Heterogeneous local order in self-assembled nanoparticle films revealed by X-ray cross-correlations

The pypadf package: computing the pair angle distribution function from fluctuation scattering data

The pair angle distribution function (PADF) is a three- and four-atom correlation function that characterizes the local angular structure of disordered materials, particles or nanocrystalline materials. The PADF can be measured using X-ray or electron fluctuation diffraction data, which can be collected by scanning or flowing a structurally disordered sample through a focused beam. It is a natural generalization of established pair distribution methods, which do not provide angular information. The software package pypadf provides tools to calculate the PADF from fluctuation diffraction data. The package includes tools for calculating the intensity correlation function, which is a necessary step in the PADF calculation and also the basis for other fluctuation scattering analysis techniques.

Angular X-ray cross-correlation analysis applied to the scattering data in 3D reciprocal space from a single crystal

An application of angular X-ray cross-correlation analysis (AXCCA) to the scattered intensity distribution measured in 3D reciprocal space from a single-crystalline sample is proposed in this work. Contrary to the conventional application of AXCCA, when averaging over many 2D diffraction patterns collected from different randomly oriented samples is required, the proposed approach provides an insight into the structure of a single specimen. This is particularly useful in studies of defect-rich samples that are unlikely to have the same structure. The application of the method is shown on an example of a qualitative structure determination of a colloidal crystal from simulated as well as experimentally measured 3D scattered intensity distributions.

Slowing down of dynamics and orientational order preceding crystallization in hard-sphere systems

Despite intensive studies in the past decades, the local structure of disordered matter remains widely unknown. We show the results of a coherent x-ray scattering study revealing higher-order correlations in dense colloidal hard-sphere systems in the vicinity of their crystallization and glass transition. With increasing volume fraction, we observe a strong increase in correlations at both medium-range and next-neighbor distances in the supercooled state, both invisible to conventional scattering techniques. Next-neighbor correlations are indicative of ordered precursor clusters preceding crystallization. Furthermore, the increase in such correlations is accompanied by a marked slowing down of the dynamics, proving experimentally a direct relation between orientational order and sample dynamics in a soft matter system. In contrast, correlations continuously increase for nonequilibrated, glassy samples, suggesting that orientational order is reached before the sample slows down to reach (quasi-)equilibrium.

Shear-induced ordering in liquid microjets seen by x-ray cross correlation analysis

We applied shear to a silica nanoparticle dispersion in a microfluidic jet device and observed direction-dependent structure along and across the flow direction. The asymmetries of the diffraction patterns were evaluated by x-ray cross correlation analysis. For different Rayleigh nozzle sizes and shapes, we measured the decay of the shear-induced ordering after the cessation of the shear. At large tube sizes and small shear rates, the characteristic times of the decay become longer, but Péclet-weighted times do not scale linearly with Péclet numbers. By modeling particle distributions with the corresponding diffraction patterns and comparing measured shape asymmetry to simulations, we determined the variation of volume fraction over the azimuthal angle for the maximum ordered state in the jet.

Interaction among Spherical Polyelectrolyte Brushes in Concentrated Aqueous Solution

Interaction among concentrated spherical polyelectrolyte brushes (SPB) dispersions in water was systematically investigated by means of small-angle X-ray scattering (SAXS), wide-angle X-ray scattering (WAXS), and rheological methods. SPB consist of a core of polystyrene (PS) and a poly(acrylic acid) (PAA) brush shell. The "polyelectrolyte peak" appeared in SAXS spectra and was observed in WAXS curves for the first time. The size of the polyelectrolyte peak and the rheological properties of SPB were found to be strongly effected by SPB concentration, pH, and ionic strength. Combined with SAXS, WAXS, and rheological results, it is confirmed that the polyelectrolyte peak is originated from local ordered structures of polyelectrolyte chains bridged by counterions in the overlapping area among SPB driven by electrostatic interactions.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.

Coexistence of hcp and bct Phases during In Situ Superlattice Assembly from Faceted Colloidal Nanocrystals

We study the in situ self-assembly of faceted PbS nanocrystals from colloidal suspensions upon controlled solvent evaporation using time-resolved small-angle X-ray scattering and X-ray cross-correlation analysis. In our bulk-sensitive experiment in transmission geometry, the superlattice crystallization is observed in real time, revealing a hexagonal closed-packed (hcp) structure followed by formation of a body-centered cubic (bcc) superlattice. The bcc superlattice undergoes continuous tetragonal distortion in the solvated state shortly after its formation, resulting in the body-centered tetragonal (bct) structure. Upon solvent evaporation, the bct superstructure becomes more pronounced with the still coexisting hcp phase. These findings corroborate the existing simulations of assembling cuboctahedral-shaped particles and illustrate that we observed the predicted equilibrium states. This work is essential for a deeper understanding of the fundamental forces that direct nanocrystal assembly including nanocrystal shape and ligand coverage.

