Nanoscale Critical Phenomena in a Complex Fluid Studied by X-Ray Photon Correlation Spectroscopy

Insights into water extraction and aggregation mechanisms of malonamide-alkane mixtures

Structure at the nanoscale in the organic phase of liquid-liquid extraction systems is often tied to separation performance. However, the weak interactions that drive extractant assembly lead to poorly defined structures that are challenging to identify. Here, we investigate the mechanism of water extraction for a malonamide extractant commonly applied to f-element separations. We measure extractant concentration fluctuations in the organic phase with small angle X-ray scattering (SAXS) before and after contact with water at fine increments of extractant concentration, finding no qualitative changes upon water uptake that might suggest significant nanoscopic reorganization of the solution. The critical composition for maximum fluctuation intensity is consistent with small water-extractant adducts. The extractant concentration dependence of water extraction is consistent with a power law close to unity in the low concentration regime, suggesting the formation of 1 : 1 water-extractant adducts as the primary extraction mechanism at low concentration. At higher extractant concentrations, the power law slope increases slightly, which we find is consistent with activity effects modeled using Flory-Huggins theory without introduction of additional extractant-water species. Molecular dynamics simulations are consistent with these findings. The decrease in interfacial tension with increasing extractant concentration shows a narrow plateau region, but it is not correlated with any change in fluctuation or water extraction trends, further suggesting no supramolecular organization such as reverse micellization. This study suggests that water extraction in this system is particularly simple: it relies on a single mechanism at all extractant concentrations, and only slightly enhances the concentration fluctuations characteristic of the dry binary extractant/diluent mixture.

Rheology and dynamics of a solvent segregation driven gel (SeedGel)

Bicontinuous structures promise applications in a broad range of research fields, such as energy storage, membrane science, and biomaterials. Kinetically arrested spinodal decomposition is found responsible for stabilizing such structures in different types of materials. A recently developed solvent segregation driven gel (SeedGel) is demonstrated to realize bicontinuous channels thermoreversibly with tunable domain sizes by trapping nanoparticles in a particle domain. As the mechanical properties of SeedGel are very important for its future applications, a model system is characterized by temperature-dependent rheology. The storage modulus shows excellent thermo-reproducibility and interesting temperature dependence with the maximum storage modulus observed at an intermediate temperature range (around 28 °C). SANS measurements are conducted at different temperatures to identify the macroscopic solvent phase separation during the gelation transition, and solvent exchange between solvent and particle domains that is responsible for this behavior. The long-time dynamics of the gel is further studied by X-ray Photon Correlation Spectroscopy (XPCS). The results indicate that particles in the particle domain are in a glassy state and their long-time dynamics are strongly correlated with the temperature dependence of the storage modulus.

Direct measurement of Stokes-Einstein diffusion of Cowpea mosaic virus with 19 µs-resolved XPCS

Brownian motion of Cowpea mosaic virus (CPMV) in water was measured using small-angle X-ray photon correlation spectroscopy (SA-XPCS) at 19.2 µs time resolution. It was found that the decorrelation time τ(Q) = 1/DQ² up to Q = 0.091 nm^-1. The hydrodynamic radius R_H determined from XPCS using Stokes-Einstein diffusion D = kT/(6πηR_H) is 43% larger than the geometric radius R₀ determined from SAXS in the 0.007 M K₃PO₄ buffer solution, whereas it is 80% larger for CPMV in 0.5 M NaCl and 104% larger in 0.5 M (NH₄)₂SO₄, a possible effect of aggregation as well as slight variation of the structures of the capsid resulting from the salt-protein interactions.

pyXPCSviewer: an open-source interactive tool for X-ray photon correlation spectroscopy visualization and analysis

pyXPCSviewer, a Python-based graphical user interface that is deployed at beamline 8-ID-I of the Advanced Photon Source for interactive visualization of XPCS results, is introduced. pyXPCSviewer parses rich X-ray photon correlation spectroscopy (XPCS) results into independent PyQt widgets that are both interactive and easy to maintain. pyXPCSviewer is open-source and is open to customization by the XPCS community for ingestion of diversified data structures and inclusion of novel XPCS techniques, both of which are growing demands particularly with the dawn of near-diffraction-limited synchrotron sources and their dedicated XPCS beamlines.

