Percus–Yevick structure factors made simple

Measurable structure factors of dense dispersions containing polydisperse optically inhomogeneous particles

Here, it is investigated how optical properties of single scatterers in interacting multi-particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core-shell structures evoke characteristic deviations between the weighted sum 〈S(Q)〉 of partial structure factors in a multi-component system and experimentally accessible measurable structure factors S M(Q). While 〈S(Q)〉 contains only the structural information of self-organizing systems, S M(Q) is additionally influenced by the optical properties of their constituents, resulting in features such as changing amplitudes, additional peaks in the low-wavevector region or splitting of higher-order maxima, which are not related to structural reasons. It is shown that these effects can be systematically categorized according to the qualitative behaviour of the form factor in the Guinier region, which enables assessing the suitability of experimentally obtained structure factors to genuinely represent the microstructure of complex systems free from any particular model assumption. Hence, a careful data analysis regarding size distribution and optical properties of single scatterers is mandatory to avoid a misinterpretation of measurable structure factors.

Catalyst Supraparticles: Tuning the Structure of Spray-Dried Pt/SiO2 Supraparticles via Salt-Based Colloidal Manipulation to Control their Catalytic Performance

The structure of supraparticles (SPs) is a key parameter for achieving advanced functionalities arising from the combination of different nanoparticle (NP) types in one hierarchical entity. However, whenever a droplet-assisted forced assembly approach is used, e.g., spray-drying, the achievable structure is limited by the inherent drying phenomena of the method. In particular, mixed NP dispersions of differently sized colloids are heavily affected by segregation during the assembly. Herein, the influence of the colloidal arrangement of Pt and SiO2 NPs within a single supraparticulate entity is investigated. A salt-based electrostatic manipulation approach of the utilized NPs is proposed to customize the structure of spray-dried Pt/SiO2 SPs. By this, size-dependent separation phenomena of NPs during solvent evaporation, that limit the catalytic performance in the reduction of 4-nitrophenol, are overcome by achieving even Pt NP distribution. Additionally, the textural properties (pore size and distribution) of the SiO2 pore framework are altered to improve the mass transfer within the material leading to increased catalytic activity. The suggested strategy demonstrates a powerful, material-independent, and universally applicable approach to deliberately customize the structure and functionality of multi-component SP systems. This opens up new ways of colloidal material combinations and structural designs in droplet-assisted forced assembly approaches like spray-drying.

pH-dependent structural transitions in cationic ionizable lipid mesophases are critical for lipid nanoparticle function

Lipid nanoparticles (LNPs) are advanced core-shell particles for messenger RNA (mRNA) based therapies that are made of polyethylene glycol (PEG) lipid, distearoylphosphatidylcholine (DSPC), cationic ionizable lipid (CIL), cholesterol (chol), and mRNA. Yet the mechanism of pH-dependent response that is believed to cause endosomal release of LNPs is not well understood. Here, we show that eGFP (enhanced green fluorescent protein) protein expression in the mouse liver mediated by the ionizable lipids DLin-MC3-DMA (MC3), DLin-KC2-DMA (KC2), and DLinDMA (DD) ranks MC3 ≥ KC2 > DD despite similar delivery of mRNA per cell in all cell fractions isolated. We hypothesize that the three CIL-LNPs react differently to pH changes and hence study the structure of CIL/chol bulk phases in water. Using synchrotron X-ray scattering a sequence of ordered CIL/chol mesophases with lowering pH values are observed. These phases show isotropic inverse micellar, cubic Fd3m inverse micellar, inverse hexagonal [Formula: see text] and bicontinuous cubic Pn3m symmetry. If polyadenylic acid, as mRNA surrogate, is added to CIL/chol, excess lipid coexists with a condensed nucleic acid lipid [Formula: see text] phase. The next-neighbor distance in the excess phase shows a discontinuity at the Fd3m inverse micellar to inverse hexagonal [Formula: see text] transition occurring at pH 6 with distinctly larger spacing and hydration for DD vs. MC3 and KC2. In mRNA LNPs, DD showed larger internal spacing, as well as retarded onset and reduced level of DD-LNP-mediated eGFP expression in vitro compared to MC3 and KC2. Our data suggest that the pH-driven Fd3m-[Formula: see text] transition in bulk phases is a hallmark of CIL-specific differences in mRNA LNP efficacy.

