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 de-velopment 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 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. Different data analysis methods are compared, and we show that they yield nearly identical estimates of the NC diameter in the case of a NC ensemble with a monodisperse and monomodal size distribution. Extending the analysis to PbSe, CdSe and CdS NCs, we provide SAXS calibrated sizing curves, which relate the NC diameter and the NC band-gap energy as determined using absorbance spectroscopy. In compari-son with sizing curves calibrated by means of transmission electron microscopy (TEM), we systematically find that SAXS calibration assigns a larger diameter than TEM calibration to NCs with a given band gap. We attribute this difference to the difficulty of accurately sizing small objects in TEM images. To close, we demonstrate that NC concentrations can be directly extracted from SAXS patterns normalized to an absolute scale, and we show that SAXS-based concentrations agree with concentration estimates based on absorption spectroscopy. File list (2) download file view on ChemRxiv sizingcurves_chemrxiv.pdf (3.58 MiB) download file view on ChemRxiv suppinfo_chemrxiv.pdf (0.98 MiB)

Probing Solvent–Ligand Interactions in Colloidal Nanocrystals by the NMR Line Broadening

“…The optical band gap of the CdSe and PbS nanocrystals were determined by UV-VIS-NIR absorption spectroscopy (Perkin Elmer Lambda 900) and correlated to a nanocrystal diameter by aid of sizing curves that were recently re-evaluated by SAXS. 53 Transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) were performed on a FEI Talos Bruker Avance III Spectrometer operating at a 1 H frequency of 500.13 MHz and featuring a BBI probe. The sample temperature was set to 298.15 K. For the quantitative 1D 1 H measurements, 64k data points were sampled with the spectral width set to 16 ppm and a relaxation delay of 30s.…”

Exploring the self-assembly of dumbbell-shaped polyoxometalate hybrids, from molecular building units to nanostructured soft materials

“…SAXS is a powerful technique to characterize the structures of large synthetic molecules, molecular assemblies, nanoparticles 34 and aggregates with sizes ranging from 1 to 100 nm. 35,36 With regard to POM chemistry, we and others have shown that this technique is particularly well-suited to characterize nanosized metal-oxo cluster assemblies.…”

Interface Engineering Strategies for Fabricating Nanocrystal-Based Organic–Inorganic Nanocomposites

“…Characterization techniques used thus far to investigate the surface properties of NCs include X-ray photoelectron spectroscopy [45,46], UV-vis spectroscopy [47], infrared spectroscopy [48], photoluminescence spectroscopy [49][50][51], and nuclear magnetic resonance (NMR) spectroscopy [52,53]. To determine the properties of surface ligands or the interfacial properties between organic and inorganic elements, various characterization techniques must be combined [54].…”

“…Several researchers have reported a correlation between the first absorption peak of semiconducting QDs (e.g., CdS, CdSe, PbTe, PbSe, and CdTe) and their size. Peng et al summarized these values and suggested empirical fitting functions [40,46,47]. These equations are only valid in the size range covered by the data shown in Figure 6 [47].…”

“…It greatly relies on the NC concentration, based on Beer-Lambert's equation [47]. Therefore, the main obstacle for calculating ε has been the difficulty in determining the QD concentrations [10,46,61]. In the early studies, the extinction coefficient per NC was determined by measuring the NC concentration, based on precursor mass, assuming that all the precursors are converted into NCs.…”