Multiscale modelling of Carbon nanotubes
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Multiscale modelling of Carbon nanotubes Marc Hamm, James A. Elliott, Huw J. Smithson, Alan H. Windle Macromolecular Materials Laboratory, Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QE ABSTRACT A comprehensive understanding of nanotube materials requires the ability to link different carbon nanotube models, which were developed to work at different length scales. Here we describe the mapping of a molecular dynamics (MD) model for single-wall carbon nanotubes onto a wormlike chain. This mapping employs a mode analysis of the bending fluctuations of the nanotube, similar to those used in experiments [1]. The essence of this mapping is to find an appropriate bending stiffness for the wormlike cha in in order to represent the nanotube on a coarsened scale. We find that this mapping will only work well, if the wavelength probing the nanotube stiffness is sufficiently large. For single-wall (9,9) armchair nanotubes vibration modes with node distances of 3 nm underestimate the long wavelength limit of the bending constant by about 50%. This mismatch tends to increase for tubes with larger radii. INTRODUCTION Carbon nanotubes are attracting a lot of interest due to their intriguing mechanical and electrical properties [2]. Hence, these materials are widely discussed as a filler material in composites. In order to acquire an understanding of nanotube materials, models need to be developed which are adapted to describe material structures giving rise to a desired property. The internal material structures exist on a variety of scales, which is mirrored in the models describing them. This is in particular true for carbon nanotubes, which are characterised by an extreme aspect ratio where the typical diameter is on the order of 10-9 m close to atomistic dimensions, while their length can reach to the macroscopic scale. In order to arrive at a comprehensive understanding these models, which are adapted to different length scales, need to be linked. Here, we discuss a mapping for carbon nanotubes onto a wormlike chain model from molecular dynamics (MD) simulations. The wormlike chain is determined by two parameters, which are its length, L , and its bending stiffness, κ . In the limit of very high bending stiffnesses, κ , the wormlike chains behaves like rods, which in high enough concentrations will form liquid crystals [3]. If the bending stiffness is small, the wormlike chain will coil to a random path under thermal excitation. The length over which the orientational correlation in the random path decays by 1/e is commonly referred to as its persistence length κ / kT , which corresponds to the bending stiffness divided by the thermal energy kT . Thus, we will use the terms bending stiffness and persistence length interchangeably. While there are various ways to extract the bending stiffness for a wormlike chain from molecular dynamics MD simulations, both representations of the nanotube should behave the same on the coarse scale for a given external condi
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