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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

Protein Electric Fields Enable Faster and Longer-Lasting Covalent Inhibition of β-Lactamases

The widespread design of covalent drugs has focused on crafting reactive groups of proper electrophilicity and positioning towards targeted amino-acid nucleophiles. In this work, we found that environmental electric fields projected onto a reactive chemical bond, an overlooked design element, play essential roles in the covalent inhibition of TEM-1 beta-lactamase by avibactam. Using the vibrational Stark effect, the magnitudes of the electric fields that are exerted by TEM active sites onto avibactam’s reactive C=O were measured and demonstrate an electrostatic gating effect that promotes bond formation yet relatively suppresses the reverse dissociation. These results suggest new principles of covalent drug design and off-target site prediction. Unlike shape and electrostatic complementary which address binding constants, electrostatic catalysis drives reaction rates, essential for covalent inhibition, and deepens our understanding of chemical reactivity, selectivity, and stability in complex systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular Interlocking Multidimensional Modulations of Cathode‐Electrolyte Interface for Constructing High Energy Density Quasi‐Solid‐State Batteries

Gel polymers are regarded as a promising candidate electrolyte for lithium-metal quasi-solid-state batteries, primarily due to their high ionic conductivity and solid-liquid synergistic properties. However, challenges such as interfacial side reactions, limitations in Li + transport caused by interfacial issues, and leaching of transition metals from the cathode have yet to be effectively solved. Herein, a novel gel electrolyte modulation strategy based on electrostatic filler assembly is proposed to address the issues of ineffective capacity utilization and inadequate cycling stability of high-energy-density cathode materials in solid-state lithium-ion batteries. It constructs a 3D interpenetrating charge-bridge network that effectively tackles the phase-separation challenge between fillers and electrolytes at the molecular level. Meanwhile, the molecular interlocking structure effectively inhibits the electrolyte erosion. More critically, it optimizes and stabilizes the cathode-electrolyte interface film, which facilitates the conduction of Li + -ions through a size-sieving mechanism. Consequently, this strategy enables effective adaptation across diverse high-energy-density cathode materials with satisfactory capacity performance (170.4 mAh g −1 at 4.5 V/1 C for LiNi 0.6 Co 0.2 Mn 0.2 O 2 and 194.0 mAh g −1 at 4.3 V/1 C for LiNi 0.9 Co 0.08 Mn 0.02 O 2 ). In conclusion, this investigation offers a straightforward and effective reference for addressing the critical challenges of ionic transport and interface stabilization in the design of gel electrolytes.

cathode-electrolyte interface↗

Voltage mapping and local defects identification in solar cells using non-contact method

Electroluminescence, infrared imaging, and current–voltage curve techniques are used to detect and map underperforming cells in a photovoltaic module or the modules in a photovoltaic string. In this work, we present a non-contact electrostatic voltmeter technique to detect and map the underperforming spots in a cell and the cells in a module. This non-contact technique directly maps the charged surface voltage (671mV) of the superstrate glass, and it had an 11-mV difference with the voltmeter values (660mV). Another data set of voltage values obtained by electroluminescence images conversion into a voltage map showed a difference of 7mV with the non-contact voltmeter values. Further, the direct voltage values obtained at various good and poor-performing spots of the cells using this technique are 3.69V and 3.79V and are validated using the voltage values obtained in electroluminescence analysis and the difference in voltage obtained by the two techniques is determined to be less than 2%. In this work, we combine the strengths of two complementary techniques of the electrostatic voltmeter (strength: quantitative) and electroluminescence (strength: spatial mapping) to obtain a quantitative spatial mapping of defects. Furthermore, this work is extendable to detect the poor-performing modules in solar PV power plants.

