC-FILM and NAMD modeling was performed in tiny teeth where atoms self-assemble into molecular structures. The interactions between different modules of MSCF in a time interval from to, where is the mesoscopic time step, was conducted as follows. NAMD performed MD modeling for a nanoscopic time in each tiny tooth and computed the rates of surface processes and their derivatives in time. This was accomplished by using a reactive MD approach introduced by Nyden et al, 2003. The MD results were transferred to the Coarse timestepper module which calculated the time-dependent rates using the Newton-Raphson method. The rates were used by KMC-FILM for simulating system evolution in teeth using a microscopic time step. Subsequent to each KMC-FILM iteration, the Coarse timestepper module performed the stability analysis of the solution and repeated a KMC-FILM iteration if necessary. If the check for stability was successful, the incoming fluxes for each tooth were updated by the Gap-tooth module from the fractions of outgoing KMC fluxes obtained in the nearest teeth and NAMD was called by the Coarse timestepper module for updating time-dependent rates. Once the simulation time in KMC-FILM reaches, the continuum CFD-ACE was called by the Gap-tooth module for modeling the majority of surface and gas/plasma-phase processes and providing the fluxes of absorbed species for KMC. The feasibility of MSCE was investigated for plasma-assisted growth of carbon nanotubes (CNTs). An example of KMC-FILM results is shown in Fig. 2 where catalytic growth of CNTs includes the diffusion of carbon atoms through catalyst particle, and incorporation of carbon into CNT. Dominant path for delivering the supply of carbon onto growing CNT surface and existence of two different modes during CNT growth are discussed.

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