Quantifying the Hierarchical Order in Self-Aligned Carbon Nanotubes from Atomic to Micrometer Scale

Fundamental understanding of structure–property relationships in hierarchically organized nanostructures is crucial for the development of new functionality, yet quantifying structure across multiple length scales is challenging. In this work, we used nondestructive X-ray scattering to quantitatively map the multiscale structure of hierarchically self-organized carbon nanotube (CNT) “forests” across 4 orders of magnitude in length scale, from 2.0 Å to 1.5 μm. Fully resolved structural features include the graphitic honeycomb lattice and interlayer walls (atomic), CNT diameter (nano), as well as the greater CNT ensemble (meso) and large corrugations (micro). Correlating orientational order across hierarchical levels revealed a cascading decrease as we probed finer structural feature sizes with enhanced sensitivity to small-scale disorder. Furthermore, we established qualitative relationships for single-, few-, and multiwall CNT forest characteristics, showing that multiscale orientational order is directly correlated with number density spanning 109–1012 cm–2, yet order is inversely proportional to CNT diameter, number of walls, and atomic defects. Lastly, we captured and quantified ultralow-q meridional scattering features and built a phenomenological model of the large-scale CNT forest morphology, which predicted and confirmed that these features arise due to microscale corrugations along the vertical forest direction. Providing detailed structural information at multiple length scales is important for design and synthesis of CNT materials as well as other hierarchically organized nanostructures.