14 SOLAR ENERGY↗

Field-Coupled Water Splitting with Metal-Free Donor–Acceptor Covalent Organic-Framework Junctions

Advancing metal-free electrocatalysts for hydrogen and oxygen evolution reactions (HER/OER) across acidic and alkaline media requires coordinated control of intermediate binding thermodynamics, interfacial charge delivery, and near-electrode transport dynamics. Here, we design amide-linked benzene–triazine covalent organic frameworks (BTA/TzTA-Hz COFs) and integrate them with carbon nanotubes (CNTs) to form COF–CNT junctions that establish a built-in interfacial electric field. Density functional theory (DFT) and electrostatic potential maps indicate complementary active motifs, with benzene-proximal fragments associated with HER and triazine-proximal motifs associated with OER. CNT integration shifts the contact-potential difference by ≈0.20 V, while operando electrochemical impedance spectroscopy suggests partially separable high-frequency junction-charging and lower-frequency Faradaic/transport responses. A 300 mT static magnetic field lowers the HER and OER overpotentials by tens of millivolts. Under anodic bias, the effective interfacial charging capacitance increases, and Mott–Schottky analysis shows an apparent ∼0.15 V flat-band shift with an essentially unchanged slope. Together, these observations are consistent with field-perturbed interfacial charging and altered bias partitioning. Field-dependent impedance and bubble imaging are consistent with magnetohydrodynamic convection that promotes bubble detachment and near-electrode mass transport for both half-reactions, and they reveal an OER-specific high-frequency perturbation under anodic bias. Under field, the heterostructure reaches an OER onset overpotential of ∼261 mV and requires an overpotential of 366 mV at 10 mA cm –2 in alkaline electrolyte. These results illustrate how reticular-framework chemistry, junction engineering, and both built-in and applied fields can program reactivity through interfacial electrostatics and near-electrode transport in organic-framework electrocatalysts.

Garcia-Enriquez, Lissette [Univ. of Texas at El Pa↗

Anionic Lipids Regulate the Light-Harvesting Complex 1-Reaction Center Photocycle in Purple Bacteria

Photosynthetic purple bacteria can capture and convert sunlight with a remarkable, nearly 100% quantum efficiency. The light-harvesting complex 1-reaction center (LH1-RC) core complex is the membrane complex fundamentally responsible for solar energy conversion. LH1-RC has a highly conserved surrounding lipid composition known to favor anionic lipids for an unknown function. Here, in this work, we compared experimentally the rate of LH1-to-RC energy transfer in detergent, membrane nanodiscs with varying lipid compositions, purified membrane fragments, and live cells. The energy transfer rate indicated that RC turnover decreased in neutral lipids, yet was partially restored in anionic lipids, revealing an unexpected lipid dependence. In complementary molecular dynamics simulations, the anionic lipid cardiolipin showed electrostatic interactions with LH1-RC that may mediate quinone exchange, providing a mechanism for the observed lipid dependence. Overall, these results revealed that anionic lipids facilitate LH1-RC redox cycling, identifying a functional role for membrane composition in photosynthetic solar energy conversion.

bacteria↗

Multidimensional Coherent Spectroscopy of van der Waals materials and heterostructures (Final Technical Report)

This project advanced multidimensional coherent spectroscopy (MDCS) and related spectroscopic-imaging methods as quantitative probes of many-body optical excitations in two-dimensional (2D) van der Waals (vdW) semiconductors and their heterostructures. Monolayer transition-metal dichalcogenides (TMDs) such as MoSe 2 and WSe 2 provide a uniquely strong platform for excitonic physics due to reduced dielectric screening, which enhances Coulomb interactions and makes higher-order correlated states (e.g., biexcitons and exciton–trion correlations) more prominent than in conventional bulk semiconductors. At the same time, the same sensitivity that enables strong interactions also increases susceptibility to spatial inhomogeneity—e.g., strain gradients, wrinkles, nanoscale disorder potentials, and charge puddling—which can broaden resonances, obscure interaction signatures, and complicate device-to-device reproducibility. The work reported here addressed this dual opportunity and challenge by: (i) developing and deploying coherent multidimensional methods (including double-quantum MDCS) capable of isolating interaction signals with reduced background, (ii) integrating electrostatic control to tune carrier populations and interaction strengths in situ, and (iii) introducing complementary spatially resolved photoluminescence (PL) techniques—hyperspectral PL imaging and polarization-/field-dependent PL lineshape analysis—to directly quantify disorder, strain, and localization that govern the coherent response.

