Competition between the Spring Force Constant and the Phonon Energy Renormalization in Electrochemically Doped Semiconducting Single-Walled Carbon Nanotubes

A detailed analysis of the in situ Raman spectroelectrochemical behavior of individual semiconducting single-walled carbon nanotubes (SWCNTs) is presented. Special attention has been paid to the development of the tangential (TG) mode frequency, which shifts when the externally applied potential V-e is shifted away from V-e = 0. The magnitude and direction (upshift or downshift) of the tangential mode band has been found to be dependent on the diameter of the semiconducting tubes. For negative charging, the small-diameter tubes exhibit a downshift while the large-diameter tubes exhibit an upshift. This behavior is explained by a competition between two effects which cause opposite shifts in the TG mode frequency during negative charging: a phonon renormalization effect and a C-C bond weakening during the charging process. Positive charging always causes an upshift of the TG mode frequency. However, the magnitude of the upshift is dependent on the tube diameter.