Size and Concentration Determination of Colloidal Nanocrystals by Small-Angle X-ray Scattering

Abstract

The accurate determination of the dimensions of a nano-object is paramount to the development of nanoscience and technology. Here we provide procedures for sizing quasi-spherical colloidal nanocrystals (NCs) by means of small-angle X-ray scattering (SAXS). Using 2.5 to 10 nm PbS NCs as a model system, the protocols outline the extraction of the net NC SAXS pattern by background correction and address the calibration of scattered X-ray intensity to an absolute scale. The NC size distribution is retrieved by fitting the corrected SAXS pattern either to parametrized analytical distributions or to a distribution constructed through a Monte Carlo approach. We compare the two methods and show that they yield nearly identical estimates of the NC diameter in the case of an NC ensemble with a monodisperse and monomodal size distribution. Extending the analysis to PbSe, CdSe, and CdS NCs, we provide SAXS-calibrated sizing curves ranging from 2.5 to 7 nm, which relate the NC diameter and the NC band-gap energy as de...