Using the singular value decomposition to extract 2D correlation functions from scattering patterns

Shape-induced superstructure formation in concentrated ferrofluids under applied magnetic fields

The field-induced ordering of concentrated ferrofluids based on spherical and cuboidal maghemite nanoparticles is studied using small-angle neutron scattering, revealing a qualitative effect of the faceted shape on the interparticle interactions as shown in the structure factor and correlation lengths. Whereas a spatially disordered hard-sphere interaction potential with a short correlation length is found for ∼9 nm spherical nanoparticles, nanocubes of a comparable particle size exhibit a more pronounced interparticle interaction and the formation of linear arrangements. Analysis of the anisotropic two-dimensional pair distance correlation function gives insight into the real-space arrangement of the nanoparticles. On the basis of the short interparticle distances found here, oriented attachment, i.e. a face-to-face arrangement of the nanocubes, is likely. The unusual field dependence of the interparticle correlations suggests a field-induced structural rearrangement.

Robust approaches for model-free small-angle scattering data analysis

The small-angle neutron scattering data of nanostructured magnetic samples contain information regarding their chemical and magnetic properties. Often, the first step to access characteristic magnetic and structural length scales is a model-free investigation. However, due to measurement uncertainties and a restricted q range, a direct Fourier transform usually fails and results in ambiguous distributions. To circumvent these problems, different methods have been introduced to derive regularized, more stable correlation functions, with the indirect Fourier transform being the most prominent approach. Here, the indirect Fourier transform is compared with the singular value decomposition and an iterative algorithm. These approaches are used to determine the correlation function from magnetic small-angle neutron scattering data of a powder sample of iron oxide nanoparticles; it is shown that with all three methods, in principle, the same correlation function can be derived. Each method has certain advantages and disadvantages, and thus the recommendation is to combine these three approaches to obtain robust results.

Combination of Group Singular Value Decomposition and eLORETA Identifies Human EEG Networks and Responses to Transcranial Photobiomodulation

Transcranial Photobiomodulation (tPBM) has demonstrated its ability to alter electrophysiological activity in the human brain. However, it is unclear how tPBM modulates brain electroencephalogram (EEG) networks and is related to human cognition. In this study, we recorded 64-channel EEG from 44 healthy humans before, during, and after 8-min, right-forehead, 1,064-nm tPBM or sham stimulation with an irradiance of 257 mW/cm². In data processing, a novel methodology by combining group singular value decomposition (gSVD) with the exact low-resolution brain electromagnetic tomography (eLORETA) was implemented and performed on the 64-channel noise-free EEG time series. The gSVD+eLORETA algorithm produced 11 gSVD-derived principal components (PCs) projected in the 2D sensor and 3D source domain/space. These 11 PCs took more than 70% weight of the entire EEG signals and were justified as 11 EEG brain networks. Finally, baseline-normalized power changes of each EEG brain network in each EEG frequency band (delta, theta, alpha, beta and gamma) were quantified during the first 4-min, second 4-min, and post tPBM/sham periods, followed by comparisons of frequency-specific power changes between tPBM and sham conditions. Our results showed that tPBM-induced increases in alpha powers occurred at default mode network, executive control network, frontal parietal network and lateral visual network. Moreover, the ability to decompose EEG signals into individual, independent brain networks facilitated to better visualize significant decreases in gamma power by tPBM. Many similarities were found between the cortical locations of SVD-revealed EEG networks and fMRI-identified resting-state networks. This consistency may shed light on mechanistic associations between tPBM-modulated brain networks and improved cognition outcomes.

Using small-angle scattering to guide functional magnetic nanoparticle design

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

Probing the stability and magnetic properties of magnetosome chains in freeze-dried magnetotactic bacteria

Magnetospirillum gryphiswaldense biosynthesize high-quality magnetite nanoparticles, called magnetosomes, and arrange them into a chain that behaves like a magnetic compass. Here we perform magnetometry and polarized small-angle neutron scattering (SANS) experiments on a powder of freeze-dried and immobilized M. gryphiswaldense. We confirm that the individual magnetosomes are single-domain nanoparticles and that an alignment of the particle moments along the magnetic field direction occurs exclusively by an internal, coherent rotation. Our magnetometry results of the bacteria powder indicate an absence of dipolar interactions between the particle chains and a dominant uniaxial magnetic anisotropy. Finally, we can verify by SANS that the chain structure within the immobilized, freeze-dried bacteria is preserved also after application of large magnetic fields up to 1 T.