Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Evidence for liquid-liquid phase separation during the early stages of Mg-struvite formation

The precipitation of struvite, a magnesium ammonium phosphate hexahydrate (MgNH4PO4 · 6H2O) mineral, from wastewater is a promising method for recovering phosphorous. While this process is commonly used in engineered environments, our understanding of the underlying mechanisms responsible for the formation of struvite crystals remains limited. Specifically, indirect evidence suggests the involvement of an amorphous precursor and the occurrence of multi-step processes in struvite formation, which would indicate non-classical paths of nucleation and crystallization. In this study, we use synchrotron-based in situ x-ray scattering complemented by cryogenic transmission electron microscopy to obtain new insights from the earliest stages of struvite formation. The holistic scattering data captured the structure of an entire assembly in a time-resolved manner. The structural features comprise the aqueous medium, the growing struvite crystals, and any potential heterogeneities or complex entities. By analysing the scattering data, we found that the onset of crystallization causes a perturbation in the structure of the surrounding aqueous medium. This perturbation is characterized by the occurrence and evolution of Ornstein-Zernike fluctuations on a scale of about 1 nm, suggesting a non-classical nature of the system. We interpret this phenomenon as a liquid-liquid phase separation, which gives rise to the formation of the amorphous precursor phase preceding actual crystal growth of struvite. Our microscopy results confirm that the formation of Mg-struvite includes a short-lived amorphous phase, lasting >10 s.

Surface Modification of Kraft Lignin by Mechanochemical Processing with Sodium Percarbonate

In this article, we present a novel one-pot mechanochemical reaction for the surface activation of lignin. The process involves environmentally friendly oxidation with hydrogen peroxide, depolymerization of fractions with high molecular mass, and introduction of new carbonyl functions into the lignin backbone. Kraft lignin was ground with sodium percarbonate and sodium hydroxide in a ball mill at different time intervals. Analyses by infrared spectroscopy (IR), nuclear magnetic resonance spectroscopy (NMR), size exclusion chromatography (SEC), dynamic vapor sorption (DVS), and small-angle X-ray scattering (SAXS) showed significant improvements. After only 5 min of reaction, there was a 47% reduction in mass-average molecular weight and an increase in carboxyl functionalities. Chemical activation resulted in an approximately 2.8-fold increase in water adsorption. Principal component analysis (PCA) provided further insight into the correlations between IR spectra and SAXS parameters.

Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size

Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-to-gel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle X-ray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.

Multiscale structures and rheology of bisurea-loaded resins for anti-sagging applications

Four representative bisurea molecules (HDI-BA, MDI-BA, TDI-BA, and IPDI-BA) were synthesized and dispersed simultaneously by reacting benzylamine (BA) with various types of diisocyanates in a polyester/ortho-xylene resin medium to produce bisurea-loaded resins (BLRs) for anti-sagging application with paints and coating materials. These bisurea molecules are symmetric and differ only in the central spacer unit, thereby presenting an ideal and simplest model system to delve into the structure-performance relationship. The multiscale structural features arising from self-assembly in each of the BLRs were scrutinized using the combination of multi-angular dynamic light scattering (DLS), small-angle light/X-ray scattering (SALS/SAXS), rheology, and scanning electron/optical microscopy (SEM/OM) characterization. All four BLRs were revealed to foster micron-sized, mostly sphere-like agglomerates, with distinct hierarchical structures that correlate well with their thixotropic and anti-sagging performances. Three BLRs (HDI-BA, MDI-BA, and TDI-BA) produce similar rod-like packing units (10 × 1 × 1 nm³), with only one exception (IPDI-BA) that produces a spherical packing unit (2 nm in diameter). However, the bulk feature of the agglomeration state, which dictates the thixotropic and anti-sagging properties, cannot be readily foreseen from the chemical structure or elementary packing unit of a bisurea. The present findings, while confirming the importance of optimum molecular design that controls the early-stage self-assembly behavior of a bisurea in resin media, highlight the necessity of resolving detailed (multiscale) structural features in order to establish the full structure-performance relationship imperatively needed for like material systems and applications.

