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At least 145 records · Page 8

Experimental observation of nonlinear relation between pressure and water flux is consistent with the solution-diffusion model

In several recent studies, it has been proposed that the fundamental understanding of penetrant transport in dense polymer membranes occurring via the solution-diffusion model, which has been the generally accepted theoretical framework for describing penetrant transport in such materials for the past several decades, is flawed. An alternate mechanistic framework based on the idea of two-phase flow in a porous medium (i.e., pore-flow) has been broadly advanced instead, with proponents of this approach claiming that the pore-flow theoretical framework provides the necessary mechanistic insight to design novel polymeric membrane materials for emerging applications. In this study, we show experimental results for hydraulic permeation of water that are entirely consistent with the solution-diffusion theory, without modification, for three dense polymeric membranes: crosslinked poly(ethylene glycol diacrylate) (XLPEGDA), Nafion 117 ionomer in the sodium counterion form (Nafion 117-Na), and cellulose acetate (CA). By measuring water flux at transmembrane pressures up to 240 bar, we observe a nonlinear relationship between the transmembrane pressure (TMP) and water flux, J w , for XLPEGDA and Nafion 117-Na, while this relationship is linear for CA. We demonstrate that the behavior of these three materials is described via the solution-diffusion model. According to the solution-diffusion model, flux is, to a good approximation, proportional to the transmembrane concentration difference induced by the pressure difference across the membrane, rather than to TMP itself. Water sorption isotherms are reported for all three materials. They further justify the nonlinear relationship between TMP and J w observed in XLPEGDA and Nafion 117-Na, emphasizing that the nonlinearity in the flux/TMP relationship stems from nonlinearities in the sorption isotherm with pressure. Additionally, the relationship between water flux and TMP can be predicted, a priori, with no adjustable parameters when a predictive model for the diffusion coefficient of water is employed in conjunction with the experimental water sorption isotherms in the solution-diffusion model. Furthermore, our results demonstrate the validity of the solution-diffusion model to describe transport of penetrants in dense polymer membranes, while highlighting the sensitivity of the solution-diffusion model to the many physical and mathematical simplifications commonly applied to the theory in literature.

materials↗

Closed-loop pressure retarded osmosis draw solutions and their regeneration processes: A review

Pressure-Retarded Osmosis (PRO) is an osmotic process that has been used to harvest energy from salinity gradients using a semi permeable membrane. A comparison between open-loop PRO (OLPRO) and closed-loop PRO (CLPRO) was made regarding their performance and costs. In CLPRO, where the diluted draw solution is re-concentrated in the regeneration system to be reutilized in the process, has recently received an intensive focus as the most viable configuration for a standalone power plant. The choice of the PRO draw solution in CLPRO is crucial to garner a high osmotic pressure as the key for the feasibility of the process. Here, in this review, the draw solutions are critically evaluated in the literature in terms of energy output as well as the method of regeneration used to recirculate them. A set of practical criteria has been suggested to appraise the adequacy of the solution for CLPRO application. It was concluded that NH 3 – CO 2 theoretically can produce 170 W/m 2 of power density. Inorganic draw solutes such as NaCl can generate high power density up to 87 W/m 2 . Organic draw solutes with their remarkably low reverse salt flux (RSF) have promising potential for future application in PRO. Similarly, the regeneration systems of the diluted draw solutions have also been reviewed and discussed. How the energy consumption of the regeneration process affects the feasibility of CLPRO is explained. For the specific case of osmotic heat engines (OHEs), when the energy of the regeneration process is supplied by heat waste, the range of applicability of the heat waste in CLPRO in terms of efficiency is defined and compared to Organic Rankine Cycle (ORC). The results showed that CLPRO has better efficiency than ORC for temperatures T < 80 °C, which makes it a promising process or low-grade heat energy recovery. In addition, a PRO-RO hybrid system coupled with solar power can reduce the net specific energy consumption (SEC) to 0.39 kWh/m 3 . The conditions that regeneration processes should operate under to make PRO viable are discussed in the last section. Overall, the study indicates the key factors for optimizing the performance of CLPRO process.

