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At least 91 records · Page 5

Structure–Function Relationships in Sequence-Controlled Copolymers for Rare Earth Element Chelation

The ability to tune material function through primary sequence is a defining feature of biological macromolecules, allowing precise control over structure and target interactions in complex aqueous environments. However, translating sequence–structure–function relationships to synthetic macromolecules is challenging due to their dispersity in sequence, conformation, and composition. Here, we report systematic studies of amphiphilic polymer chelators designed to probe how composition and patterning influence binding affinity and selectivity for rare earth elements (REEs), a series of technologically relevant metals with challenging separation profiles. A library of copolymers varying hydrophobic monomer composition and patterning was synthesized via reversible addition–fragmentation chain transfer (RAFT) polymerization, spanning statistical, gradient, and block architectures. REE binding was quantified using a high-throughput colorimetric assay, and reconstruction of polymer ensembles using kinetic stochastic simulations enabled quantitative comparisons of sequence heterogeneity, linking local monomer colocalization to emergent REE binding. Further, we investigated the role of different hydrophobic comonomers in tuning metal coordination, with binding trends linked to structural features that influence binding site desolvation. Complementary dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS) measurements showed that both polymer and monomer architecture modulate metal-induced conformational changes, and that multichain assembly behavior emerges beyond critical hydrophobic thresholds. Sequence control also altered REE selectivity, with nonmonotonic differences observed across compositionally identical polymers with different sequence architectures. Together, these findings establish design principles that connect polymer sequence and structure to binding performance, guiding the design of macromolecular chelators with enhanced affinity and selectivity for applications in separations, sensing, and catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology-Informed Design Rules for Deconstructable Thermoset Copolymer Networks

Existing models of thermoset deconstruction facilitated by incorporating cleavable comonomers rely on a mean-field reverse gel point paradigm, which predicts network dissolution once cleavable bonds reach a critical stoichiometric threshold, but does not account for where those bonds reside within the network architecture. Using reactive coarse-grained molecular dynamics simulations coupled with graph-theoretic analysis, we extend this stoichiometric picture to show that deconstructability is governed by the curing-imprinted network topology rather than stoichiometry alone. This topological organization is hierarchical: at the local scale, the elastic effectiveness of cross-link junctions determines which cross-links constitute the load-bearing scaffold; at the mesoscale, the cross-linking rate kinetically templates that scaffold into topologically modular communities─densely cross-linked clusters connected by sparse bridging strands that sustain network connectivity. Using betweenness centrality to identify nodes that disproportionately lie on intercommunity shortest paths, we demonstrate that effective deconstruction of the network into macromolecular fragments requires cleavable comonomers to intercept these high-centrality bridging strands. We further find that under uniform, disassortative comonomer incorporation, this topological requirement provides a mechanistic basis for extending the reverse gel point to incorporate network topology. We also show that modularity imposes a fundamental limit on fragment uniformity that persists even when the centrality requirement is met. Finally, we demonstrate that chain stiffness provides a nearly independent lever to suppress mechanically redundant cross-links and raise the glass transition temperature without significantly altering the deconstruction outcome. Together, these findings reframe the thermoset design space around network topology and provide actionable guidelines for engineering thermoset copolymers with predictable deconstructability and targeted thermomechanical performance.

coarse-grained molecular dynamics↗

Dual C–H functionalization of polyolefins for covalent adaptable network formation via cooperative electrolysis

The increasing demand for carbon fibre-reinforced polymer composites with polyolefin thermoset matrices will lead to the generation of large volumes of low molecular weight waste oligomers during the fibre recovery process. To address this challenge, we present a cooperative electrolytic dual C–H bond functionalization strategy for the one-step installation of two key functional groups essential for dynamic linkages of these deconstructed oligomers. Through direct competition studies, we reveal the predominance of tertiary allylic C–H activation along the complex, branched oligomer backbone. The resulting difunctionalized oligomers form covalently adaptable networks with exceptional circularity. By establishing a sustainable pathway for upcycling deconstructed oligomers from carbon fibre-reinforced polymer fibre recovery, this strategy introduces thermoset materials derived directly from waste. Here, it advances sustainable manufacturing practices, contributing to a net-zero waste synthetic ecosystem, and highlights the prospects of mediated electrolysis in macromolecular transformations.