36 MATERIALS SCIENCE↗

Ion-gel-gating-induced oxygen vacancy formation in epitaxial L a 0.5 S r 0.5 Co O 3 – δ films from in operando x-ray and neutron scattering

Ionic-liquid/gel-based transistors have emerged as a potentially ideal means to accumulate high charge-carrier densities at the surfaces of materials such as oxides, enabling control over electronic phase transitions. Substantial gaps remain in the understanding of gating mechanisms, however, particularly with respect to charge carrier vs oxygen defect creation, one contributing factor being the dearth of experimental probes beyond electronic transport. Here we demonstrate the use of synchrotron hard x-ray diffraction and polarized neutron reflectometry as in operando probes of ion-gel transistors based on ferromagnetic La 0.5 Sr 0.5 CoO 3-δ . An asymmetric gate-bias response is confirmed to derive from electrostatic hole accumulation at negative gate bias vs oxygen vacancy formation at positive bias. The latter is detected via a large gate-induced lattice expansion (up to 1%), complementary bulk measurements and density functional calculations enabling quantification of the bias-dependent oxygen vacancy density. Remarkably, the gate-induced oxygen vacancies proliferate through the entire thickness of 30-40-unit-cell-thick films, quantitatively accounting for changes in the magnetization depth profile. In conclusion, these results directly elucidate the issue of electrostatic vs redox-based response in electrolyte-gated oxides, also demonstrating powerful approaches to their in operando investigation.

36 MATERIALS SCIENCE↗

Impact of proton irradiation on 4H-SiC Low Gain Avalanche Detectors (LGADs)

Silicon carbide (SiC) particle detectors have the potential to provide time resolutions and robust performance in extreme environments which exceed that of silicon detectors. In this work 4H-SiC low gain avalanche detectors (LGADs) and complementary PiN diodes were irradiated with 2.5 GeV protons at fluences up to 3.33 × 10 14 p/cm 2 . The electrostatic performance of both irradiated and non-irradiated devices was evaluated using I-V and C-V measurements. Moreover, charge collection measurements using α particles were also conducted. SiC LGADs displayed a loss in rectification, high ON-state resistances >10 10 Ω-cm 2 , and the complete removal of gain when exposed to the highest proton fluence. Additionally, the reductions in capacitance and OFF-state current pointed to compensation of the gain layer as a gain reducing mechanism. The introduction of radiation-induced defects also hinders carrier acceleration, which reduces impact ionization and further gain reduction. LGADs exposed to a fluence of 1 × 10 14 p/cm 2 experienced a partial recovery in gain (originally having a value of ∼ 2) with a value of ∼ 1.65 when applying a bias of 500 V. Charge trapping was also seen in the reduction of charge collection efficiency (CCE) to ∼ 65% for the PiN diode. However, despite the reduction in device performance, the demonstration of a measurable signal after irradiation points to the potential of SiC LGAD detectors for future high energy physics applications.

43 PARTICLE ACCELERATORS↗

Mechanistic Insights into the Demethylation of Lignin‐Derived Structures Using Protic Ionic Liquids: A Density Functional Theory Study

