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DOE OSTI2023

Molecular interactions in short-chain perfluoroalkyl carboxylic acids and aqueous solutions

The presence of short-chain per- and polyfluoroalkyl substances in water poses a major health and environmental challenge. Here, we have performed high-energy small- and wide-angle X-ray scattering measurements on CF 3 [CF 2 ] n COOH (where n = 1, 2, 3 represents the chain length) and their aqueous solutions at 10% mole concentrations to characterize their molecular interactions at the atomic and nanometer length scales. The experimental wide-angle structure factors have been modelled using Empirical Potential Structural Refinement. The oxygen–oxygen partial X-ray pair distribution functions show that the coordination number between the hydroxyl oxygen on the acid and surrounding oxygen water molecules increases significantly with acid chain length, rising from 3.2 for n = 1 to 4.1 for n = 3. The small-angle scattering is dominated by a sharp, high-intensity peak at Q 1 ~ 0.2 Å -1 and a smaller peak at Q 2 = 1.2 Å -1 for n = 3, both of which decrease with decreasing chain length. The Q 2 peak is attributed to groups of adjacent non-bonded acid molecules, and Q 1 has contributions from both correlations between acid molecules and water–water interactions. In all cases, the models show nanoscale aggregation occurs in the form of denser channels of winding hydrogen-bonded chains, approximately 20 water molecules in length, surrounding clusters of acid molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Patternable Mesoporous Thin Film Quantum Materials via Block Copolymer Self-Assembly: An Emergent Technology?

Recent developments in quantum materials hold promise for revolutionizing energy and information technologies. The use of soft matter self-assembly, for example, by employing block copolymers (BCPs) as structure directing or templating agents, offers facile pathways toward quantum metamaterials with highly tunable mesostructures via scalable solution processing. Here, we report the preparation of patternable mesoporous niobium carbonitride-type thin film superconductors through spin-coating of a hybrid solution containing an amphiphilic BCP swollen by niobia sol precursors and subsequent thermal processing in combination with photolithography. Spin-coated as-made BCP-niobia hybrid thin films on silicon substrates after optional photolithographic definition are heated in air to produce a porous oxide, and subsequently converted in a multistep process to carbonitrides via treatment with high temperatures in reactive gases including ammonia. Grazing incidence small-angle X-ray scattering suggests the presence of ordered mesostructures in as-made BCP-niobia films without further annealing, consistent with a distorted alternating gyroid morphology that is retained upon thermal treatments. Wide-angle X-ray scattering confirms the synthesis of phase-pure niobium carbonitride nanocrystals with rock-salt lattices within the mesoscale networks. Electrical transport measurements of unpatterned thin films show initial exponential rise in resistivity characteristic of thermal activation in granular systems down to 12.8 K, at which point resistivity drops to zero into a superconducting state. Magnetoresistance measurements determine the superconducting upper critical field to be over 16 T, demonstrating material quality on par with niobium carbonitrides obtained from traditional solid-state synthesis methods. Here. we discuss how such cost-effective and scalable solution-based quantum materials fabrication approaches may be integrated into existing microelectronics processing, promising the emergence of a technology with tremendous academic and industrial potential by combining the capabilities of soft matter self-assembly with quantum materials.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Shear-induced polydomain structures of nematic lyotropic chromonic liquid crystal disodium cromoglycate

Lyotropic chromonic liquid crystals (LCLCs) represent aqueous dispersions of organic disk-like molecules that form cylindrical aggregates. Despite the growing interest in these materials, their flow behavior is poorly understood. Here, we explore the effect of shear on dynamic structures of the nematic LCLC, formed by 14 wt% water dispersion of disodium cromoglycate (DSCG). We employ in situ polarizing optical microscopy (POM) and small-angle and wide-angle X-ray scattering (SAXS/WAXS) to obtain independent and complementary information on the director structures over a wide range of shear rates. The DSCG nematic shows a shear-thinning behavior with two shear-thinning regions (Region I at $\dot{\gamma}$ < 1 s -1 and Region III at $\dot{\gamma}$ > 10 s -1 ) separated by a pseudo-Newtonian Region II (1 s-1 < $\dot{\gamma}$ < 10 s -1 ). The material is of a tumbling type. In Region I, $\dot{\gamma}$ < 1 s -1 , the director realigns along the vorticity axis. An increase of [small gamma, Greek, dot above] above 1 s -1 triggers nucleation of disclination loops. The disclinations introduce patches of the director that deviates from the vorticity direction and form a polydomain texture. Extension of the domains along the flow and along the vorticity direction decreases with the increase of the shear rate to 10 s -1 . Above 10 s -1 , the domains begin to elongate along the flow. At $\dot{\gamma}$ > 100 s -1 , the texture evolves into periodic stripes in which the director is predominantly along the flow with left and right tilts. The period of stripes decreases with an increase of $\dot{\gamma}$. The shear-induced transformations are explained by the balance of the elastic and viscous energies. In particular, nucleation of disclinations is associated with an increase of the elastic energy at the walls separating nonsingular domains with different director tilts. The uncovered shear-induced structural effects would be of importance in the further development of LCLC applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

