“We know from previous studies that nanotubes are very stiff in the axial direction, but little is known about their radial elasticity,” said Elisa Riedo of Georgia Tech, “mainly because when you’re working with tubes that small, it’s difficult to poke them without pushing them beyond the point at which they will be irremediably damaged.”

Riedo and colleagues used an atomic-force microscope (AFM) to perform modulated nano-indentation on the nanotubes. The AFM incorporated silicon nitride cantilevers with an average tip radius of 35 nm.

The team tested tubes with diameters of 0.2 - 12 nm. The nanotubes, which had a constant ratio of external:internal radius of 2.2, were grown by chemical vapour deposition using acetylene as a carbon feedstock. It’s likely that the tubes of smallest diameter were actually single-walled.

Nanotubes with a diameter of 2 nm had a radial stiffness of almost 600 GPa. But the radial stiffness for larger diameter nanotubes was much lower, decreasing to around 30 GPa for tubes with diameters of more than 4 nm. This value is similar to the Young’s modulus for graphite along its c axis, which is 36 GPa.

“We started with single-walled nanotubes and then measured tubes with an increasing number of layers, keeping the external radius twice as large as the internal radius,” said Riedo. “Our experiments show that for nanotubes with small internal radii, increasing the radii makes them softer. This means that for these tubes, the radial rigidity is controlled by the magnitude of the internal radius, whereas the number of layers plays a minor role.”

The researchers believe that knowing the radial stiffness of nanotubes is important for their application in nano-electromechanical and nano-electronic systems. For example, radial deformation of the nanotubes may affect their electrical properties.

The researchers reported their work in Physical Review Letters.