42 ENGINEERING↗

Contributions of biofilm-induced flow heterogeneities to solute retention and anomalous transport features in porous media

We report that microbial biofilms are ubiquitous within porous media and the dynamics of their growth influence surface and subsurface flow patterns which impacts the physical properties of porous media and large-scale transport of solutes. Here, a two-dimensional pore-scale numerical model was used to evaluate the impact of biofilm-induced flow heterogeneities on conservative transport. Our study integrates experimental biofilm images of Paenibacillus 300A strain in a microfluidic device packed with cylindrical grains in a hexagonal distribution, with mathematical modeling. Biofilm is represented as a synthetic porous structure with locally varying physical properties that honors the impact of biofilm on the porous medium. We find that biofilm plays a major role in shaping the observed conservative transport dynamics by enhancing anomalous characteristics. More specifically, when biofilm is present, the pore structure in our geometry becomes more spatially correlated. We observe intermittent behavior in the Lagrangian velocities that switches between fast transport periods and long trapping events. Our results suggest that intermittency enhances solute spreading in breakthrough curves which exhibit extreme anomalous slope at intermediate times and very marked late solute arrival due to solute retention. The efficiency of solute retention by the biofilm is controlled by a transport regime which can extend the tailing in the concentration breakthrough curves. These results indicate that solute retention by the biofilm exerts a strong control on conservative solute transport at pore-scale, a role that to date has not received enough attention.

54 ENVIRONMENTAL SCIENCES↗

A Semi-Empirical Density Law for Ternary, Homogeneous PuCl 3 /HCl/H 2 O Solutions

Nuclear material operations pose unique hazards that are not encountered in other chemical, energy, or manufacturing industries. One of these hazards is the potential for a nuclear criticality accident when handling fissile isotopes such as 235 U and 239 Pu. These hazards are particularly high when fissile material is dissolved in solution as the neutron behaviors of the system can change rapidly with the physical and chemical changes accessible in solution. Current estimates of solution density used for criticality safety are outdated and hinder fissile material handling. Developing new estimates for these safety calculations requires experimental characterization and the derivation of empirical density models. We have derived a density law describing PuCl 3 /HCl/H 2 O solutions from experimental data characterizing solution density. Density data was treated using a Pitzer-derived eight-parameter equation, defining density as a function of analyte concentrations, temperature, and interactions between these variables. The model is predictive across the concentration and temperature ranges from which it was derived. The potential effects of varying oxidation states of plutonium, which are easily accessible in aqueous media, on the bulk solution density of the ternary system were also investigated. The resulting Pitzer-derived density law was applied to a nuclear criticality safety model, and the impact of the experimental characterization of solution density relative to previous estimates was demonstrated to be significant and suggest that the current approach to estimating density in nuclear criticality safety calculations may lead to overly conservative controls.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Determination of Intermolecular Distances in Dilute Solutions of Macroions and Their Direct Correlations with Self-Assembly and Macrophase Transitions

Here, this work demonstrates new attempts to determine the intermolecular distances between charged macroionic solutes in their dilute solutions, which regulate the solute’s microphase (self-assembly) and macrophase transitions. Small-angle X-ray scattering (SAXS) and analytical ultracentrifuge (AUC) techniques were applied to determine the intermolecular distances for the 2.42 nm-sized, spherical uranyl peroxide molecular cluster {U 60 } in their self-assembled states in dilute aqueous solution and concentrated phases, respectively. The counterion-mediated attraction among {U 60 } leads to characteristic, inter-{U 60 } distances in solutions, which increase gradually with decreasing the strength of introduced counterions (e.g., lower valency). The gradual increment of inter-{U 60 } distance demonstrates a nice correlation with the macroscopic phase transitions of {U 60 }, from single crystals to concentrated fluids containing rigid 2-D sheets, then to dilute solutions containing a small amount of standalone, floating 2-D sheets of {U 60 }, and finally to dilute solutions containing a limited amount of self-assembled single-layered, spherical blackberry structures of different sizes from the bending of more flexible 2-D sheets.

36 MATERIALS SCIENCE↗

Elucidating molecular scale interactions underlying the freezing behavior of salt solutions in silica nanopores

Elucidating the influence of nanoscale confinement on the freezing behavior of salt solutions is of fundamental interest to environmental security and materials science and engineering. Specific structural information such as the coordination environment of ions in confined aqueous medium, effects on the extended hexagonal network of water molecules and their mutual non-bonding interactions in confinement are sparse in the literature along with the change in the dynamical characteristics of water in the presence of ions. To address these knowledge gaps, the current study is focused on investigating the influence of reduced dimensionality arising from nanoscale confinement on the structural evolution of salt solutions on freezing and the associated fluid–surface interactions. In this regard, operando wide-angle X-ray scattering (WAXS) measurements and classical molecular dynamics (MD) simulations are conducted with water and 0.5 M CaCl 2 , MgCl 2 and KCl solutions confined in 4 nm sized SBA-15 silica pores upon cooling from 300 K to 200 K. The freezing point of the salt solutions is depressed to 235 K which is about 10 K lower than that of confined water. The translational dynamics of confined salt solutions indicates shifts in the fragile-to-strong dynamical crossover to a lower temperature compared to pure water. The strong electrostatic attraction between the cations and the surrounding water molecules contributes to the freezing point depression in confined salt solutions. These insights unlock the molecular-scale basis and mechanisms underlying the freezing behavior of confined salt solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cations impact radical reaction dynamics in concentrated multicomponent aqueous solutions

