A generalized kinetic model for the formation and growth of single-walled metal oxide nanotubes

Abstract

We demonstrate a generalized kinetic modeling and experimental approach to describe the formation and growth of single-walled metal oxide nanotubes. These materials can now be synthesized using solution-based methods at temperatures as low as 95°C. Ultimately, it is desired to produce nanotubes on a larger scale (e.g., kilogram or ton) for technological applications. However, a quantitative multiscale understanding of nanotube growth, via a detailed growth model, is critical in order to predict and control key properties such as the length distribution and concentration of the nanotubes. Such a model can then be used to design liquid-phase reactors for scale-up of nanotube synthesis. The present model considers three types of species present in the synthesis solution: molecular precursors, amorphous nanoparticles, and nanotubes. The nucleation of a nanotube embryo is due to the rearrangement of an amorphous nanoparticle into an ordered tubular structure, as revealed by recent works. The nanotube growth model is represented by up to 800 population-balance differential equations. Parameterization, validation, and predictive evaluation of the model is carried out via detailed statistical TEM measurements of nanotube length distributions throughout the synthesis. This model is capable of explaining and predicting the evolution of nanotube populations as a function of kinetic parameters. It also allows insight into mesoscale and microscale nanotube growth processes. For example, it shows that two different mechanisms operate during nanotube growth: (1) growth by precursor addition, and (2) oriented attachment of nanotubes to each other.