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

Abstract

The accurate determination of the\ndimensions of a nano-object is\nparamount to the development of nanoscience and technology. Here we\nprovide procedures for sizing quasi-spherical colloidal nanocrystals\n(NCs) by means of small-angle X-ray scattering (SAXS). Using 2.5 to\n10 nm PbS NCs as a model system, the protocols outline the extraction\nof the net NC SAXS pattern by background correction and address the\ncalibration of scattered X-ray intensity to an absolute scale. The\nNC size distribution is retrieved by fitting the corrected SAXS pattern\neither to parametrized analytical distributions or to a distribution\nconstructed through a Monte Carlo approach. We compare the two methods\nand show that they yield nearly identical estimates of the NC diameter\nin the case of an NC ensemble with a monodisperse and monomodal size\ndistribution. Extending the analysis to PbSe, CdSe, and CdS NCs, we\nprovide SAXS-calibrated sizing curves ranging from 2.5 to 7 nm, which\nrelate the NC diameter and the NC band-gap energy as determined using\nabsorbance spectroscopy. In comparison with sizing curves calibrated\nby means of transmission electron microscopy (TEM), we systematically\nfind that SAXS calibration assigns a larger diameter than TEM calibration\nto NCs with a given band gap. We attribute this difference to the\ndifficulty of accurately sizing small objects in TEM images. To close,\nwe demonstrate that NC concentrations can be directly extracted from\nSAXS patterns normalized to an absolute scale and that SAXS-based\nconcentrations differ less than 10% from concentrations obtained using\nabsorbance spectroscopy.