Mechanism of structural colors in binary mixtures of nanoparticle-based supraballs

Inspired by structural colors in avian species, various synthetic strategies have been developed to produce noniridescent, saturated colors using nanoparticle assemblies. Nanoparticle mixtures varying in particle chemistry and size have additional emergent properties that affect the color produced. For complex multicomponent systems, understanding the assembled structure and a robust optical modeling tool can empower scientists to identify structure-color relationships and fabricate designer materials with tailored color. Here, we demonstrate how we can reconstruct the assembled structure from small-angle scattering measurements using the computational reverse-engineering analysis for scattering experiments method and use the reconstructed structure in finite-difference time-domain calculations to predict color. We successfully, quantitatively predict experimentally observed color in mixtures containing strongly absorbing nanoparticles and demonstrate the influence of a single layer of segregated nanoparticles on color produced. The versatile computational approach that we present is useful for engineering synthetic materials with desired colors without laborious trial-and-error experiments.

Computational Reverse-Engineering Analysis for Scattering Experiments for Form Factor and Structure Factor Determination ("P(q) and S(q) CREASE")

In this paper, we present an open-source machine learning (ML)-accelerated computational method to analyze small-angle scattering profiles [I(q) vs q] from concentrated macromolecular solutions to simultaneously obtain the form factor P(q) (e.g., dimensions of a micelle) and the structure factor S(q) (e.g., spatial arrangement of the micelles) without relying on analytical models. This method builds on our recent work on Computational Reverse-Engineering Analysis for Scattering Experiments (CREASE) that has either been applied to obtain P(q) from dilute macromolecular solutions (where S(q) ∼1) or to obtain S(q) from concentrated particle solutions when P(q) is known (e.g., sphere form factor). This paper's newly developed CREASE that calculates P(q) and S(q), termed as "P(q) and S(q) CREASE", is validated by taking as input I(q) vs q from in silico structures of known polydisperse core(A)-shell(B) micelles in solutions at varying concentrations and micelle-micelle aggregation. We demonstrate how "P(q) and S(q) CREASE" performs if given two or three of the relevant scattering profiles-I _total(q), I _A(q), and I _B(q)-as inputs; this demonstration is meant to guide experimentalists who may choose to do small-angle X-ray scattering (for total scattering from the micelles) and/or small-angle neutron scattering with appropriate contrast matching to get scattering solely from one or the other component (A or B). After validation of "P(q) and S(q) CREASE" on in silico structures, we present our results analyzing small-angle neutron scattering profiles from a solution of core-shell type surfactant-coated nanoparticles with varying extents of aggregation.

Dense random packing with a power-law size distribution: The structure factor, mass-radius relation, and pair distribution function

We consider a dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation, and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1D) is solved exactly. It is shown theoretically in 1D and numerically in 1D and 2D that such a packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimensions is derived, which can be used as a fitting formula in small-angle scattering. These findings can be useful for understanding the microstructural properties of various systems such as ultra-high performance concrete, high-internal-phase-ratio emulsions, or biological systems.

Computational Reverse-Engineering Analysis for Scattering Experiments (CREASE) with Machine Learning Enhancement to Determine Structure of Nanoparticle Mixtures and Solutions

We present a new open-source, machine learning (ML) enhanced computational method for experimentalists to quickly analyze high-throughput small-angle scattering results from multicomponent nanoparticle mixtures and solutions at varying compositions and concentrations to obtain reconstructed 3D structures of the sample. This new method is an improvement over our original computational reverse-engineering analysis for scattering experiments (CREASE) method (ACS Materials Au2021, 1 (2 (2), ), 140-156), which takes as input the experimental scattering profiles and outputs a 3D visualization and structural characterization (e.g., real space pair-correlation functions, domain sizes, and extent of mixing in binary nanoparticle mixtures) of the nanoparticle mixtures. The new gene-based CREASE method reduces the computational running time by >95% as compared to the original CREASE and performs better in scenarios where the original CREASE method performed poorly. Furthermore, the ML model linking features of nanoparticle solutions (e.g., concentration, nanoparticles' tendency to aggregate) to a computed scattering profile is generic enough to analyze scattering profiles for nanoparticle solutions at conditions (nanoparticle chemistry and size) beyond those that were used for the ML training. Finally, we demonstrate application of this new gene-based CREASE method for analysis of small-angle X-ray scattering results from a nanoparticle solution with unknown nanoparticle aggregation and small-angle neutron scattering results from a binary nanoparticle assembly with unknown mixing/segregation among the nanoparticles.