Seeds of imperfection rule the mesocrystalline disorder in natural anhydrite single crystals

In recent years, we have come to appreciate the astounding intricacies associated with the formation of minerals from ions in aqueous solutions. In this context, a number of studies have revealed that the nucleation of calcium sulfate systems occurs nonclassically, involving the aggregation and reorganization of nanosized prenucleation species. In recent work, we have shown that this particle-mediated nucleation pathway is actually imprinted in the resultant micrometer-sized CaSO₄ crystals. This property of CaSO₄ minerals provides us with the unique opportunity to search for evidence of nonclassical nucleation pathways in geological environments. In particular, we focused on large anhydrite crystals extracted from the Naica Mine in Mexico. We were able to shed light on this mineral's growth history by mapping defects at different length scales. Based on this, we argue that the nanoscale misalignment of the structural subunits, observed in the initial calcium sulfate crystal seeds, propagates through different length scales both in morphological, as well as in strictly crystallographic aspects, eventually causing the formation of large mesostructured single crystals of anhydrite. Hence, the nonclassical nucleation mechanism introduces a "seed of imperfection," which leads to a macroscopic "single" crystal whose fragments do not fit together at different length scales in a self-similar manner. Consequently, anisotropic voids of various sizes are formed with very well-defined walls/edges. However, at the same time, the material retains in part its single crystal nature.

Multiscale structural and rheological features of colloidal low-methoxyl pectin solutions and calcium-induced sol-gel transition

The multiscale structural and rheological features of a series of dilute and semidilute low-methoxyl (LM) pectin solutions and a representative pectin/calcium sol-gel sample were systematically explored using a comprehensive combination of dynamic (DLS) and static light/X-ray scattering (SALS/SLS/SAXS), rheology, and microscopy (OM/SEM) characterizations. The study focused on the rarely explored colloidal aspect of LM pectin solutions and sol-gel transition, in contrast to the polymeric features extensively explored in previous studies. A highly uniform colloid-like, micron-sized agglomerate species was revealed in dilute solutions, with a progressively increased degree of flocculation in the semidilute regime (≥1.5 wt%). The agglomerate species in these solutions was resolved to be formed by random associations of individual pectin chains (L = 30 nm, r = 0.4 nm). Adding a critical amount of Ca²⁺ (10 wt%) to a semidilute solution (2 wt%) has an instant and pronounced effect of enhancing the agglomerate flocculation and resulting in a locally jammed state. Meanwhile, the agglomerate interior underwent microstructural transformation, leading to hierarchical structures defined by intermediate (spherical) aggregate species (R_g,aggregate ≈ 150 nm) and its packing cylindrical bundle (d ≈ 4 nm) composed of five pectin chains. Novel rheological features observed during the LM pectin/Ca²⁺ sol-gel transition include the following: the dynamic modulus data exhibited excellent TTS (gelling time/relaxation time superposition) as previously observed for weakly attractive colloidal gels. Three yield points were noticed for the final gel sample, suggested to mark the bond breaking of the cluster network, cage breaking of the resulting jammed flocculates, and, eventually, breakup of a flocculate into smaller agglomerates with increasing stress amplitude.

I22: SAXS/WAXS beamline at Diamond Light Source - an overview of 10 years operation

Beamline I22 at Diamond Light Source is dedicated to the study of soft-matter systems from both biological and materials science. The beamline can operate in the range 3.7 keV to 22 keV for transmission SAXS and 14 keV to 20 keV for microfocus SAXS with beam sizes of 240 µm × 60 µm [full width half-maximum (FWHM) horizontal (H) × vertical (V)] at the sample for the main beamline, and approximately 10 µm × 10 µm for the dedicated microfocusing platform. There is a versatile sample platform for accommodating a range of facilities and user-developed sample environments. The high brilliance of the insertion device source on I22 allows structural investigation of materials under extreme environments (for example, fluid flow at high pressures and temperatures). I22 provides reliable access to millisecond data acquisition timescales, essential to understanding kinetic processes such as protein folding or structural evolution in polymers and colloids.

Toward a Chemical Control of Colloidal YVO4 Nanoparticles Microstructure

Rare-earth-doped oxides are a class of compounds that have been largely studied in the context of the development of luminescent nanocrystals for various applications including fluorescent labels for bioimaging, MRI contrast agents, luminescent nanocomposite coatings, etc. Elaboration of colloidal suspensions is usually achieved through coprecipitation. Particles exhibit emission properties that are similar to the bulk counterparts, although altered by crystalline defects or surface quenching species. Focusing on YVO₄:Eu, one of the first reported systems, the aim of this work is to revisit the elaboration of nanoparticles obtained through a simple aqueous coprecipitation route. The objective is more precisely to get a better understanding of the parameters affecting the particles' internal microstructure, a feature that is poorly controlled and characterized. We show that the hydroxyl concentration in the precursor solution has a drastic effect on the particles' microstructure. Moreover, discrepancies in the reported particle structure are shown to possibly arise from the carbonation of the strongly basic orthovanadate precursor. For this study, SAXS/WAXS is shown to be a powerful tool to characterize the multiscale structure of the particles. It could be shown that playing on the precursor composition, it may be varied between almost monocrystalline nanocrystals to particles exhibiting a hierarchical microstructure well described by a surface fractal model. This work provides a new methodology for the characterization of nanoparticles microstructure and opens new directions for its optimization in view of applications.