Lignin valorization is restricted by the stability of its methoxy groups, creating a critical need for efficient demethylation strategies. Here, in this study, density functional theory (DFT) is employed to dissect the mechanistic pathways of demethylation in lignin model compounds, guaiacol and syringol, using protic ionic liquids (PILs) that act as both solvent and catalyst. Conductor‐like Screening Model for Real Solvents (COSMO‐RS) analysis identifies monoethanolammonium acetate ([MEOA][Ace]) as the most promising medium, attributed to its strong hydrogen bonding network and solvation ability. By integrating implicit and explicit solvation models, it is revealed that an acid‐catalyzed hydrolytic mechanism governs demethylation, with PILs stabilizing crucial transition states and intermediates. Complementary electronic structure evaluations, including highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO‐LUMO) gap analysis, charge distribution, and electrostatic potential mapping, demonstrate how PILs lower energetic barriers and enhance reactivity. To simulate realistic environments, this study is extended to lignin dimer complexes with varying water content, uncovering how water‐bridged solvation reverses demethylation preference from guaiacyl to syringyl units. This mechanistic shift aligns with experimental observations showing faster S‐unit reactivity in hydrated systems. Together, these findings provide atomic‐level insight into lignin demethylation dynamics and highlight how tuning acid concentration in PILs can accelerate kinetics, enabling a rational pathway toward next‐generation biomass conversion technologies.

COSMO-RS↗

High Voltage Mg-Ion Battery Cathode via a Solid Solution Cr–Mn Spinel Oxide

We discuss how lattice Mg 2+ in a tailored solid solution spinel, MgCrMnO 4 , is electrochemically utilized at high Mn-redox potentials in a nonaqueous electrolyte. Complementary evidence from experimental and theoretical analyses supports bulk Mg 2+ (de)intercalation throughout the designed oxide frame where strong electrostatic interaction between Mg 2+ and O 2- exists. Mg/Mn antisite inversion in the spinel is lowered to similar to 10% via postannealing at 350 degrees C to further improve Mg 2+ mobility. Spinel lattice is preserved upon removal of Mg 2+ without any phase transformations, denoting structural stability at the charged state at a high potential similar to 3.0 V (vs Mg/Mel. Clear remagnesiation upon first discharge, harvesting up to similar to 180 Wh/kg at 60 degrees C is shown. In the remagnesiated state, insertion of Mg 2+ into interstitial sites in the spinel is detected, possibly resulting in partial reversibility which needs to be addressed for structural stability. The observations constitute a first clear path to the development of a practical high voltage Mg-ion cathode using a spinel oxide.

25 ENERGY STORAGE↗

Efficient Removal of Per- and Polyfluoroalkyl Substances from Water with Zirconium-Based Metal–Organic Frameworks

Per- and polyfluoroalkyl substances (PFASs) are an emerging class of contaminants raising increased levels of concern due to their toxic, bioaccumulative, and persistent nature. Current solutions for removing PFAS from contaminated water rely on adsorption-based methods where commonly used sorbents, for example, activated carbons and ion-exchange resins, exhibit low adsorption capacity and a long equilibration time. Motivated by the generally deficient performance of these current materials, this work addresses the need for the discovery of advanced sorbents for high capacity and efficient PFAS removal. The zirconium-based metal–organic framework (MOF) NU-1000 was characterized for the adsorption of three perfluorosulfonic acids (PFSAs, C4–C8) and six perfluorinated carboxylic acids (PFCAs, C1–C9) from aqueous solutions. Here, the results indicate that NU-1000 exhibits outstanding adsorption capacities of 400–620 mg/g for PFSAs and 201–604 mg/g for PFCAs coupled with ultrafast adsorption kinetics featuring equilibrium times of <1 min. Complementary density functional theory calculations reveal that the PFAS@MOF adsorption mechanism is dominated by a combination of hydrogen bonding, electrostatic, and hydrophobic non-covalent PFAS–MOF interactions. Excellent regeneration and reusability characteristics were found, particularly nearly quantitative removal and recovery rates of NU-1000 after five consecutive adsoption and desorption cycles of PFAS. Additional adsorption testing using PFAS-contaminated groundwater samples obtained from U.S. Air Force bases revealed impressive PFAS removal rates of 75–98% within 10 min regardless of the presence of co-contaminants. To the best of our knowledge, the suite of herein presented PFAS sorption characteristics—capacity, kinetics, regeneration, and reusability—significantly outperforms other current sorbents, rendering NU-1000 as a promising platform for the rapid and effective removal of PFAS from aqueous media.

