The intrinsic mechanical strength of single-walled carbon nanotubes (SWNTs)within the diameter range of 0.3-0.8 nm has been studied based on ab initiodensity functional theory calculations. In contrast to predicting "smaller isstronger and more elastic" in nanomaterials, the strength of the SWNTs issignificantly reduced when decreasing the tube diameter. The results obtainedshow that the Young`s modulus E significantly reduced in the ultra-small SWNTswith the diameter less than 0.4 nm originates from their very large curvatureeffect, while it is a constant of about 1.0 TPa, and independent of thediameter and chiral index for the large tube. We find that the Poisson`s ratio,ideal strength and ideal strain are dependent on the diameter and chiral index.Furthermore, the relations between E and ideal strength indicate thatGriffith`s estimate of brittle fracture could break down in the smallest (2, 2)nanotube, with the breaking strength of 15% of E. Our results provide importantinsights into intrinsic mechanical behavior of ultra-small SWNTs under theircurvature effect.
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