PVDF-based backsheet cracking: Mapping in situ phase evolution by X-ray scattering

One of the most common polymers used in commercial photovoltaic backsheets is polyvinylidene fluoride (PVDF). However, recent reports have shown the potential for PVDF-based backsheets to crack and fail prematurely. Previous work has suggested that polymer phase changes play a role in the failure mechanism. Here, in situ wide-angle X-ray scattering maps are used to show that α- to β-phase transformations occur at crack tips in aged PVDF-based backsheets under stretching. Substantial β-phase formation is shown to be associated with strain hardening. In addition, our work demonstrates that β-phase formation is not required for crack growth and only occurs at crack tips when plastic deformation of the PVDF polymer has occurred. In conclusion, the anisotropy in the strength of aged PVDF-based backsheets is linked to the lack of β-phase formation when strain is applied to aged backsheets in the transverse direction.

14 SOLAR ENERGY↗

DOE OSTI2022

In situ synchrotron tensile investigations on ultrasonic additive manufactured (UAM) zirconium

The microstructure evolution during room temperature uniaxial tensile straining of ultrasonic additive manufactured (UAM) zirconium was evaluated using the Advanced Photon Source (APS) facility. Miniature dog-bone tensile specimens of two orientations were cut from a UAM-fabricated zirconium bar for in situ synchrotron tensile tests. Wide-angle X-ray scattering (WAXS) scanning was used to unveil the changes in microstructure of the entire gauge regions throughout the straining. A series of WAXS data analysis methods were utilized to quantify both elastic and plastic deformation mechanisms within the strained specimens. Stress concentrations were identified during early stages of plastic deformation, which become candidate necking positions and eventually lead to failure. Additionally, fracture surface analysis implied that these stress concentration locations may be correlated to the fabrication defects, providing insightful guidance for future improvements of the UAM zirconium fabrication process.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Structure of ice confined in silica nanopores

Observed anomalous thermodynamic properties of confined water such as deviations in the melting point and freezing point motivate the determination of the structure of confined water as a function of pore size and temperature. Here, we investigate the dynamic evolution of the structure of confined ice in SBA-15 porous materials with pore diameters of 4 nm, 6 nm, and 8 nm at temperatures ranging from 183 K to 300 K using in operando Wide-Angle X-Ray Scattering (WAXS) measurements, X-Ray Partial Distribution Function (PDF) measurements, and classical Molecular Dynamics (MD) simulations. Formation of hexagonal ice structures is noted in all the three pore sizes. In silica nanopores with diameters of 4 nm, cubic ice formation is noted in addition to hexagonal ice. Longer lasting hydrogen bonds and longer residence times of the water molecules in the first coordination shell contribute to observed crystalline organization of ice in confinement. Self-diffusion coefficients of confined liquid water, predicted from classical MD simulations, are four orders of magnitude higher compared to ice formed in confinement. These experimental and simulation results provide comprehensive insights underlying the organization of confined water and ice in silica nanopores and the underlying physico-chemical interactions that contribute to the observed structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer

Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI) 2 ], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI) 2 ], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.

Science & Technology - Other Topics↗

DOE OSTI2024

Deciphering Charge Transfer Processes in Transition Metal Complexes from the Perspective of Ultrafast Electronic and Nuclear Motions

Chemical transformations in charge transfer states result from the interplay between electronic dynamics and nuclear reorganization along excited-state trajectories. Here, in this study, we investigate the ultrafast structural dynamics following photoinduced electron transfer from the metal-metal-to-ligand charge transfer state of an electron donor, a Pt dimer complex, to a covalently linked electron acceptor group using ultrafast time-resolved wide-angle X-ray scattering and optical transient absorption spectroscopy methods to disentangle the interdependence of the excited-state electronic and nuclear dynamics. Following photoexcitation, Pt-Pt bond formation and contraction takes up to 1 ps, much slower than the corresponding process in analogous complexes without electron acceptor groups. Because the Pt-Pt distance change is slow with respect to excited-state electron transfer, it can affect the rate of electron transfer. These results have potential impacts on controlling electron transfer rates via structural alterations to the electron donor group, tuning the charge transfer driving force.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

