Population growth dynamics of carbon nanotubes.

Understanding the population growth behavior of filamentary nanostructures, such as carbon nanotubes (CNTs), is hampered by the lack of characterization techniques capable of probing statistical variations with high spatial resolution. We present a comprehensive methodology for studying the population growth dynamics of vertically aligned CNT forests, utilizing high-resolution spatial mapping of synchrotron X-ray scattering and attenuation, along with real-time height kinetics. We map the CNT alignment and dimensions within CNT forests, revealing broadening and focusing of size distributions during different stages of the process. Then, we calculate the number density and mass density of the CNT population versus time, which are true measures of the reaction kinetics. We find that the mass-based kinetics of a CNT population is accurately represented by the S-shaped Gompertz model of population growth, although the forest height and CNT length kinetics are essentially linear. Competition between catalyst activation and deactivation govern the rapid initial acceleration and slow decay of the CNT number density. The maximum CNT density (i.e., the overall catalyst activity) is limited by gas-phase reactions and catalyst-surface interactions, which collectively exhibit autocatalytic behavior. Thus, we propose a comprehensive picture of CNT population growth which combines both chemical and mechanical cooperation. Our findings are relevant to both bulk and substrate-based CNT synthesis methods and provide general insights into the self-assembly and collective growth of filamentary nanostructures.