Macroscopic wall number analysis of single-walled, double-walled, and few-walled carbon nanotubes by X-ray diffraction

The layer number is of great importance for nanocarbon materials, such as carbon nanotubes (CNTs) and graphene. While simple optical methods exist to evaluate few-layer graphene, equivalent analysis for CNTs is limited to transmission electron microscopy. We present a simple macroscopic method based on the (002) X-ray diffraction peak to evaluate the average wall number of CNTs in the range from single- to few-walled. The key was the finding that the (002) peak could be decomposed into two basic components: the intertube structure (outer-wall contacts) and the intratube structure (concentric shells). Decomposition of the peaks revealed a linear relationship between the average wall number and the ratio of the intertube and intratube contributions to the (002) peak. Good agreement with CNTs having average wall numbers ranging from 1 to ～5 demonstrated this as a macroscopic method for average wall number analysis.