The Roles of Oil–Water Interfaces in Forming Ultrasmall CaSO 4 Nanoparticles

In natural and engineered environmental systems, calcium sulfate (CaSO 4 ) nucleation commonly occurs at dynamic liquid–liquid interfaces. Although CaSO 4 is one of the most common minerals in oil spills and oil–water separation, the mechanisms driving its nucleation at these liquid–liquid interfaces remain poorly understood. Here, in this study, using in situ small-angle X-ray scattering (SAXS), we examined CaSO 4 nucleation at oil–water interfaces and found that within 60 minutes of reaction, short rod-shaped nanoparticles (with a radius of gyration (R g ) of 17.2 ± 2.7 nm and a length of 38.2 ± 5.8 nm) had formed preferentially at the interfaces. Wide-angle X-ray scattering (WAXS) analysis identified these nanoparticles as gypsum (CaSO 4 ·2H 2 O). In addition, spherial nanoparticles measuring 4.1 nm in diameter were observed at oil–water interfaces, where surface-enhanced Raman spectroscopy (SERS) revealed an elevated pH compared to the bulk solution. The negatively charged oil–water interfaces preferentially adsorb calcium ions, collectively promoting CaSO 4 formation there. CaSO 4 particle formation at the oil–water interface follows a nonclassical nucleation (N-CNT) pathway by forming ultrasmall amorphous spherical particles which then aggregate to form intermediate nanoparticles, subsequently growing into nanorod-shaped gypsum. These findings of this study provide insights into mineral scaling during membrane separation and can inform more efficient oil transport in energy recovery systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Amorphous nonstoichiometric oxides with tunable room-temperature ferromagnetism and electrical transport

Material functionalities strongly depend on the stoichiometry, crystal structure, and homogeneity. Here we demonstrate an approach of amorphous nonstoichiometric inhomogeneous oxides to realize tunable ferromagnetism and electrical transport at room temperature. In order to verify the origin of the ferromagnetism, we employed a series of structural, chemical, and electronic state characterizations. Combined with electron microscopy and transport measurements, synchrotron-based grazing incident wide angle X-ray scattering, soft X-ray absorption and circular dichroism clearly reveal that the room-temperature ferromagnetism originates from the In 0.23 Co 0.77 O 1-v amorphous phase with a large tunable range of oxygen vacancies. The room-temperature ferromagnetism is tunable from a high saturation magnetization of 500 emu cm -3 to below 25 emu cm -3 , with the evolving electrical resistivity from 5 × 10 3 μΩ cm to above 2.5 × 10 5 μΩ cm. Inhomogeneous nano-crystallization emerges with decreasing oxygen vacancies, driving the system towards non-ferromagnetism and insulating regime. Our work unfolds the novel functionalities of amorphous nonstoichiometric inhomogeneous oxides, which opens up new opportunities for developing spintronic materials with superior magnetic and transport properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Matrix polysaccharides affect preferred orientation of cellulose crystals in primary cell walls

The spatial organization and interactions of constituent components influence cell growth and determine physical and chemical properties of the cell wall, including its rigidity, flexibility, and degradability. Elucidating the interactions between cell wall polysaccharides is crucial for advancing our knowledge of how cell walls are assembled and for designing approaches to efficiently break down cell walls to produce renewable energy and biomaterials. Here, we investigated the effect of defects in the biosynthesis of cell wall components on the nanoscale organization of cellulose in primary cell walls through grazing incidence wide angle X-ray scattering (GIWAXS) measurements of hypocotyls of wild type Arabidopsis thaliana and of cellulose, pectin, and xyloglucan (hemicellulose) deficient mutants. GIWAXS reveals changes in lattice spacings, coherence lengths, and relative crystalline content for cellulose between wild type and mutant plants. In addition, X-ray pole figures constructed using GIWAXS and X-ray diffraction (XRD) rocking scans quantify an emerging measure of cellulose organization, the degree of preferred orientation (texture) of cellulose crystals with respect to the cell wall plane. Comparing X-ray pole figures from pectin-deficient and xyloglucan-deficient mutants to that of wild type plants reveals that cellulose texture is disrupted in pectin-deficient mutants, but not in xyloglucan mutants. Furthermore, our results indicate that a deficiency of pectin during cell wall biosynthesis alters cellulose organization in plant cell walls.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Ionic Liquid-Mediated Interfacial Polymerization for Fabrication of Reverse Osmosis Membranes