Electrocatalysis↗

Biobased Semi-Interpenetrating Polymer Networks of Poly(ε-caprolactone) and Epoxidized Soybean Oil with Nanoscale Morphology, Shape-Memory Effect, and Biocompatibility

Creating biobased polymer blends with outstanding properties, nanoscale morphology, shape-memory capability, and biocompatibility is very crucial and requires a fundamental understanding of the phase behavior, macromolecular structure, and biological compatibility of the polymer blends with living cells. It is very critical to understand the complex relationships among the polymer structure, morphology, and performance of multifunctional smart materials under conditions that they are likely to encounter during use, particularly in biomedical applications. Biobased semi-interpenetrating polymer networks of poly(ε-caprolactone) and epoxidized soybean oil with nanoscale morphology have been successfully synthesized via in situ cationic polymerization and compatibilization in a homogeneous solution. Varies analytical and characterization techniques, such as Fourier transform infrared spectroscopy, differential scanning calorimetry, dynamic mechanical analysis, transmission electron microscopy, X-ray scattering, cell toxicity, and shape-memory effects (SMEs), have been employed to understand the structure–properties relationship of these smart, biobased nanostructured polymer blends. The synthesized nano blends were nontoxic or biocompatible and supported attachment of human vein endothelial cells, showing their potential use in biomedical applications. The current versatile, low-cost strategy for synthesizing the nanoscale morphology of semi-interpenetrating polymer networks with SMEs and biocompatibility should be widely applicable for polymer systems. This study is also considered as a continuation to our efforts in the area of biobased polymers to develop innovative technologies to transform natural resources into smart multifunctional materials for a wide range of applications, including coatings, adhesives, and medical devices.

36 MATERIALS SCIENCE↗

Organic Components of Small Bodies in the Outer Solar System: Some Results of the New Horizons Mission

The close encounters of the Pluto–Charon system and the Kuiper Belt object Arrokoth (formerly 2014 MU 69 ) by NASA’s New Horizons spacecraft in 2015 and 2019, respectively, have given new perspectives on the most distant planetary bodies yet explored. These bodies are key indicators of the composition, chemistry, and dynamics of the outer regions of the Solar System’s nascent environment. Pluto and Charon reveal characteristics of the largest Kuiper Belt objects formed in the dynamically evolving solar nebula inward of ~30 AU, while the much smaller Arrokoth is a largely undisturbed relic of accretion at ~45 AU. The surfaces of Pluto and Charon are covered with volatile and refractory ices and organic components, and have been shaped by geological activity. On Pluto, N 2 , CO and CH 4 are exchanged between the atmosphere and surface as gaseous and condensed phases on diurnal, seasonal and longer timescales, while Charon’s surface is primarily inert H 2 O ice with an ammoniated component and a polar region colored with a macromolecular organic deposit. Arrokoth is revealed as a fused binary body in a relatively benign space environment where it originated and has remained for the age of the Solar System. Its surface is a mix of CH 3 OH ice, a red-orange pigment of presumed complex organic material, and possibly other undetected components.

Solar System↗

Design of materials with supramolecular polymers

One hundred years ago Hermann Staudinger was strongly criticized by his scientific peers for his macromolecular hypothesis, but today it is hard to imagine a world without polymers. His hypothesis described polymers as macromolecules composed of large numbers of structural units connected by covalent bonds. In the 1990s the concept of supramolecular polymers emerged in the scientific literature as discrete entities of large molar mass comparable to that of classical polymers but built through non-covalent bonds among monomers. Supramolecular polymers exist in biological systems, and potentially blend the physical properties of covalent polymers with unique features such as high degrees of internal order within the polymeric structure, defined shapes, and novel dynamics. This trend article provides a summary of seminal contributions in supramolecular polymerization and provides recent examples from the Stupp laboratory to demonstrate the potential applications of an exciting class of materials composed fully or partially of supramolecular polymers. Finally, in closing, we provide our perspective on future opportunities provided by this field at the onset of a second century of polymers. It is our objective here to demonstrate that this second century could be as prosperous, if not more so, than the preceding one.

