Angular X-ray Cross-correlation Analysis Research Articles

Revealing the Impact of Polystyrene Functionalization of Au Octahedral Nanocrystals of Different Sizes on the Formation and Structure of Mesocrystals

AbstractThe self‐assembly of anisotropic nanocrystals (stabilized by organic capping molecules) with pre‐selected composition, size, and shape allows for the creation of nanostructured materials with unique structures and features. For such a material, the shape and packing of the individual nanoparticles play an important role. This work presents a synthesis procedure for ω‐thiol‐terminated polystyrene (PS‐SH) functionalized gold nanooctahedra of variable size (edge length 37, 46, 58, and 72 nm). The impact of polymer chain length (Mw: 11k, 22k, 43k, and 66k g⋅mol−1) on the growth of colloidal crystals (e. g. mesocrystals) and their resulting crystal structure is investigated. Small‐angle X‐ray scattering (SAXS) and scanning transmission electron microscopy (STEM) methods provide a detailed structural examination of the self‐assembled faceted mesocrystals based on octahedral gold nanoparticles of different size and surface functionalization. Three‐dimensional angular X‐ray cross‐correlation analysis (AXCCA) enables high‐precision determination of the superlattice structure and relative orientation of nanoparticles in mesocrystals. This approach allows us to perform non‐destructive characterization of mesocrystalline materials and reveals their structure with resolution down to the nanometer scale.

Going beyond ensemble average angular cross-correlation analysis.

Commentary is given on a paper [Lapkin et al. (2022). IUCrJ, 9, 425-438] reporting the application of angular X-ray cross-correlation analysis to the scattered intensity distribution measured in 3D reciprocal space from a single-crystalline sample.

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.

Structure–Transport Correlation Reveals Anisotropic Charge Transport in Coupled PbS Nanocrystal Superlattices

The assembly of colloidal semiconductive nanocrystals into highly ordered superlattices predicts novel structure-related properties by design. However, those structure-property relationships, such as charge transport depending on the structure or even directions of the superlattice, have remained unrevealed so far. Here, electric transport measurements and X-ray nanodiffraction are performed on self-assembled lead sulfide nanocrystal superlattices to investigate direction-dependent charge carrier transport in microscopic domains of these materials. By angular X-ray cross-correlation analysis, the structure and orientation of individual superlattices is determined, which are directly correlated with the electronic properties of the same microdomains. By that, strong evidence for the effect of superlattice crystallinity on the electric conductivity is found. Further, anisotropic charge transport in highly ordered monocrystalline domains is revealed, which is attributed to the dominant effect of shortest interparticle distance. This implies that transport anisotropy should be a general feature of weakly coupled nanocrystal superlattices.

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.

Ultrafast structural dynamics of photo-reactions observed by time-resolved x-ray cross-correlation analysis.

We applied angular X-ray Cross-Correlation analysis (XCCA) to scattering images from a femtosecond resolution X-ray free-electron laser pump-probe experiment with solvated PtPOP {[Pt2(P2O5H2)4]4–} metal complex molecules. The molecules were pumped with linear polarized laser pulses creating an excited state population with a preferred orientational (alignment) direction. Two time scales of 1.9 ± 1.5 ps and 46 ± 10 ps were revealed by angular XCCA associated with structural changes and rotational dephasing of the solvent molecules, respectively. These results illustrate the potential of XCCA to reveal hidden structural information in the analysis of time-resolved x-ray scattering data from molecules in solution.

Structural studies of the bond-orientational order and hexatic–smectic transition in liquid crystals of various compositions

We report on the X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of the existence of the hexatic phase for all three compounds. The temperature dependence of the BO order parameters in the vicinity of the hexatic-smectic transition was fitted by a conventional power law with a critical exponent β ≈ 0.1 of extremely small value. We found that the temperature dependence of higher order harmonics of the BO order scales as the powers of the first harmonic, with an exponent equal to the harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. We demonstrate that compounds of various compositions, possessing different phase sequences at low temperatures, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition.

Spatially resolved x-ray studies of liquid crystals with strongly developed bond-orientational order.

We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC. Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the formation of large-scale hexatic domains at lower temperatures. Deep in the hexatic phase up to 25 successive sixfold BO order parameters have been directly determined by means of angular x-ray cross-correlation analysis (XCCA). Such strongly developed hexatic order allowed us to determine higher order correction terms in the scaling relation predicted by the multicritical scaling theory over a full temperature range of the hexatic phase existence.

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. By applying two-point angular-intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order.

X-Ray Cross-Correlation Analysis of Disordered Ensembles of Particles: Potentials and Limitations

Angular X-ray cross-correlation analysis (XCCA) is an approach to study the structure of disordered systems using the results of X-ray scattering experiments. In this paper we summarize recent theoretical developments related to the Fourier analysis of the cross-correlation functions. Results of our simulations demonstrate the application of XCCA to two- and three-dimensional (2D and 3D) disordered ensembles of particles. We show that the structure of a single particle can be recovered using X-ray data collected from a 2D disordered system of identical particles. We also demonstrate that valuable structural information about the local structure of 3D systems, inaccessible from a standard small-angle X-ray scattering experiment, can be resolved using XCCA.

X-ray cross-correlation analysis applied to disordered two-dimensional systems

Angular x-ray cross-correlation analysis (XCCA) is an approach to study the structure of disordered systems using the results of coherent x-ray scattering experiments. Here, we present the results of simulations that validate our theoretical findings for XCCA obtained in a previous paper [M. Altarelli et al., Phys. Rev. B 82, 104207 (2010)]. We consider as a model two-dimensional (2D) disordered systems composed of non-interacting colloidal clusters with fivefold symmetry and with orientational and positional disorder. We simulate a coherent x-ray scattering in the far field from such disordered systems and perform the angular cross-correlation analysis of calculated diffraction data. The results of our simulations show the relation between the Fourier series representation of the cross-correlation functions (CCFs) and different types of correlations in disordered systems. The dependence of structural information extracted by XCCA on the density of disordered systems and the degree of orientational disorder of clusters is investigated. The statistical nature of the fluctuations of the CCFs in the model `single-shot' experiments is demonstrated and the potential of extracting structural information from the analysis of CCFs averaged over a set of diffraction patterns is discussed. We also demonstrate the effect of partial coherence of x-rays on the results of XCCA.