This study revealed the effects of incorporating ionic liquid (IL) molecules: 1-ethyl, 1-butyl, and 1-octyl-3-methyl-imidazolium chlorides with different alkyl chain lengths, in interfacial polymerization (IP) on the structure and property (i.e., permeate-flux and salt rejection ratio) relationships of resulting RO membranes. The IL additive was added in the aqueous meta-phenylene diamine (MPD; 0.1% w/v) phase, which was subsequently reacted with trimesoyl chloride (TMC; 0.004% w/v) in the hexane phase to produce polyamide (PA) barrier layer. The structure of resulting free-standing PA thin films was characterized by grazing incidence wide-angle X-rays scattering (GIWAXS), which results were correlated with the performance of thin-film composite RO membranes having PA barrier layers prepared under the same IP conditions. Additionally, the membrane surface properties were characterized by zeta potential and water contact angle measurements. It was found that the membrane prepared by the longer chain IL molecule generally showed lower salt rejection ratio and higher permeation flux, possibly due to the inclusion of IL molecules in the PA scaffold. This hypothesis was supported by the GIWAXS results, where a self-assembled surfactant-like structure formed by IL with the longest aliphatic chain length was detected.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Effects of Polymer Morphology on Solvent and Catalyst Accessibility during Polyethylene and Polystyrene Autoxidation

Efficient catalytic deconstruction of plastics requires facile solvent and catalyst access to polymer substrates to minimize mass transfer effects. Autoxidation using Co(II) acetate, Mn(II) acetate, and a radical carrier in acetic acid is a promising strategy to deconstruct mixed plastic waste, yet the role of polymer morphology in governing solvent and catalyst accessibility remains poorly understood. Here, in situ simultaneous small- and wide-angle X-ray scattering (SAXS/WAXS), complemented by X-ray fluorescence (XRF) imaging and high-pressure differential scanning calorimetry (DSC), were used to elucidate interactions between acetic acid, a Co/Mn catalyst solution, and semicrystalline polyethylene (PE) and amorphous polystyrene (PS) from room temperature to 160 °C. In PE, acetic acid and catalyst access were confined to amorphous regions and cryomilled particle interfaces at room temperature, while crystalline lamellae remained intact after soaking for up to 34 h. Increasing temperature enabled solvent uptake into PE, followed by solvent-assisted softening above 100 °C, and a modest melting-point depression that removed lamellar transport barriers upon melting. Conversely for PS, acetic acid penetrated the glassy polymer without inducing chain mobility until the glass transition was reached, above which the observed structural changes were consistent with enhanced segmental mobility which enabled bulk penetration. These results suggest that polymer morphology and thermally activated physical transitions arising from diffusion and polymer–solvent interactions can influence whether autoxidation of plastics is transport-limited or kinetically controlled, providing a framework for aligning reaction conditions with reaction outcomes.

09 BIOMASS FUELS↗

DOE OSTI2026

Unveiling the mechanism of lithium-mediated nitrogen reduction via operando X-ray scattering in a flow cell with hydrogen oxidation

The lithium-mediated nitrogen reduction reaction (Li-NRR) is currently the most promising strategy for electrochemical ammonia synthesis. In this study, we present an operando grazing incidence wide angle X-ray scattering (GI WAXS) investigation using an improved electrochemical flow cell that enables hydrogen oxidation at the anode and thereby eliminates the need of a sacrificial proton donor. The improved cell design also increases nitrogen availability and mass transport, achieving ammonia faradaic efficiencies (FEs) up to 36%. This setup allows direct analysis of reaction intermediates and the solid electrolyte interphase (SEI) using state-of-the-art diglyme-based electrolytes. We identify lithium amide (LiNH2) as the only stable, crystalline intermediate, providing direct insight into the Li-NRR mechanism. Notably, in diglyme-based electrolytes, the SEI composition differs significantly from that in tetrahydrofuran-based systems, with reduced LiF content and the formation of previously unreported crystalline diglyme–lithium salt complexes. These species likely influence ammonia selectivity and long-term stability. Our findings highlight how the electrolyte composition and cell architecture govern Li-NRR selectivity and efficiency, offering a foundation for the rational design of next-generation SEI layers and solid electrolytes to enable scalable electrochemical ammonia synthesis.

