Kinetics of Carbon Nanotube scission under Sonication

A dispersion of individualised carbon nanotubes is commonly obtained by means of sonication. Under sonication bundles of nanotubes are debundled, a process known as exfoliation. During sonication small bubbles within a liquid are brought into oscillation by an acoustic field. Under certain conditions these oscillations can end in the violent collapse of the bubble. This disruptive process disperses the nanotubes and is known as transient cavitation. From experiments it is well known that this process is also responsible for the scission of individual nanotubes. The scission of carbon nanotubes under sonication is investigated in this report. A mechanical model for scission based on the interaction between a single bubble and nanotube is constructed. The model indicates that scission will occur at the middle of the nanotube as long as it is sufficiently long. Furthermore it is shown how a length-dependent scission rate can be derived and how the presence of defects can slow down the scission process. The scission process is modeled as a series of consecutive first-order ‘reactions’. A mathematical description of the length distribution is obtained and the possibility of scale invariance in the length distribution is investigated. Finally both the mechanical model and the mathematical description of a consecutive process are combined to obtain a mathematical description of the scission process. This description is compared to simulation results and it is shown that theory and simulation are mostly in agreement.