36 MATERIALS SCIENCE↗

Time-Resolved Electrical Scanning Probe Microscopy of Layered Perovskites Reveals Spatial Variations in Photoinduced Ionic and Electronic Carrier Motion

We study light-induced dynamics in thin films comprising Ruddlesden–Popper phases of the layered 2D perovskite (C 4 H 9 NH 3 ) 2 PbI 4 . We probe ionic and electronic carrier dynamics using two complementary scanning probe methods, time-resolved G-mode Kelvin probe force microscopy and fast free time-resolved electrostatic force microscopy, as a function of position, time, and illumination. Here, we show that the average surface photovoltage sign is dominated by the band bending at the buried perovskite–substrate interface. However, the film exhibits substantial variations in the spatial and temporal response of the photovoltage. Under illumination, the photovoltage equilibrates over hundreds of microseconds, a time scale associated with ionic motion and trapped electronic carriers. Surprisingly, we observe that the surface photovoltage of the 2D grain centers evolves more rapidly in time than at the grain boundaries. We propose that the slower evolution at grain boundaries is due to a combination of ion migration occurring between PbI 4 planes, as well as electronic carriers traversing grain boundary traps, thereby changing the time-dependent band unbending at grain boundaries. These results provide a model for the photoinduced dynamics in 2D perovskites and are a useful basis for interpreting photovoltage dynamics on hybrid 2D/3D structures.

14 SOLAR ENERGY↗

A Crystalline Polyimide Porous Organic Framework for Selective Adsorption of Acetylene over Ethylene

The separation of acetylene from ethylene is a crucial process in the petrochemical industry, as even small acetylene impurities can lead to premature termination of ethylene polymerization. Herein, we present the synthesis of a robust, crystalline naphthalene diimide porous aromatic framework via imidization of linear naphthalene-1,4,5,8-tetracarboxylic dianhydride and triangular tris(4-aminophenyl)amine. The resulting material, PAF-110, exhibits impressive thermal and long-term structural stability, as indicated by thermogravimetric analysis and powder X-ray diffraction characterization. Gas adsorption characterization reveals that PAF-110 has a capacity for acetylene that is more than twice its ethylene capacity at 273 K and 1 bar, and it exhibits a moderate acetylene selectivity of 3.9 at 298 K and 1 bar. Complementary computational investigation of each guest binding in PAF-110 suggests that this affinity and selectivity for acetylene arises from its stronger electrostatic interaction with the carbonyl oxygen atoms of the framework. As a result, to the best of our knowledge, PAF-110 is the first crystalline porous organic material to exhibit selective adsorption of acetylene over ethylene, and its properties may provide insight into the further optimized design of porous organic materials for this key gas separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of counterion substitution on the properties of imidazolium-based ionic liquid clusters

Due to their unique physiochemical properties that may be tailored for specific purposes, ionic liquids (ILs) have been investigated for various applications, including chemical separations, catalysis, energy storage, and space propulsion. The different cations and anions comprising ILs may be selected to optimize a range of desired properties, such as thermal stability, ionic conductivity, and volatility, leading to the designation of certain ILs as designer “green” solvents. The effect of counterions on the properties of ILs is of both fundamental scientific interest and technological importance. Herein, we report a systematic experimental and theoretical investigation of the size, charge, stability toward dissociation, and geometric/electronic structure of 1-ethyl-3-methyl imidazolium (EMIM)-based IL clusters containing two different atomic counterions (i.e., bromide [Br − ] and iodide [I − ]). This work extends our studies of EMIM + cations with atomic chloride (Cl − ) and molecular tetrafluoroborate (BF 4 − ) anions reported previously by Baxter et al. [Chem. Mater. 34, 2612 (2022)] and Zhang et al . [J. Phys. Chem. Lett. 11, 6844 (2020)], respectively. Distributions of anionic IL clusters were generated in the gas phase using electrospray ionization and characterized by high mass resolution mass spectrometry, energy-resolved collision-induced dissociation, and negative ion photoelectron spectroscopy experiments. The experimental results reveal anion-dependent trends in the size distribution, relative abundance, ionic charge state, stability toward dissociation, and electron binding energies of the IL clusters. Complementary global optimization theory provides molecular-level insights into the bonding and electronic structure of a selected subset of clusters, including their low energy structures and electrostatic potential maps, and how these fundamental characteristics are influenced by anion substitution. Collectively, our findings demonstrate how the fundamental properties of ILs, which determine their suitability for many applications, may be tuned by substituting counterions. These observations are critical in the sub-nanometer cluster size regime where phenomena do not scale predictably to the bulk phase, and each atom counts toward determining behavior.

