Chirality-dependent properties of carbon nanotubes: electronic structure, optical dispersion properties, Hamaker coefficients and van der Waals–London dispersion interactions
Optical dispersion spectra at energies up to 30 eV play a vital role in understanding the chirality-dependent van der Waals–London dispersion interactions of single wall carbon nanotubes (SWCNTs). We use one-electron theory based calculations to obtain the band structures and the frequency dependent dielectric response function from 0–30 eV for 64 SWCNTs differing in radius, electronic structure classification, and geometry. The resulting optical dispersion properties can be categorized over three distinct energy intervals (M, π, and σ, respectively representing 0–0.1, 0.1–5, and 5–30 eV regions) and over radii above or below the zone-folding limit of 0.7 nm. While π peaks vary systematically with radius for a given electronic structure type, σ peaks are independent of tube radius above the zone folding limit and depend entirely on SWCNT geometry. We also observe the so-called metal paradox, where a SWCNT has a metallic band structure and continuous density of states through the Fermi level but still behaves optically like a material with a large optical band gap between M and π regions. This paradox appears to be unique to armchair and large diameter zigzag nanotubes. Based on these calculated one-electron dielectric response functions we compute and review van der Waals–London dispersion spectra, full spectral Hamaker coefficients, and van der Waals–London dispersion interaction energies for all calculated frequency dependent dielectric response functions. Our results are categorized using a new optical dielectric function classification scheme that groups the nanotubes according to observable trends and notable features (e.g. the metal paradox) in the 0–30 eV part of the optical dispersion spectra. While the trends in these spectra begin to break down at the zone folding diameter limit, the trends in the related van der Waals–London dispersion spectra tend to remain stable all the way down to the smallest single wall carbon nanotubes in a given class.