Ultraviolet (UV) photolysis of nitrite ions (NO 2 – ) in aqueous solutions produces a suite of radicals, viz., NO · , O – , · OH, and · NO 2 . The O – and NO · radicals are initially formed from the dissociation of photoexcited NO 2 – . The O – radical undergoes reversible proton transfer with water to generate · OH. Both · OH and O – oxidize the NO 2 – to · NO 2 radicals. The reactions of · OH occur at solution diffusion limits, which are influenced by the nature of the dissolved cations and anions. Here, we systematically varied the alkali metal cation, spanning the range from strongly to weakly hydrating ions, and measured the production of NO · , · OH, and · NO 2 radicals during UV photolysis of alkaline nitrite solutions using electron paramagnetic resonance spectroscopy with nitromethane spin trapping. Comparing the data for the different alkali cations revealed that the nature of the cation had a significant effect on production of all three radical species. Radical production was inhibited in solutions with high charge density cations, e.g., lithium, and promoted in solutions containing low charge density cations, e.g., cesium. Through complementary investigations with multinuclear single pulse direct excitation nuclear magnetic resonance (NMR) spectroscopy and pulsed field gradient NMR diffusometry, cation-controlled solution structures and extent of NO 2 – solvation were determined to alter the initial yields of · NO and · OH radicals as well as alter the reactivity of NO 2 – toward · OH, impacting the production of · NO 2 . The implications of these results for the retrieval and processing of low-water, highly alkaline solutions that comprise legacy radioactive waste are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Uncoupling Electrokinetic Flow Solutions

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.

58 GEOSCIENCES↗

Grain boundary segregation beyond the dilute limit: Separating the two contributions of site spectrality and solute interactions

Solute segregation at grain boundaries (GBs) is known to have a profound impact on material properties, and as such is becoming routinely used as an element in alloy design. Beyond the dilute limit, the extent of solute GB segregation is known to be concentration dependent. Using hybrid Monte Carlo/Molecular Statics simulations of Mg segregation in Al, in this work we decouple the two contributions to this composition dependence: (i) spectrality of atomic environments at the boundary and (ii) solute-solute interactions. Although only contribution (ii) is typically considered in the literature, we argue that both contributions are equally important to understand concentration dependence and correctly quantify GB solute segregation in a binary alloy. Finally, a thermodynamic segregation isotherm is outlined that accounts for both the spectrality of grain boundary sites and solute-solute interactions. Unlike classical isotherms like those of McLean or Fowler-Guggenheim, which can be successfully fitted to GB segregation data only over a limited range of composition and temperature, our proposed model is shown to be accurate across the composition-temperature space.

36 MATERIALS SCIENCE↗

Single and Dual-Solute Transport in Quaternary Ammonium-Functionalized Anion Exchange Membranes: Isolating the Impact of Water Volume Fraction

Membranes are essential components of photoelectrochemical CO 2 reduction cells (PEC-CRC), as they regulate solute transport and impact device efficiency. These cells are a promising approach for converting carbon dioxide into valuable chemicals. However, electrochemical reactions involve not just a single electrolyte; membrane transport typically includes multiple electrolytes. When a mixture of solutes is present, the presence of one solute in the membrane can impact the diffusion and sorption of other solutes. In complex systems where multiple solutes are diffusing simultaneously through a hydrated, dense polymer membrane, the resulting transport behavior is poorly understood. This study highlights the individual and two solute transport behavior of potassium formate, acetate, and bicarbonate ions in neutral membranes and quaternary ammonium-functionalized anion exchange membranes (AEMs) based on phenyl acrylate polymer backbones. By isolating the effect of water content, we emphasize how fixed charge density and solute-membrane interactions influence transport behavior. In neutral membranes, the diffusivity follows the order of potassium formate > potassium acetate > potassium bicarbonate. However, in AEMs, the order shifts due to changes in ion-membrane interactions, with potassium bicarbonate diffusivity surpassing that of potassium acetate. These results underscore the importance of ion exchange membranes and ion-membrane interaction in modulating transport properties, providing valuable insights for optimizing membranes in electrochemical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct observation of key aluminum hydroxide prenucleation oligomers for gibbsite nucleation and crystallization in sodium aluminate solution by liquid ToF-SIMS

