Dynamical phenomena in fast sliding nanotube models

The experimentally known fact that coaxial carbon nanotubes can be forced to slide one inside the other stimulated in the past much detailed modelling of the dynamical sliding process. Molecular dynamics simulations of sliding coaxial nanotubes showed the existence of strong frictional peaks when, at large speed, one tube excites the other with a ‘washboard’ frequency that happens to resonate with some intrinsic vibration frequency. At some of these special speeds we discover a striking example of dynamical symmetry breaking taking place at the nanoscale. Even when both nanotubes are perfectly left–right symmetric and nonchiral, precisely in correspondence with the large peaks of sliding friction occurring at a series of critical sliding velocities, a nonzero angular momentum spontaneously appears. A detailed analysis shows that this internal angular momentum is of phonon origin, in particular arising from preferential excitation of a right polarized (or, with equal probability, of a left polarized) outer-tube ‘pseudorotation’ mode, thus spontaneously breaking their exact twofold right–left degeneracy. We present and discuss a detailed analysis of nonlinear continuum equations governing this phenomenon, showing the close similarity of this phenomenon with the well-known rotational instability of a forced string, which takes place under sufficiently strong periodic forcing of the string. We also point out new elements appearing in the present problem which are ‘nano’, in particular the involvement of Umklapp processes and the role of sliding nanofriction.