Universal Response of Single-Wall Carbon Nanotubes to Radial Compression

The mechanical response of single-wall carbon nanotubes to radial compression is investigated via atomic force microscopy (AFM). We find that the force F applied by an AFM tip (with radius R) onto a nanotube (with diameter d), rescaled through the quantity Fd;{3/2}(2R);{-1/2}, falls into a universal curve as a function of the compressive strain. Such universality is reproduced analytically in a model where the graphene bending modulus is the only fitting parameter. The application of this model to the radial Young's modulus Eᵣ leads to a further universal-type behavior which explains the large variations of nanotube Eᵣ reported in the literature.