Isolated single-walled carbon nanotubes (SWNTs), SWNT bundles, and ropes (or strands) show a structural self-similar characteristic. By calculating the Hausdorff dimension, it was found that their self-similar organization leads to surface fractality and the value of the surface dimension (D-s) depends on self-similar patterns. Experimentally, D-s obtained by nitrogen adsorption measurements at 77.3 K and by the small-angle x-ray scattering technique in our study proved our calculation that the surface dimension of SWNTs is nonintegral, 2
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