(Invited) Variance Spectroscopy: A New Bridge Between Ensemble and Single-Particle Studies

We have developed a new experimental technique that probes variations in the spectra from small regions of heterogeneous bulk samples resulting from statistical variations in composition. The method is demonstrated with suspensions of single-walled carbon nanotubes (SWCNTs) containing mixtures of distinct structural species. Using dilute SWCNT samples, focused excitation beams, multichannel detection, and quick data collection, we capture several thousand emission spectra sampling different spatial regions of the sample. The data are analyzed to find both the mean emission intensity and the variance of emission intensity as a function of wavelength. Those spectra are then combined to extract information that is not available from conventional experiments, including the abundances of different (n,m) species and their relative emission efficiencies. The variance data are further analyzed for correlations between intensity fluctuations at different wavelengths. This gives novel two-dimensional maps that reveal the spectra of homogeneous sub-populations within the heterogeneously broadened bulk spectra. The off-diagonal features in these maps show spatially correlated concentration variations for nanotubes of different types, which expose the earliest stages of SWCNT aggregation. Variance spectroscopy should prove a powerful new experimental tool that can extract sub-ensemble level detail from measurements on bulk nanoparticle samples.