Mechanics of carbon nanotube scission under sonication

As-produced carbon nanotubes come in bundles that must be exfoliated for practical applications in nanocomposites. Sonication not only causes the exfoliation of nanotube bundles but also unwanted scission. An understanding of how precisely sonication induces the scission and exfoliation of nanotubes will help maximising the degree of exfoliation while minimising scission. We present a theoretical study of the mechanics of carbon nanotube scission under sonicaton, based on the accepted view that it is caused by strong gradients in the fluid velocity near a transiently collapsing bubble. We calculate the length-dependent scission rate by taking the actual movement of the nanotube during the collapse of a bubble into account, allowing for the prediction of the temporal evolution of the length distribution of the nanotubes. We show that the dependence of the scission rate on the sonication settings and the nanotube properties results in non-universal, experiment-dependent scission kinetics potentially explaining the variety in experimentally observed scission kinetics. The non-universality arises from the dependence of the maximum strain rate of the fluid experienced by a nanotube on its length. The maximum strain rate that a nanotube experiences increases with decreasing distance to the bubble. As short nanotubes are dragged along more easily by the fluid flow they experience a higher maximum strain rate than longer nanotubes. This dependence of the maximum strain rate on nanotube length affects the scaling of tensile strength with terminal length. We find that the terminal length scales with tensile strength to the power of 1/1.16 instead of with an exponent of 1/2 as found when nanotube motion is neglected. Finally, we show that the mechanism we propose responsible for scission can also explain the exfoliation of carbon nanotube bundles.