Robust determination of Youngʹs modulus of individual carbon nanotubes by quasi-static interaction with Lorentz forces

Youngʹs modulus of an individual multi-wall carbon nanotube has been determined by the method of quasi-static transverse bending due to a Lorentz force observed in situ in a transmission electron microscope. The deflection of the nanotube allows the determination of Youngʹs modulus using Euler–Bernoulliʹs beam equation. Because we determine the specific dependence of the deflection on the position along the nanotube axis, it is possible to gain insight into the type of mountings and furthermore allows for an estimation of the homogeneity of the nanotube. Both properties have been found to be of importance to determine Youngʹs modulus. It was found to be higher by up to a factor of 1.6 compared to the value obtained by assuming rigid mountings.