Characterization of colloidal nanocrystal surface structure using small angle neutron scattering and efficient Bayesian parameter estimation

Complete structural characterization of colloidal nanocrystals is challenging due to rapid variation in the electronic, vibrational, and elemental properties across the nanocrystal surface. While electron microscopy and X-ray scattering techniques can provide detailed information about the inorganic nanocrystal core, these techniques provide little information about the molecular ligands coating the nanocrystal surface. Moreover, because most models for scattering data are parametrically nonlinear, uncertainty estimates for parameters are challenging to formulate robustly. Here, using oleate-capped PbS quantum dots as a model system, we demonstrate the capability of small angle neutron scattering (SANS) in resolving core, ligand-shell, and solvent structure for well-dispersed nanocrystals using a single technique. SANS scattering data collected at eight separate solvent deuteration fractions were used to characterize the structure of the nanocrystals in reciprocal space. Molecular dynamics simulations were used to develop a coarse-grained form factor describing the scattering length density profile of ligand-stabilized nanocrystals in solution. We introduce an affine invariant Markov chain Monte Carlo method to efficiently perform nonlinear parameter estimation for the form factor describing such dilute solutions. This technique yields robust uncertainty estimates. This experimental design is broadly applicable across colloidal nanocrystal material systems including emergent perovskite nanocrystals, and the parameter estimation protocol significantly accelerates characterization and provides new insights into the atomic and molecular structure of colloidal nanomaterials.