Strain energy and lateral friction force distributions of carbon nanotubes manipulated into shapes by atomic force microscopy

The interplay between local mechanical strain energy and lateral frictional forces determines
the shape of carbon nanotubes on substrates. In turn, because of its nanometer-size diameter,
the shape of a carbon nanotube strongly influences its local electronic, chemical, and
mechanical properties. Few, if any, methods exist for resolving the strain energy and static
frictional forces along the length of a deformed nanotube supported on a substrate. We present a
method using nonlinear elastic rod theory in which we compute the flexural strain energy and
static frictional forces along the length of single walled carbon nanotubes (SWCNTs)
manipulated into various shapes on a clean SiO2 substrate. Using only high resolution atomic
force microscopy images of curved single walled nanotubes, we estimate flexural strain energy
distributions on the order of attojoules per nanometer and the static frictional forces between a
SWCNT and SiO2 surface to be a minimum of 230 pN nm−1.