36 MATERIALS SCIENCE↗

Conserved Macromolecular Architecture of Poplar Secondary Cell Walls Revealed by ssNMR and Atomistic Modeling

The macromolecular architecture of plant secondary cell walls governs wood's mechanical and biochemical properties, yet its natural intra-species variability remains poorly characterized. Here, we combined 13C solid-state NMR (ssNMR), multivariate statistical analysis, and molecular modeling to profile nanoscale structure across 13 genetically diverse Populus trichocarpa genotypes grown in 13C-enriched atmospheres. SsNMR-derived phenotypes spanning composition, structure, mobility, and inter-polymer proximities reveal a conserved architecture, with a subtle yet coordinated variation organizing into dominant structural and secondary mobility axes. A representative atomistic model captures these features and reproduces experimental metrics. Molecular dynamics simulations support a weak but consistent positive correlation between cellulose abundance and crystalline-like order, with interior cellulose chains enriched in tg (trans-gauche) conformations without expanding crystalline cores. Together, experiment and simulation reveal a genetically buffered, broadly conserved nanoscale architecture across genotypes, where subtle fine-tuning of cellulose bundling and matrix packing balances mechanical performance with biological function.

09 BIOMASS FUELS↗

Virus-Like Particles (VLPs) as a Platform for Hierarchical Compartmentalization

Hierarchically self-assembled structures are common in biology, but it is often challenging to design and fabricate synthetic analogs. The archetypal cell is defined by hierarchically organized multicompartmentalized structures with boundaries that delineate the interior from exterior environments and is an inspiration for complex functional materials. Here, we have demonstrated an approach to the design and construction of a nested protein cage system that can additionally incorporate the packing of other functional macromolecules and exhibit some of the features of a minimal synthetic cell-like material. We have demonstrated a strategy for controlled co-packaging of subcompartments, ferritin (Fn) cages, together with active cellobiose-hydrolyzing β-glycosidase enzyme macromolecules, CelB, inside the sequestered volume of the bacteriophage P22 capsid. Using controlled in vitro assembly, we were able to modulate the stoichiometry of Fn cages and CelB encapsulated inside the P22 to control the degree of compartmentalization. The co-encapsulated enzyme CelB showed catalytic activity even when packaged at high total macromolecular concentrations comparable to an intracellular environment. Here, this approach could be used as a model to create synthetic protein-based protocells that can confine smaller functionalized proto-organelles and additional macromolecules to support a range of biochemical reactions.

59 BASIC BIOLOGICAL SCIENCES↗

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

59 BASIC BIOLOGICAL SCIENCES↗

Solution Structure and Scaling Laws of Cylindrical and Tapered Bottlebrush Polymers

Bottlebrush polymers are a unique class of macromolecular architectures with a plethora of potential industrial and pharmaceutical applications that critically depend on the bottlebrush shape and dimensions. Here, a systematic series of 12 cylindrical and 12 cone-shaped (tapered) bottlebrush polymers with poly(tert-butyl acrylate) (PtBA) or polystyrene (PS) side chains were synthesized using the sequential addition of macromonomers ring-opening metathesis polymerization (SAM-ROMP) grafting-through method. Small-angle neutron scattering (SANS) studies on dilute solutions of the two types of bottlebrush polymers provided noninvasive characterization of their structural dimensions and chain conformations. Simulated SANS traces, generated using coarse-grained molecular dynamics simulations, reproduced the distinctive features observed in the experimental SANS signals and provided necessary validation for data modeling. The combined analysis of experimental and simulated SANS signals yielded key structural and conformational parameters, including the bottlebrush radius, length, and Kuhn length as well as the excluded volume parameter and the correlation length of the polymer side chains. Importantly, the obtained structural parameters followed well-defined scaling laws as a function of the backbone and side chain degrees of polymerization, as predicted by mean field theories. In conclusion, these findings provide clear experimental and computational evidence of the interdependence of structural and conformational properties in an important class of polymer architectures.

36 MATERIALS SCIENCE↗

Plastocyanin is the long-range electron carrier between photosystem II and photosystem I in plants

In photosynthetic electron transport, large multiprotein complexes are connected by small diffusible electron carriers, the mobility of which is challenged by macromolecular crowding. For thylakoid membranes of higher plants, a long-standing question has been which of the two mobile electron carriers, plastoquinone or plastocyanin, mediates electron transport from stacked grana thylakoids where photosystem II (PSII) is localized to distant unstacked regions of the thylakoids that harbor PSI. Here, we confirm that plastocyanin is the long-range electron carrier by employing mutants with different grana diameters. Furthermore, our results explain why higher plants have a narrow range of grana diameters since a larger diffusion distance for plastocyanin would jeopardize the efficiency of electron transport. In the light of recent findings that the lumen of thylakoids, which forms the diffusion space of plastocyanin, undergoes dynamic swelling/shrinkage, this study demonstrates that plastocyanin diffusion is a crucial regulatory element of plant photosynthetic electron transport.

