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

Abstract

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.

Controlling the structures of organic semiconductor–quantum dot nanocomposites through ligand shell chemistry

“…5). In recent studies, 19,[21][22][23] small-angle scattering has been able to unambiguously elucidate the structures of both QD core and ligand structures when QDs are isolated in solution or in the regularly arranged in the solid state as thin-film colloidal crystals. In contrast, this work demonstrates that when QDs self-assemble together in solution with a small organic molecule the assembly process generates much less well-defined, fractal or disordered agglomerate features.…”

“…17,18 Small angle scattering (both X-ray [SAXS] and neutron [SANS]) have provided quantitative structural insight into a range of QDs systems, from the size and distribution of the inorganic core radii (via SAXS) and the coverage and conformation of the native oleic acid (OA) ligand layer of as-synthesized QDs (via SANS). [19][20][21][22][23] Here, the ability of such scattering techniques to probe multiple lengthscales is employed to quantify QD ligand exchange processes and consequent OSC:QD self-assembly. Such scattering approaches provide direct insight into the routes by which a range of QD structures are formed with an OSC, from extended and disordered fractal aggregates at the early stages in solution, to final, longtime, OSC:QD nanocomposite aggregate forms.…”

Optimal loading for injection

“…Finally, in recent experiments we have scaled up the batch synthesis of PbS nanocrystals via burst nucleation and found this framework for optimizing injection an indispensable tool 24 . In this synthetic procedure, a concentrated solution of sulfur precursor suspended in oleylamine is injected by hand using a 20 ml syringe into a solution of lead chloride precursor being stirred at 120°C 25 .…”

Using Voltammetry Augmented with Physics-Based Modeling and Bayesian Hypothesis Testing to Estimate Electrolyte Composition

“…Physical models can also be readily evaluated with the Bayesian framework. 35 However, despite its use in multiple disciplines [36][37][38]34 and within the field of electrochemistry, 35,[39][40][41][42] to the best of our knowledge, Bayesian inference has not been used for voltammetric labeling; as such, this work seeks to develop a simple yet versatile protocol for identifying electroactive components using Bayesian inference.…”