**Optimizing load transfer in multiwall nanotubes through interwall
coupling: Theory and simulation**

EM Byrne and A Letertre and MA McCarthy and WA Curtin and Z Xia, ACTA MATERIALIA, 58, 6324-6333 (2010).

DOI: 10.1016/j.actamat.2010.07.054

An analytical model is developed to determine the length scales over which load is transferred from outer to inner walls of multiwall carbon nanotubes (MWCNTs) as a function of the amount of bonding between walls. The model predicts that the characteristic length for load transfer scales as l similar to t root E/(mu) over bar, where t is the CNT wall spacing, E is the effective wall Young's modulus, and (mu) over bar is the average interwall shear modulus due to interwall coupling. Molecular dynamics simulations for MWCNTs with up to six walls, and with interwall coupling achieved by interwall sp(3) bonding at various densities, provide data against which the model is tested. For interwall bonding having a uniform axial distribution, the analytic and simulation models agree well, showing that continuum mechanics concepts apply down to the atomic scale in this problem. The simulation models show, however, that load transfer is sensitive to natural statistical fluctuations in the spatial distribution of the interwall bonding between pairs of walls, and such fluctuations generally increase the net load transfer length needed to fully load an MWCNT. Optimal load transfer is achieved when bonding is uniformly distributed axially, and all interwall regions have the same shear stiffness, implying a linear decrease in the number of interwall bonds with distance from the outer wall. Optimal load transfer into an n-wall MWCNT is shown to occur over a length of similar to 1.5nl. The model can be used to design MWCNTs for structural materials, and to interpret load transfer characteristics deduced from experiments on individual MWCNTs. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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