plastoquinone↗

Sequence-defined Pareto frontier of a copolymer structure

The correlations between the sequence of monomers in a macromolecule and its three-dimensional (3D) structure is a grand challenge in polymer science. The properties and functions of macromolecules depend on their 3D shape that has appeared to be dictated by their monomer sequence. However, the progress towards understanding the sequence–structure-property correlations and their utilization in materials engineering are slow because it is almost impossible to characterize an astronomically large number of possible sequences of a copolymer using traditional experimental and simulation methods. To address this problem, here, we combine evolutionary computing and coarse-grained molecular dynamics (CGMD) simulation and study the sequence-structure correlations of a model AB-type copolymer in a solution and assess the impact of sequence on the packing density in its bulk phase. The CGMD-based evolutionary algorithm (EA) screens the sequence space of a single chain copolymer efficiently and identifies a wide range of single-molecule structures including extremal radii of gyration. The data are utilized to estimate the Pareto front of the structure-space of a binary copolymer as a function of its composition. The monomer packings in single-molecule solution phase and multimolecular bulk phase are found to be identical. Finally, this work highlights the opportunities of sequence-specific control of macromolecular structure for designing target materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inferring assembly-curving trends of bacterial micro-compartment shell hexamers from crystal structure arrangements

Bacterial microcompartments (BMC) are complex macromolecular assemblies that participate in varied chemical processes in about one fourth of bacterial species. BMC-encapsulated enzymatic activities are segregated from other cell contents by means of semipermeable shells, justifying why BMC are viewed as prototype nano-reactors for biotechnological applications. Herein, we undertook a comparative study of bending propensities of BMC hexamers (BMC-H), the most abundant shell constituents. Published data show that some BMC-H, like β -carboxysomal CcmK, tend to assemble flat whereas other BMC-H often build curved objects. Inspection of available crystal structures presenting BMC-H in tiled arrangements permitted us to identify two major assembly modes with a striking connection with experimental trends. All-atom molecular dynamics (MD) supported that BMC-H bending is triggered robustly only from the arrangement adopted in crystals by BMC-H that experimentally form curved objects, leading to very similar arrangements to those found in structures of recomposed BMC shells. Simulations on triplets of planar-behaving hexamers, which were previously reconfigured to comply with such organization, confirmed that bending propensity is mostly defined by the precise lateral positioning of hexamers, rather than by BMC-H identity. Finally, an interfacial lysine was pinpointed as the most decisive residue in controlling PduA spontaneous curvature. Globally, results presented herein should contribute to improve our understanding of the variable mechanisms of biogenesis characterized for BMC, and of possible strategies to regulate BMC size and shape.

59 BASIC BIOLOGICAL SCIENCES↗

Computer simulation of ion channel gating: the M(2) channel of influenza A virus in a lipid bilayer

The transmembrane fragment of the influenza virus M(2) protein forms a homotetrameric channel that transports protons. In this paper, we use molecular dynamics simulations to help elucidate the mechanism of channel gating by four histidines that occlude the channel lumen in the closed state. We test two competing hypotheses. In the "shuttle" mechanism, the delta nitrogen atom on the extracellular side of one histidine is protonated by the incoming proton, and, subsequently, the proton on the epsilon nitrogen atom is released on the opposite side. In the "water-wire" mechanism, the gate opens because of electrostatic repulsion between four simultaneously biprotonated histidines. This allows for proton transport along the water wire that penetrates the gate. For each system, composed of the channel embedded in a hydrated phospholipid bilayer, a 1.3-ns trajectory was obtained. It is found that the states involved in the shuttle mechanism, which contain either single-protonated histidines or a mixture of single-protonated histidines plus one biprotonated residue, are stable during the simulations. Furthermore, the orientations and dynamics of water molecules near the gate are conducive to proton transfer. In contrast, the fully biprotonated state is not stable. Additional simulations show that if only two histidines are biprotonated, the channel deforms but the gate remains closed. These results support the shuttle mechanism but not the gate-opening mechanism of proton gating in M(2).