The mechanism of gibbsite (aluminum hydroxide) crystallization from highly alkaline solutions such as Bayer liquors remains poorly understood, where aluminum (Al) transforms from largely tetrahedrally coordinated aluminate monomers in sodium aluminate solutions into a network of octahedra in gibbsite crystals. A variety of traditional analytical approaches applied to this system do not readily reveal the presence of higher-order oligomeric intermediates. To overcome this limitation, we employed in-situ liquid Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) to examine the Al species present in concentrated sodium aluminate solutions favoring crystallization of gibbsite or sodium aluminate. A complex mixture of Al oligomers was found. By comparing the change in the relative concentration of Al oligomers with +1 and -1 charge, we were able to identify three major Al oligomer candidates, iso-tetramers, iso-pentamers, and cyclic-hexamers, for the nucleation and crystallization of gibbsite. The concentrations of iso-tetramers and iso-pentamers significantly surpass those of cyclic-hexamers. Time-dependent in-situ Raman spectroscopy analysis indicated that the appearance of gibbsite coincided with the peak concentration of these oligomers. The Density-functional theory (DFT) calculation suggests that the formation of iso-oligomers is more favorable than that of cyclic-hexamers. The combined results suggest that iso-tetramers and iso-pentamers play the most substantial role in the nucleation and growth of gibbsite in the sodium aluminate solutions. Our findings also suggest that the oligomers that promote gibbsite crystallization are more stable in dilute sodium aluminate solutions, making these solutions particularly suitable for efficient gibbsite crystallization. In conclusion, our study fills a major knowledge gap in understanding Al speciation that leads to the nucleation and crystallization of gibbsite in concentrated sodium aluminate solutions.

Bayer liquor↗

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F – over Cl – in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory–experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

EELS Studies of Cerium Electrolyte Reveal Substantial Solute Concentration Effects in Graphene Liquid Cells

Graphene liquid cell transmission electron microscopy is a powerful technique to visualize nanoscale dynamics and transformations at atomic resolution. However, the solution in liquid cells is known to be affected by radiolysis, and the stochastic formation of graphene liquid cells raises questions about the solution chemistry in individual pockets. In this study, electron energy loss spectroscopy (EELS) was used to evaluate a model encapsulated solution, aqueous CeCl 3 . First, the ratio between the O K-edge and Ce M-edge was used to approximate the concentration of cerium salt in the graphene liquid cell. It was determined that the ratio between oxygen and cerium was orders of magnitude lower than what is expected for a dilute solution, indicating that the encapsulated solution is highly concentrated. To probe how this affects the chemistry within graphene liquid cells, the oxidation of Ce 3+ was measured using time-resolved parallel EELS. Here, it was determined that Ce 3+ oxidizes faster under high electron fluxes, but reaches the same steady-state Ce 4+ concentration regardless of flux. The time-resolved concentration profiles enabled direct comparison to radiolysis models, which indicate rate constants and g-values of certain molecular species are substantially different in the highly concentrated environment. Finally, electron flux-dependent gold nanocrystal etching trajectories showed that gold nanocrystals etch faster at higher electron fluxes, correlating well with the Ce 3+ oxidation kinetics. Understanding the effects of the highly concentrated solution in graphene liquid cells will provide new insight on previous studies and may open up opportunities to systematically study systems in highly concentrated solutions at high resolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Preferential Solute Transport in Low Permeability Zones During Spontaneous Imbibition in Heterogeneous Porous Media

Multiphase flows in porous media|and the associated solute transport processes|are controlled by a combination of gravity, capillary, and viscous forces. Geologic heterogeneity influences flow and transport processes, yet gaps exist in our understanding of how heterogeneity impacts capillary-driven transport, such as during spontaneous imbibition. Here we use positron emission tomography, combined with a newly developed method for conducting spontaneous imbibition experiments, to observe solute transport into low permeability regions during imbibition. Using an experimentally parameterized 2D numerical model, we demonstrate how capillary-driven ow near the imbibition front can carry solutes into low permeability regions. This process displaces solutes from high permeability zones while the cumulative amount of solute in low permeability zones increases- opposite of what is observed under fully saturated solute transport conditions. These results highlight the complex flow and solute transport behavior that arise during multiphase displacements in heterogeneous geologic porous media.

