Statistical length measurement method by direct imaging of carbon nanotubes

The influence of carbon nanotube (CNT) length on their macroscopic properties requires an accurate methodology for CNT length measurement. So far, existing techniques are limited to short (less than a few micrometers) CNTs and sample preparation methods that bias the measured values. Here, we show that the average length of carbon nanotubes (CNTs) can be measured by cryogenic transmission electron microscopy (cryo-TEM) of CNTs in chlorosulfonic acid. The method consists of dissolving at low concentration CNTs in chlorosulfonic acid (a true solvent), imaging the individual CNTs by cryo-TEM, and processing and analyzing the images to determine CNT length. By measuring the total CNT contour length and number of CNT ends in each image, and by applying statistical analysis, we extend the method to cases where each CNT is long enough to span many cryo-TEM images, making the direct length measurement of an entire CNT impractical. Hence, this new technique can be used effectively to estimate samples in a wide range of CNT lengths, although we find that cryo-TEM imaging may bias the measurement towards longer CNTs, which are easier to detect. Our statistical method is also applied to AFM images of CNTs to show that, by using only a few AFM images, it yields estimates that are consistent with literature techniques, based on individually measuring a higher number of CNTs.