Bilayer Plots for Accurately Determining the Chirality of Single-Walled Carbon Nanotubes Under Complex Environments

The chirality (n,m) determines all structures and properties of a single-walled carbon nanotube (SWNT), therefore, accurate and convenient (n,m) assignments are vital in nanotube-related science and technology. Previously, a so-called Kataura plot that protracts the excitonic transition energies (E_ii's) of SWNTs with various (n,m) with respect to the tube diameter (d_t) has been widely utilized by researchers in the nanotube community for all (n,m)-related studies. However, the facts that both E_ii and the calculated d_t are subject to interactions with the environments make it inconvenient to accurately determine the (n,m) under complex environments. Here, we propose a series of bilayer plots that take into account the interactions between the SWNTs and the environments so that the (n,m) of SWNTs can be accurately determined. These plots have more advantages than the Kataura plot in concision, less data overlapping, and the suitability to be used in complex environments. We strongly encourage the researchers in the carbon nanotube community to utilize the bilayer plots for all (n,m)-related studies, especially for accurate and convenient (n,m) determination.