cluster↗

Quantifying the Relevance of Long-Range Forces for Crystal Nucleation in Water

Understanding nucleation from aqueous solutions is of fundamental importance in a multitude of fields, ranging from materials science to biophysics. The complex solvent-mediated interactions in aqueous solutions hamper the development of a simple physical picture, elucidating the roles of different interactions in nucleation processes. In this study, we make use of three complementary techniques to disentangle the role played by short- and long-range interactions in solvent-mediated nucleation. Specifically, the first approach we utilize is the local molecular field (LMF) theory to renormalize long-range Coulomb electrostatics. Second, we use well-tempered metadynamics to speed up rare events governed by short-range interactions. Third, the deep learning-based State Predictive Information Bottleneck approach is employed in analyzing the reaction coordinate of the nucleation processes obtained from the LMF treatment coupled with well-tempered metadynamics. We find that the two-step nucleation mechanism can largely be captured by the short-range interactions, while the long-range interactions further contribute to the stability of the primary crystal state under ambient conditions. Furthermore, by analyzing the reaction coordinate obtained from the combined LMF-metadynamics treatment, we discern the fluctuations on different time scales, highlighting the need for long-range interactions when accounting for metastability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

pH‐ and Redox‐Responsive Pickering Emulsions Based on Cellulose Nanocrystal Surfactants

Abstract Nanoparticle surfactants (NPSs), formed by using dynamic interactions between nanoparticles and complementary ligands at the liquid‐liquid interface, have emerged as “smart emulsifiers” with attributes of high emulsification efficiency, long‐term stability, and on‐demand emulsification/demulsification capabilities. However, only pH‐responsiveness can be adopted for the assembly of reported NPSs formed by electrostatic interactions. Here, we propose an alternative design strategy, by taking advantage of the ferrocenium (Fc + ) sulfate ion pair, to develop a new type of cellulose nanocrystal (CNC) surfactant. The Fc + groups are sensitive to pH, redox reagents and voltage, imparting the CNC surfactants and derived Pickering emulsions with multi‐stimuli‐responsiveness, and showing promising applications in controllable delivery, release, and biphasic biocatalysis.

Yang, Yang↗

pH- and Redox-Responsive Pickering Emulsions Based on Cellulose Nanocrystal Surfactants

Nanoparticle surfactants (NPSs), formed by using dynamic interactions between nanoparticles and complementary ligands at the liquid-liquid interface, have emerged as “smart emulsifiers” with attributes of high emulsification efficiency, long-term stability, and on-demand emulsification/demulsification capabilities. However, only pH-responsiveness can be adopted for the assembly of reported NPSs formed by electrostatic interactions. Here, we propose an alternative design strategy, by taking advantage of the ferrocenium (Fc + ) sulfate ion pair, to develop a new type of cellulose nanocrystal (CNC) surfactant. In conclusion, the Fc + groups are sensitive to pH, redox reagents and voltage, imparting the CNC surfactants and derived Pickering emulsions with multi-stimuli-responsiveness, and showing promising applications in controllable delivery, release, and biphasic biocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