Neither Sphere nor Cube—Analyzing the Particle Shape Using Small-Angle Scattering and the Superball Model

Abstract

Accurate characterization of the nanocrystal shape with high statistical relevance is essential for exploiting the strongly shape-dependent properties of cuboidal nanoparticles toward applications. This work presents the development of a new small-angle scattering form factor based on the superball geometry. The superball quantifies the characteristic rounding of corners and edges of cuboidal nanoparticles with a single parameter. Applied to small-angle scattering data of sufficiently monodisperse nanoparticles, the superball form factor enables differentiation between the effects of extended particle size distribution and irregular particle shape. The quantitative application of the superball form factor is validated against microscopy data for a series of monodisperse nanoparticles and implemented into the user-friendly, open-source software Sasview.

Time‐Resolved SAXS Study of Polarity‐ and Surfactant‐Controlled Superlattice Transformations of Oleate‐Capped Nanocubes During Solvent Removal

“…Using a fixed SD = 0.06, we obtain an edge length of e SAXS = 10.3 nm using a cubic form factor, a dia meter of d SAXS = 12.9 nm using a spherical form factor, and an edge length of a SAXS = 11.4 nm with p = 1.5, which corresponds to τ = 0.41, using a superball form factor (Figure 1e). [30] The normalized residuals of the fitting results (see inset Figure 1e) show that the superball mode fits with our experimental curve better than the spherical and cubic modes in the high q region (q > 0.3 nm −1 ), which is consistent with the truncated cube morphology of the TCs. Indeed, the normalized residuals also suggest that the spherical model fits the data better than the cubic model.…”

“…The video was decomposed into image frames with the program VirtualDub. The radii a and c of the oblate ellipsoidal droplet were obtained by analyzing the image frames with ImageJ and the droplet volume was calculated by Fitting the SAXS Curve: The experimental SAXS curve of a dilute TC dispersion was fitted with a spherical, cubic form factor, and superball form factor [30] using the program SasView. The first frame of the timeresolved measurements, when the dispersions were free of aggregates and the contribution to the scattered intensity can be assumed to be purely by the form factor, was used for the fitting.…”

“…The experimental SAXS curve of a dilute TC dispersion was fitted with a spherical, cubic form factor, and superball form factor [ 30 ] using the program SasView. The first frame of the time‐resolved measurements, when the dispersions were free of aggregates and the contribution to the scattered intensity can be assumed to be purely by the form factor, was used for the fitting.…”

Creating ground truth for nanocrystal morphology: a fully automated pipeline for unbiased transmission electron microscopy analysis

“…, ion exchange). 52 Here, 7082 distinct nanocrystals synthesized via the hot-injection method (without experimental size selection) were detected from 20 inputted TEM micrographs and analyzed. As determined by the unsupervised cluster evaluation algorithm, the nanocrystals were subsequently classified into four shape groups: small cuboids (group 1), large irregular nanocrystals (group 2), larger cuboids (group 3), and small platelets (group 4) (Fig.…”

Using small-angle scattering to guide functional magnetic nanoparticle design

“…the degree of truncation and roundness of cuboids. 120 The polydispersity of the nanoparticle ensembles is considered with a corresponding density distribution function. The relevant structural parameters of the particles and the corresponding distribution function can be determined by model fits of the reciprocal scattering data.…”