Chirality Dependence of the Absorption Cross Section of Carbon Nanotubes

The variation of the optical absorption of carbon nanotubes with their geometry has been a long-standing question at the heart of both metrological and applicative issues, in particular because optical spectroscopy is one of the primary tools for the assessment of the chiral species abundance of samples. Here, we tackle the chirality dependence of the optical absorption with an original method involving ultraefficient energy transfer in porphyrin-nanotube compounds that allows uniform photoexcitation of all chiral species. We measure the absolute absorption cross section of a wide range of semiconducting nanotubes at their $S_{22}$ transition and show that it varies by up to a factor of 2.2 with the chiral angle, with type I nanotubes showing a larger absorption. In contrast, the luminescence quantum yield remains almost constant.

Figure 1

Optical absorption spectra of HiPCO SWNTs (black) and SWNT/TPP compounds (red) in micellar solutions. Inset: Schematic view of the noncovalent SWNT/TPP compound.

Figure 2

PL map of the HiPCO SWNT/TPP compounds suspension. The dashed white line at 2.82 eV is a guide to the eye showing the energy transfer resonance upon excitation of the TPP molecules. The spectra are normalized to a constant incoming photon flux. The upper part intensities are reduced by a factor 0.4 for the sake of clarity.

Figure 3

Black circles: $R$ ratio between the PL intensity excited on the Soret resonance and the PL intensity excited on the intrinsic $S_{22}$ resonance in the HiPCO based SWNT/TPP compounds as a function of $q\cos (3\theta )$. Green triangles: same ratio $R$ evaluated for a sample made from CoMoCat material. Blue line: linear fit of $R$. Red squares: Inverse of the action cross section $A$ of pristine nanotubes (from Ref. 17) scaled with a simple proportionality factor.

Figure 4

Inverse of the $R$ ratio (which is directly proportional to the absorption cross section), as a function of $q\cos (3\theta )$ for HiPCO (black dots) and CoMoCat nanotubes (green triangles). Purple down triangles: Theoretically calculated absorption probability (arb. units, from Ref. 15). Blue line: fit to the data leading to the empirical formula (2). Inset: PL quantum yield as a function of $q\cos (3\theta )$ deduced from the action cross section measured in Ref. 17 and from the absorption cross section presented in the main figure.