Microscopic Dynamics of Inverse Wormlike Micelles Probed Using X-ray Photon Correlation Spectroscopy

Wormlike micelles (WLMs) are ubiquitous viscoelastic modifiers that share properties with polymer solutions. While their macroscopic rheology is well-understood, their microscopic dynamics remain difficult to measure because they span a large range of time and length scales. In this work, we demonstrate the use of X-ray photon correlation spectroscopy to interrogate the segmental dynamics of inverse WLM solutions swollen with a rubidium chloride solution. We observe a diffusive scaling of the dynamics and extract a temperature-dependent diffusion coefficient, which we associate with the thermal interactions of the slow segmental dynamics near entanglement points. We probe this relaxation process across the unbranched to branched topological transition and find no microstructural evidence of branch formation in the slow mode. Instead, we observe that the dynamics become more homogeneous and prominent as the temperature is reduced and water content increases.

Advancing Chemical Separations: Unraveling the Structure and Dynamics of Phase Splitting in Liquid-Liquid Extraction

Liquid-liquid extraction (LLE), the go-to process for a variety of chemical separations, is limited by spontaneous organic phase splitting upon sufficient solute loading, called third phase formation. In this study we explore the applicability of critical phenomena theory to gain insight into this deleterious phase behavior with the goal of improving separations efficiency and minimizing waste. A series of samples representative of rare earth purification were constructed to include each of one light and one heavy lanthanide (cerium and lutetium) paired with one of two common malonamide extractants (DMDOHEMA and DMDBTDMA). The resulting postextraction organic phases are chemically complex and often form rich hierarchical structures whose statics and dynamics near the critical point were probed herein with small-angle X-ray scattering and high-speed X-ray photon correlation spectroscopy. Despite their different extraction behaviors, all samples show remarkably similar critical behavior with exponents well described by classical critical point theory consistent with the 3D Ising model, where the critical behavior is characterized by fluctuations with a single diverging length scale. This unexpected result indicates a significant reduction in relevant chemical parameters at the critical point, indicating that the underlying behavior of phase transitions in LLE rely on far fewer variables than are generally assumed. The obtained scalar order parameter is attributed to the extractant fraction of the extractant/diluent mixture, revealing that other solution components and their respective concentrations simply shift the critical temperature but do not affect the nature of the critical fluctuations. These findings point to an opportunity to drastically simplify studies of liquid-liquid phase separation and phase diagram development in general while providing insights into LLE process improvement.

The pervasive impact of critical fluctuations in liquid-liquid extraction organic phases

Liquid-liquid extraction is an essential chemical separation technique where polar solutes are extracted from an aqueous phase into a nonpolar organic solvent by amphiphilic extractant molecules. A fundamental limitation to the efficiency of this important technology is third phase formation, wherein the organic phase splits upon sufficient loading of polar solutes. The nanoscale drivers of phase splitting are challenging to understand in the complex hierarchically structured organic phases. In this study, we demonstrate that the organic phase structure and phase behavior are fundamentally connected in a way than can be understood with critical phenomena theory. For a series of binary mixtures of trialkyl phosphate extractants with linear alkane diluents, we combine small angle x-ray scattering and molecular dynamics simulations to demonstrate how the organic phase mesostructure over a wide range of compositions is dominated by critical concentration fluctuations associated with the critical point of the third phase formation phase transition. These findings reconcile many longstanding inconsistencies in the literature where small angle scattering features, also consistent with such critical fluctuations, were interpreted as reverse micellar-like particles. Overall, this study shows how the organic phase mesostructure and phase behavior are intrinsically linked, deepening our understanding of both and providing a new framework for using molecular structure and thermodynamic variables to control mesostructure and phase behavior in liquid-liquid extraction.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Mesostructuring in Liquid-Liquid Extraction Organic Phases Originating from Critical Points

Organic phase structure plays an important role in solute extraction energetics and phase behavior of liquid-liquid extraction (LLE) systems. For a binary extractant (amphiphile)/solvent mixture of relevance to LLE, we find that the organic phase mesostructuring is consistent with extractant concentration fluctuations as the compositional isotherm traverses the Widom line above its liquid-liquid critical point. This reveals a different mechanism for the well-documented heterogeneities in LLE organic phases that are typically attributed to micellization.