Kinetics of pressure-induced nanocrystal superlattice formation

Colloidal nanocrystals (NC) are known to self-organize into superlattices that promise many applications ranging from medicine to optoelectronics. Recently, the formation of high-quality PEGylated gold NC was reported at high hydrostatic pressure and high salt concentrations. Here, we study the formation kinetics of these superlattices after pressure jumps beyond their crystallisation pressure by means of small-angle X-ray scattering with few ms experimental resolution. The timescale of NC formation was found to be reduced the larger the width of the pressure jump. This is connected to an increase of crystal quality, i.e., the faster the NC superlattice forms, the better the crystal quality. In contrast to the formation kinetics, the melting of the NC superlattice is approximately one order of magnitude slower and shows linear kinetics.

Local orientational order in self-assembled nanoparticle films: the role of ligand composition and salt

An X-ray cross-correlation study of the local orientational order in self-assembled films made from PEGylated gold nanoparticles is presented. The local structure of this model system is dominated by four- and sixfold order. Coadsorption of shorter ligands in the particle's ligand layer and variation of salt concentration in the suspension prior to self-assembly result in a change of local orientational order. The degree of sixfold order is reduced after salt addition. This decrease of order is less pronounced for the fourfold symmetry. The results presented here suggest complex symmetry-selective order formation upon ligand exchange and salt addition and demonstrate the versatility of X-ray cross-correlation methods for nanoparticle superlattices.

Monitoring Nanocrystal Self-Assembly in Real Time Using In Situ Small-Angle X-Ray Scattering

Self-assembled nanocrystal superlattices have attracted large scientific attention due to their potential technological applications. However, the nucleation and growth mechanisms of superlattice assemblies remain largely unresolved due to experimental difficulties to monitor intermediate states. Here, the self-assembly of colloidal PbS nanocrystals is studied in real time by a combination of controlled solvent evaporation from the bulk solution and in situ small-angle X-ray scattering (SAXS) in transmission geometry. For the first time for the investigated system a hexagonal closed-packed (hcp) superlattice formed in a solvent vapor saturated atmosphere is observed during slow solvent evaporation from a colloidal suspension. The highly ordered hcp superlattice is followed by a transition into the final body-centered cubic superlattice upon complete drying. Additionally, X-ray cross-correlation analysis of Bragg reflections is applied to access information on precursor structures in the assembly process, which is not evident from conventional SAXS analysis. The detailed evolution of the crystal structure with time provides key results for understanding the assembly mechanism and the role of ligand-solvent interactions, which is important both for fundamental research and for fabrication of superlattices with desired properties.

Unwarping GISAXS data

Grazing-incidence small-angle X-ray scattering (GISAXS) is a powerful technique for measuring the nanostructure of coatings and thin films. However, GISAXS data are plagued by distortions that complicate data analysis. The detector image is a warped representation of reciprocal space because of refraction, and overlapping scattering patterns appear because of reflection. A method is presented to unwarp GISAXS data, recovering an estimate of the true undistorted scattering pattern. The method consists of first generating a guess for the structure of the reciprocal-space scattering by solving for a mutually consistent prediction from the transmission and reflection sub-components. This initial guess is then iteratively refined by fitting experimental GISAXS images at multiple incident angles, using the distorted-wave Born approximation (DWBA) to convert between reciprocal space and detector space. This method converges to a high-quality reconstruction for the undistorted scattering, as validated by comparing with grazing-transmission scattering data. This new method for unwarping GISAXS images will broaden the applicability of grazing-incidence techniques, allowing experimenters to inspect undistorted visualizations of their data and allowing a broader range of analysis methods to be applied to GI data.

Pressure-Stimulated Supercrystal Formation in Nanoparticle Suspensions

Nanoparticles can self-organize into "supercrystals" with many potential applications. Different paths can lead to nanoparticle self-organization into such periodic arrangements. An essential step is the transition from an amorphous state to the crystalline one. We investigate how pressure can induce a phase transition of a nanoparticle model system in water from the disordered liquid state to highly ordered supercrystals. We observe reversible pressure-induced supercrystal formation in concentrated solutions of gold nanoparticles by means of small-angle X-ray scattering. The supercrystal formation occurs only at high salt concentrations in the aqueous solution. The pressure dependence of the structural parameters of the resulting crystal lattices is determined. The observed transition can be reasoned with the combined effect of salt and pressure on the solubility of the organic PEG shell that passivates the nanoparticles.