Measuring in Situ Length Distributions of Polymer-Wrapped Monochiral Single-Walled Carbon Nanotubes Dispersed in Toluene with Analytical Ultracentrifugation

The length of a carbon nanotube is an important dimension that has to be adjusted to the requirements of an experiment or application, e.g., through sorting methods. So far, atomic force microscopy (AFM) has been the method of choice for measuring length distributions, despite being an ex situ method with apparent shortcomings. In this work, we explore analytical ultracentrifugation (AUC) as an in situ method for measuring the length distribution of polymer-wrapped (7, 5) single-walled carbon nanotubes dispersed in toluene. This is an AUC study of nanotubes in nonaqueous media, the preferred media for nanotubes used in device fabrication. In AUC, the temporally and spatially dependent change in optical absorption of a sample is measured under centrifugation. The resulting sedimentation curves can be deconvoluted with a standard data processing procedure (SEDFIT), to yield the sedimentation coefficient distribution. However, the conversion of the sedimentation coefficient distribution into a length distribution is nontrivial and requires finding a suitable model for the nanotube friction coefficient. Also, since AUC is based on optical absorption, it yields a volume distribution and not a number distribution as obtained from AFM reference data. By meeting these challenges and finding a surprisingly simple empirical flexible-chain-like model to describe the sedimentation behavior of one specific chiral structure, we suggest AUC as a viable method for measuring in situ nanotube length distributions of nonaqueous dispersions.