Polymer Zwitterions for Stabilization of CsPbBr3 Perovskite Nanoparticles and Nanocomposite Films

Functional polymers with sulfobetaine or phosphorylcholine zwitterions as pendent groups are demonstrated as both ligands and host matrices for CsPbBr₃ perovskite nanoparticles (PNPs). These polymers produce nanocomposite films with excellent NP dispersion, optical transparency, and impressive resistance to NP degradation upon exposure to water. Multidentate interactions of the zwitterion-containing copolymers with the PNPs induce dispersed or weakly aggregated nanocomposite morphologies, depending on the extent of zwitterionic functionality in the polymer. Incorporating additional functionality into the polymers, such as benzophenone pendent groups, yields lithographically patternable films, while time-resolved photoluminescence measurements provide insight into the electronic impact of PNPs in zwitterionic polymer matrices.

PET-RAFT and SAXS: High Throughput Tools to Study Compactness and Flexibility of Single-Chain Polymer Nanoparticles

From protein science, it is well understood that ordered folding and 3D structure mainly arises from balanced and noncovalent polar and nonpolar interactions, such as hydrogen bonding. Similarly, it is understood that single-chain polymer nanoparticles (SCNPs) will also compact and become more rigid with greater hydrophobicity and intrachain hydrogen bonding. Here, we couple high throughput photoinduced electron/energy transfer reversible addition-fragmentation chain-transfer (PET-RAFT) polymerization with high throughput small-angle X-ray scattering (SAXS) to characterize a large combinatorial library (>450) of several homopolymers, random heteropolymers, block copolymers, PEG-conjugated polymers, and other polymer-functionalized polymers. Coupling these two high throughput tools enables us to study the major influence(s) for compactness and flexibility in higher breadth than ever before possible. Not surprisingly, we found that many were either highly disordered in solution, in the case of a highly hydrophilic polymer, or insoluble if too hydrophobic. Remarkably, we also found a small group (9/457) of PEG-functionalized random heteropolymers and block copolymers that exhibited compactness and flexibility similar to that of bovine serum albumin (BSA) by dynamic light scattering (DLS), NMR, and SAXS. In general, we found that describing a rough association between compactness and flexibility parameters (R g /R h and Porod Exponent, respectively) with logP, a quantity that describes hydrophobicity, helps to demonstrate and predict material parameters that lead to SCNPs with greater compactness, rigidity, and stability. Future implementation of this combinatorial and high throughput approach for characterizing SCNPs will allow for the creation of detailed design parameters for well-defined macromolecular chemistry.

A template-free and low temperature method for the synthesis of mesoporous magnesium phosphate with uniform pore structure and high surface area

Mesoporous phosphates are a group of nanostructured materials with promising applications, particularly in biomedicine and catalysis. However, their controlled synthesis via conventional template-based routes presents a number of challenges and limitations. Here, we show how to synthesize a mesoporous magnesium phosphate with a high surface area and a well-defined pore structure through thermal decomposition of a crystalline struvite (MgNH4PO4·6H2O) precursor. In a first step, struvite crystals with various morphologies and sizes, ranging from a few micrometers to several millimeters, had been synthesized from supersaturated aqueous solutions (saturation index (SI) between 0.5 and 4) at ambient pressure and temperature conditions. Afterwards, the crystals were thermally treated at 70-250 °C leading to the release of structurally bound water (H2O) and ammonia (NH3). By combining thermogravimetric analyses (TGA), scanning and transmission electron microscopy (SEM, TEM), N2 sorption analyses and small- and wide-angle X-ray scattering (SAXS/WAXS) we show that this decomposition process results in a pseudomorphic transformation of the original struvite into an amorphous Mg-phosphate. Of particular importance is the fact that the final material is characterized by a very uniform mesoporous structure with 2-5 nm wide pore channels, a large specific surface area of up to 300 m2 g-1 and a total pore volume of up to 0.28 cm3 g-1. Our struvite decomposition method is well controllable and reproducible and can be easily extended to the synthesis of other mesoporous phosphates. In addition, the so produced mesoporous material is a prime candidate for use in biomedical applications considering that magnesium phosphate is a widely used, non-toxic substance that has already shown excellent biocompatibility and biodegradability.