58 GEOSCIENCES↗

In situ Raman investigation of Dy complexation in Cl-bearing aqueous solutions at 20–300 °C

Raman spectroscopy provides a versatile tool for in situ characterization of aqueous rare earth elements (REE) speciation at the molecular level. Complexation of REE with ligands such as Cl – and OH – is of particular interest for understanding the mobility of REE in NaCl-bearing hydrothermal fluids responsible for enriching REE to economic levels in nature. Raman spectroscopic studies of REE speciation in Cl-bearing aqueous fluids are primarily conducted at ambient temperature, whereas natural systems indicate temperatures of >100–600 °C. In this study, the speciation of Dy in acidic chloride-bearing hydrothermal solutions was investigated using confocal Raman spectroscopy with a new capillary Raman heating stage at 20–300 °C. Background solutions (pure water, NaCl-solutions) and solutions with 0.14–1.8 mol kg –1 dissolved DyCl 3 were sealed in quartz capillary cells. Comparison of the spectra for Dy chloride solutions with those for background solutions and the spectra for reference Dy-bearing solids was used to identify Raman bands specific to Dy–O and Dy–Cl bonds. The Raman band for the Dy–O stretching mode of hydrated Dy 3+ aqua ions was measured at 365–384 cm –1 and a Raman band for the Dy–Cl stretching modes of Dy chloride complexes was measured near 240 cm –1 . The Dy–O band decreases systematically with temperature, whereas the Dy–Cl band systematically increases, indicating a systematic increase in the stability of Dy chloride complexes with temperature. Here, this study provides the framework for expanding the use of in situ Raman spectroscopy to investigate the speciation of REE in aqueous solutions to hydrothermal conditions.

58 GEOSCIENCES↗

Spectroscopic investigation of cation effects in U(VI)-NO3- complexation in aqueous solutions

Understanding and manipulating uranyl speciation in aqueous solutions is critical for advancing chemical separation, sensing, and understanding environmental transport of uranyl. We report on the significant enhancement in the complexation of uranyl with nitrate in aqueous solutions containing quaternary ammonium cations leading to the formation of anionic complexes. We base this on the comparative study of the effect of monovalent cations (Na+, Li+, NH4+, and N(CH3)4+) on the complexation equilibria of uranyl-nitrate in solutions, probed by time-resolved laser induced fluorescence spectroscopy (TRLFS). Lifetime-corrected spectra, obtained by extrapolating the time-resolved spectra to t = 0, were used to study speciation to mitigate the effects of variations in the fluorescence lifetimes that depend on extraneous factors such as dynamic quenching. We demonstrate that the lifetime-corrected spectra can be used to determine uranyl speciation in aqueous solutions where the mono-nitrate complex forms, and in acetonitrile with N(CH3)4NO3 where di-nitrate and tris-nitrato species are formed. Aqueous solutions containing N(CH3)4+ are shown to promote the formation of higher complexes of uranyl compared to other inorganic nitrate salts based on the higher redshift in the spectra, poor fits to the two-component model, and the higher apparent formation constants. Comparing the trends in uranyl speciation in the presence of N(CH3)4+ in aqueous and acetonitrile solutions, it is proposed that the quaternary ammonium cations (quats) promote the formation of anionic complexes of uranyl by the ion-association mechanism. These results provide a basis for designing quat-assisted separation systems that target anionic actinide species in aqueous solutions.

Nayak, Srikanth (ORCID:0000000302135796)↗

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↗

Ensuring Solution Uniqueness in Three-Phase Power System State Estimation

This paper is concerned with the issue of potential non-unique solutions in three-phase state estimation. Theory of observability analysis for positive sequence power system state estimation is based on certain assumptions that avoid possibility of multiple solutions. Also, it is shown that observability of a positive sequence network remains independent of the network parameters or the operating state. When extending single-phase observability analysis directly to the three-phase case, this paper considers the possibility of converging to multiple solutions, i.e. solution non-uniqueness, even for cases where state estimator successfully converges. The study illustrates via numerical examples the likelihood of converging to entirely different solutions for certain network parameters. It also examines how the operating state, particularly under unbalanced loading, leads to solution non-uniqueness. The paper then describes an alternative approach to ensure a unique solution in three-phase state estimation. This method aims to accurately and uniquely estimate the state of any unbalanced three-phase system, irrespective of load imbalance, network configuration, existence of synchronous generators or transformers.

Power System State Estimation, Three-Phase, Distri↗