Deissler, Niklas H. [Technical Univ. of Denmark, L↗

DOE OSTI2024

Coordinate-based simulation of pair distance distribution functions for small and large molecular assemblies: implementation and applications

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclodextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0 , which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

Zuo, Xiaobing (ORCID:0000000201344804)↗

DOE OSTI2024

Reexpansion of charged nanoparticle assemblies in concentrated electrolytes

Electrostatic forces in solutions are highly relevant to a variety of fields, ranging from electrochemical energy storage to biology. However, their manifestation in concentrated electrolytes is not fully understood, as exemplified by counterintuitive observations of colloidal stability and long-ranged repulsions in molten salts. Highly charged biomolecules, such as DNA, respond sensitively to ions in dilute solutions. Here, we use non-base-pairing DNA-coated nanoparticles (DNA-NP) to analyze electrostatic interactions in concentrated salt solutions. Despite their negative charge, these conjugates form colloidal crystals in solutions of sufficient divalent cation concentration. We utilize small-angle X-ray scattering (SAXS) to study such DNA-NP assemblies across the full accessible concentration ranges of aqueous CaCl 2 , MgCl 2 , and SrCl 2 solutions. SAXS shows that the crystallinity and phases of the assembled structures vary with cation type. For all tested salts, the aggregates contract with added ions at low salinities and then begin expanding above a cation-dependent threshold salt concentration. Wide-angle X-ray scattering (WAXS) reveals enhanced positional correlations between ions in the solution at high salt concentrations. Complementary molecular dynamics simulations show that these ion–ion interactions reduce the favorability of dense ion configurations within the DNA brushes below that of the bulk solution. Measurements in solutions with lowered permittivity demonstrate a simultaneous increase in ion coupling and decrease in the concentration at which aggregate expansion begins, thus confirming the connection between these phenomena. Our work demonstrates that interactions between charged objects continue to evolve considerably into the high-concentration regime, where classical theories project electrostatics to be of negligible consequence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Orientational analysis of atomic pair correlations in nanocrystalline indium oxide thin films

The application of grazing-incidence total X-ray scattering (GITXS) for pair distribution function (PDF) analysis using >50 keV X-rays from synchrotron light sources has created new opportunities for structural characterization of supported thin films with high resolution. Compared with grazing-incidence wide-angle X-ray scattering, which is only useful for highly ordered materials, GITXS/PDFs expand such analysis to largely disordered or nanostructured materials by examining the atomic pair correlations dependent on the direction relative to the surface of the supporting substrate. A characterization of nanocrystalline In 2 O 3 -derived thin films is presented here with in-plane-isotropic and out-of-plane-anisotropic orientational ordering of the atomic structure, each synthesized using different techniques. The atomic orientations of such films are known to vary based on the synthetic conditions. Here, an azimuthal orientational analysis of these films using GITXS with a single incident angle is shown to resolve the markedly different orientations of the atomic structures with respect to the planar support and the different degrees of long-range order, and hence, the terminal surface chemistries. It is anticipated that orientational analysis of GITXS/PDF data will offer opportunities to extend structural analyses of thin films by providing a means to qualitatively determine the major atomic orientation within nanocrystalline and, eventually, non-crystalline films.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Toward a quantitative description of solvation structure: a framework for differential solution scattering measurements

Appreciating that the role of the solute–solvent and other outer-sphere interactions is essential for understanding chemistry and chemical dynamics in solution, experimental approaches are needed to address the structural consequences of these interactions, complementing condensed-matter simulations and coarse-grained theories. High-energy X-ray scattering (HEXS) combined with pair distribution function analysis presents the opportunity to probe these structures directly and to develop quantitative, atomistic models of molecular systems in situ in the solution phase. However, at concentrations relevant to solution-phase chemistry, the total scattering signal is dominated by the bulk solvent, prompting researchers to adopt a differential approach to eliminate this unwanted background. Though similar approaches are well established in quantitative structural studies of macromolecules in solution by small- and wide-angle X-ray scattering (SAXS/WAXS), analogous studies in the HEXS regime—where sub-ångström spatial resolution is achieved—remain underdeveloped, in part due to the lack of a rigorous theoretical description of the experiment. To address this, herein we develop a framework for differential solution scattering experiments conducted at high energies, which includes concepts of the solvent-excluded volume introduced to describe SAXS/WAXS data, as well as concepts from the time-resolved X-ray scattering community. Our theory is supported by numerical simulations and experiment and paves the way for establishing quantitative methods to determine the atomic structures of small molecules in solution with resolution approaching that of crystallography.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