Structure of intermediate filament assembly in hair deduced from hydration studies using small-angle neutron scattering

Intermediate filaments (IFs) are ubiquitous in biological structures including hair. Small-angle neutron scattering (SANS) data from hydrated samples were used in this study to investigate the distribution of water in hair, and model the structure of the IF assembly. A main diffraction peak at a d-spacing of ∼90 Å, and two weaker reflections show that IFs are arranged in a ∼105 Å quasi-hexagonal lattice. Changes in the diffraction peaks show that only a small fraction of the water absorbed by hair enters between the IFs, and little water diffuses into the core of the IFs. The amount of water in the IF assembly increases rapidly up to 10% relative humidity (RH), and then slowly with further increase in RH. Most of the water appears to reside outside the IF assembly, in the voids and at the interfaces, and contribute to the central diffuse scattering. The IF assembly in the decuticled hair absorbs more water and is more ordered than that the native hair. This suggests that cuticle acts as a barrier, and might constrain the structure by compressing the cortex radially. Treatments with oils that are hydrophobic, heat treatment, and reduction of the S-S linkages that opens up the matrix by disulfide bond cleavage, all affect structure and water permeability. Coconut oil was found to impede hydration more than the soybean oil because of its ability to penetrate deeper into hair. A new model for the IF assembly that is sterically more favorable than the previous models is proposed.

Mechanism of silica-lysozyme composite formation unravelled by in situ fast SAXS

A quantitative understanding of aggregation mechanisms leading to the formation of composites of inorganic nanoparticles (NPs) and proteins in aqueous media is of paramount interest for colloid chemistry. In particular, the interactions between silica (SiO₂) NPs and lysozyme (LZM) have attracted attention, because LZM is well-known to adsorb strongly to silica NPs, while at the same time preserving its enzymatic activity. The inherent nature of the aggregation processes leading to NP-LZM composites involves structural changes at length scales from few to at least hundreds of nanometres but also time scales much smaller than one second. To unravel these we used in situ synchrotron-based small-angle X-ray scattering (SAXS) and followed the subtle interparticle interactions in solution at a time resolution of 50 ms/frame (20 fps). We show that if the size of silica NPs (ca. 5 nm diameter) is matched by the dimensions of LZM, the evolving scattering patterns contain a unique structure-factor contribution originating from the presence of LZM. We developed a scattering model and applied it to analyse this structure function, which allowed us to extract structural information on the deformation of lysozyme molecules during aggregation, as well as to derive the mechanisms of composite formation.

The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data

Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures is studied theoretically.

Following the Kinetics of Barium Titanate Nanocrystal Formation in Benzyl Alcohol Under Near-Ambient Conditions

In complex chemical syntheses (e.g., coprecipitation reactions), nucleation, growth, and coarsening often occur concurrently, obscuring the individual processes. Improved knowledge of these processes will help to better understand and optimize the reaction protocol. Here, a form-free and model independent approach, based on a combination of time-resolved small/wide-angle X-ray scattering, is employed to elucidate the effect of reaction parameters (such as precursor concentration, reactant stoichiometry, and temperature) on the nucleation, crystallization, and growth phenomena during the formation of nanocrystalline barium titanate. The strength of this approach is that it relies solely on the total scattered intensity (i.e., scattering invariant) of the investigated system, and no prior knowledge is required. As such, it can be widely applied to other synthesis protocols and material's systems. Through the scattering invariant, it is found that the amorphous-to-crystalline transformation of barium titanate is predominantly determined by the total amount of water released from the gel-like barium hydroxide octahydrate precursor, and three rate-limiting regimes are established. As a result of this improved understanding of the effect of varying reaction conditions, elementary boundary conditions can be set up for a better control of the barium titanate nanocrystal synthesis.

Scattering from surface fractals in terms of composing mass fractals

It is argued that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of a surface fractal is shown to be a sum of the amplitudes of the composing mass fractals. Various approximations for the scattering intensity of surface fractals are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of a power-law distribution of sizes of objects composing the fractal (internal polydispersity), provided the distance between objects is much larger than their size for each composing mass fractal. The power-law decay of the scattering intensityI(q) ∝ q^{D_{\rm s}-6}, where 2 <Ds< 3 is the surface-fractal dimension of the system, is realized as a non-coherent sum of scattering amplitudes of three-dimensional objects composing the fractal and obeying a power-law distribution dN(r) ∝r−τdr, withDs= τ − 1. The distribution is continuous for random fractals and discrete for deterministic fractals. A model of the surface deterministic fractal is suggested, the surface Cantor-like fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and its scattering properties are studied. The present analysis allows one to extract additional information from SAS intensity for dilute aggregates of single-scaled surface fractals, such as the fractal iteration number and the scaling factor.