Spectral challenges of individual wavelength-scale particles: strong phonons and their distorted lineshapes

Beyond our own interest in airborne particulate matter, the prediction of extinction and absorption spectra of single particles of mixed composition has wide use in astronomy, geology, atmospheric sciences, and nanotechnology. Single particle spectra present different challenges than traditional spectroscopic approaches. To quantify the amount of a material in a bulk sample (molecules in solution or the gas phase), one might employ the Beer–Lambert law assuming a simple slab-type assay geometry and averaging over orientation, whereas with single particles one might have a specific orientation and require a nonlinear, Mie-like particle theory. The complicating single particle issues include: strong and broad scattering at wavelengths similar to the particle size, phonon lineshape phase shifting, particle shape effects, distortion of transition lineshapes by strong vibrational bands, bi- and trirefringence, crystal orientation effects including dispersion, and composition mixtures. This work uses a combination of three-dimensional finite difference time domain (3D-FDTD) calculations and experimental infrared spectra on single, crystalline quartz particles to illustrate some of the challenges – in particular the distortion of lineshapes by strong phonons that lie within a range of strong scattering. It turns out that many mineral dust components in the inhalable size range have strong phonons. A Mie–Bruggeman model for single particle spectra is presented to isolate the effects of strong phonons on lineshapes which has utility for analysing the spectra of single, mixed-composition particles. This model will ultimately enable the determination of volume fractions of components in single particles that are mixtures of many materials with strong phonons, as are the dust particles breathed into people's lungs.