Single-walled carbon nanotubes (SWCNTs) are a family of 1D nanomaterials with the potential for a range for novel applications. However, accurate and convenient characterization is still an important challenge, since most SWCNT samples contain mixtures of many structural forms ((n,m) species) with different electronic, optical, mechanical, and chemical properties. Fluorescence emission, fluorescence excitation, and absorption spectra of such mixed samples are complex superpositions, with each (n,m) species giving multiple peaks. Therefore proper sample analysis requires detailed knowledge of the positions, widths, and intensities of those spectral features. Here we report progress in determining semiconducting SWCNT sample compositions by carefully analyzing the absorption and emission spectra simultaneously.

One step in this approach is determining detailed fluorescence excitation spectra. For this we have prepared samples enriched in a single (n,m) and carefully measured their excitation spectra. Each such spectrum was broken down and modeled as features representing SWCNT electronic and vibronic transitions. We then deduced Voigt or Pearson line shapes that represent positions, widths, and intensities of these peaks as a function of nanotube structure. This has allowed us to construct a model for fluorescence excitation spectra that can be applied to (n,m) species beyond those that were directly measured.

Similarly, to represent (n,m)-dependent emission spectra, we have made careful bulk and single-nanotube studies of features from the singlet bright exciton (E₁₁) and three secondary emissive sidebands. We deduced parameters describing these features as a function of nanotube structure to construct a robust model for SWCNT emission spectra. This model, when combined with the one for excitation, allows the fluorescence spectra of nanotube mixtures to be properly analyzed as a sum of contributions from multiple (n,m) species.

Although this procedure does not reveal absolute species concentrations, the fluorescence analysis can be combined with absorption analysis and recent data for SWCNT absolute absorption cross sections to obtain quantitative sample compositions. For this purpose, the absorption spectrum of a mixed sample is simulated as a background function plus components determined from the fluorescence emission and excitation profiles for the (n,m) species that were found to be present. Then the separate E₁₁ (n,m) absorbance components are divided by their structure-specific absorption cross sections to find absolute species concentrations.