Nanoparticle size distribution quantification: results of a small-angle X-ray scattering inter-laboratory comparison

This paper presents the first worldwide inter-laboratory comparison of small-angle X-ray scattering (SAXS) for nanoparticle sizing. The measurands in this comparison are the mean particle radius, the width of the size distribution and the particle concentration. The investigated sample consists of dispersed silver nanoparticles, surrounded by a stabilizing polymeric shell of poly(acrylic acid). The silver cores dominate the X-ray scattering pattern, leading to the determination of their radius size distribution using (i) the generalized indirect Fourier transformation method, (ii) classical model fitting using SASfit and (iii) a Monte Carlo fitting approach using McSAS. The application of these three methods to the collected data sets from the various laboratories produces consistent mean number- and volume-weighted core radii of R (n) = 2.76 (6) nm and R (v) = 3.20 (4) nm, respectively. The corresponding widths of the lognormal radius distribution of the particles were σ(n) = 0.65 (1) nm and σ(v) = 0.71 (1) nm. The particle concentration determined using this method was 3.0 (4) g l(−1) or 4.2 (7) × 10(−6) mol l(−1). These results are affected slightly by the choice of data evaluation procedure, but not by the instruments: the participating laboratories at synchrotron SAXS beamlines, commercial and in-house-designed instruments were all able to provide highly consistent data. This demonstrates that SAXS is a suitable method for revealing particle size distributions in the sub-20 nm region (at minimum), out of reach for most other analytical methods.