In this work, a theoretical study is performed to quantitatively understand the van der Waals interactions between single-walled carbon nanotubes (SWNTs) and sapphire substrates. The energetically preferred alignment directions of SWNTs on A-, R- and M-planes and the random alignment on the C-plane predicted by this study are all in good agreement with experiments. It is also shown that smaller SWNTs have better alignment than larger SWNTs due to their stronger interaction with sapphire substrate.
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