NASA Center ARC↗

Charged Biological Membranes Repel Large Neutral Molecules by Surface Dielectrophoresis and Counterion Pressure

Macromolecular crowding is the usual condition of cells. The implications of the crowded cellular environment for protein stability and folding, protein–protein interactions, and intracellular transport drive a growing interest in quantifying the effects of crowding. While the properties of crowded solutions have been extensively studied, less attention has been paid to the interaction of crowders with the cellular boundaries, i.e., membranes. However, membranes are key components of cells and most subcellular organelles, playing a central role in regulating protein channel and receptor functions by recruiting and binding charged and neutral solutes. While membrane interactions with charged solutes are dominated by electrostatic forces, here we show that significant charge-induced forces also exist between membranes and neutral solutes. Using neutron reflectometry measurements and molecular dynamics simulations of poly(ethylene glycol) (PEG) polymers of different molecular weights near charged and neutral membranes, we demonstrate the roles of surface dielectrophoresis and counterion pressure in repelling PEG from charged membrane surfaces. The resulting depletion zone is expected to have consequences for drug design and delivery, the activity of proteins near membrane surfaces, and the transport of small molecules along the membrane surface.

59 BASIC BIOLOGICAL SCIENCES↗

FMX – the Frontier Microfocusing Macromolecular Crystallography Beamline at the National Synchrotron Light Source II

Two new macromolecular crystallography (MX) beamlines at the National Synchrotron Light Source II, FMX and AMX, opened for general user operation in February 2017 [Schneider et al. (2013). J. Phys. Conf. Ser. 425 , 012003; Fuchs et al. (2014). J. Phys. Conf. Ser. 493 , 012021; Fuchs et al. (2016). AIP Conf. Proc. SRI2015 , 1741 , 030006]. FMX, the micro-focusing Frontier MX beamline in sector 17-ID-2 at NSLS-II, covers a 5–30 keV photon energy range and delivers a flux of 4.0 × 10 12 photons s −1 at 1 Å into a 1 µm × 1.5 µm to 10 µm × 10 µm (V × H) variable focus, expected to reach 5 × 10 12 photons s −1 at final storage-ring current. This flux density surpasses most MX beamlines by nearly two orders of magnitude. The high brightness and microbeam capability of FMX are focused on solving difficult crystallographic challenges. The beamline's flexible design supports a wide range of structure determination methods – serial crystallography on micrometre-sized crystals, raster optimization of diffraction from inhomogeneous crystals, high-resolution data collection from large-unit-cell crystals, room-temperature data collection for crystals that are difficult to freeze and for studying conformational dynamics, and fully automated data collection for sample-screening and ligand-binding studies. FMX's high dose rate reduces data collection times for applications like serial crystallography to minutes rather than hours. With associated sample lifetimes as short as a few milliseconds, new rapid sample-delivery methods have been implemented, such as an ultra-high-speed high-precision piezo scanner goniometer [Gao et al. (2018). J. Synchrotron Rad. 25 , 1362–1370], new microcrystal-optimized micromesh well sample holders [Guo et al. (2018). IUCrJ , 5 , 238–246] and highly viscous media injectors [Weierstall et al. (2014). Nat. Commun. 5 , 3309]. The new beamline pushes the frontier of synchrotron crystallography and enables users to determine structures from difficult-to-crystallize targets like membrane proteins, using previously intractable crystals of a few micrometres in size, and to obtain quality structures from irregular larger crystals.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Patterns in interactions of variably acetylated xylans with hydrophobic cellulose surfaces

The recalcitrance of plant cell wall lignocellulosic biomass to deconstruction is a major hurdle to sustainable biofuel/bioproduct economy. A multitude of interactions stabilize lignocellulosic biomass structure. Among these, tight packing of hemicellulose-cellulose is partly responsible for biomass recalcitrance. Here, unrestrained molecular dynamics simulations are employed to understand the influence of the nature and pattern of naturally-occuring acetyl decorations of the xylan backbone on interactions with the (100) hydrophobic cellulose surface. Periodically O2-acetylated xylan (2AcX) assume twofold helical screw conformations that are stabilized by a combination of multiple hydrophobic contacts and hydrogen bonds with the hydrophobic cellulose surface. In contrast, acetylation at the O3 position in xylan obstructs interactions, thereby adopting threefold helical screw conformations that potentially preferably interact with lignin rather than cellulose. Fully acetylated xylan desorbs from the surface implying a minimum number of unsubstituted residues on the xylan backbone is required for interaction with the surface. Here, the substituted residues must form ~ 20% fewer contacts than the unsubstituted residues to sustain stable twofold helical screw xylan conformations on the cellulose surface. Thus, specific roles of macromolecular conformations of cellulose and hemicellulose in influencing the supramolecular interactions and function of plant cell walls have been determined.

59 BASIC BIOLOGICAL SCIENCES↗

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↗