Reversible M−M Bonding by Alkaline Earth Metals (Mg,Ca, Sr,Ba) in Graphite Intercalation Compounds

The alkaline earth metals (M=Mg, Ca, Sr, and Ba) exhibit a +2 oxidation state in nearly all known stable compounds, but M^I dimeric complexes with M−M bonding, [M₂(en)₂]²⁺, (en=ethylenediamine) of all these metals can be stabilized within the galleries of donor-type graphite intercalation compounds (GICs). These metals can also form GICs with more conventional metal (II) ion complexes, [M(en)₂]²⁺. Here, the facile interconversion between dimeric-M^I and monomeric-M^II intercalates upon the addition/removal of en are reported. Thermogravimetry, powder X-ray diffraction, and pair distribution function analysis of total scattering data support the presence of either [M₂(en)₂]²⁺ or [M(en)₂]²⁺ guests. This phase conversion requires coupling graphene and metal redox centers, with associated reversible M−M bond formation within graphene galleries. This chemistry allows the facile isolation of unusual oxidation states, reveals M⁰→M²⁺ reaction pathways, and present new opportunities in the design of hybrid conversion/intercalation materials for applications such as charge storage.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Self‐Assembly of Uranyl–Peroxide Nanocapsules in Basic Peroxidic Environments

A wide range of uranyl–peroxide nanocapsules have been synthesized using very simple reactants in basic media; however, little is known about the process to form these species. We have performed a density functional theory study of the speciation of the uranyl ions under different experimental conditions and explored the formation of dimeric species via a ligand exchange mechanism. We shed some light onto the importance of the excess of peroxide and alkali counterions as a thermodynamic driving force towards the formation of larger uranyl–peroxide species.     

The Key Role of U28 in the Aqueous Self‐Assembly of Uranyl Peroxide Nanocages

For 11 years now, the structural diversity and aesthetic beauty of uranyl–peroxide capsules have fascinated researchers from the diverse fields of mineralogy, polyoxometalate chemistry, and nuclear fuel technologies. There is still much to be learned about the mechanisms of the self‐assembly process, and the role of solution parameters including pH, alkali template, temperature, time, and others. Here we have exploited the high solubility of the UO₂²⁺/H₂O₂/LiOH aqueous system to address the effect of the hydroxide concentration. Important techniques of this study are single‐crystal X‐ray diffraction, small‐angle X‐ray scattering, and Raman spectroscopy. Three key phases dominate the solution speciation as a function of time and the LiOH/UO₂²⁺ ratio: the uranyl–triperoxide monomer [UO₂(O₂)₃]^4?and the two capsules [(UO₂)(O₂)(OH)]₂₄^24?(U₂₄) and [(UO₂)(O₂)_1.5]₂₈^28?(U₂₈). When the LiOH/U ratio is around three, U₂₈ forms rapidly and this cluster can be isolated in high yield and purity. This result was most surprising and challenges the hypothesis that alkali templating is the most important determinant in the cluster geometry. Moreover, analogous experiments with KOH, NH₄OH, and TEAOH (TEA=tetraethylammonium) also rapidly yield U₂₈, which suggests that U₂₈ is the kinetically favored species. Complete mapping of the pH–time phase space reveals only a narrow window of the U₂₈ dominance, which is why it was previously overlooked as an important kinetic species in this chemical system, as well as others with different counterions.     

Discrete Hf18 Metal-oxo Cluster as a Heterogeneous Nanozyme for Site-Specific Proteolysis

The selective hydrolysis of proteins by non-enzymatic catalysis is difficult to achieve, yet it is crucial for applications in biotechnology and proteomics. Herein, we report that discrete hafnium metal-oxo cluster [Hf₁₈O₁₀(OH)₂₆(SO₄)₁₃⋅(H₂O)₃₃] ( Hf₁₈ ), which is centred by the same hexamer motif found in many MOFs, acts as a heterogeneous catalyst for the efficient hydrolysis of horse heart myoglobin (HHM) in low buffer concentrations. Among 154 amino acids present in the sequence of HHM, strictly selective cleavage at only 6 solvent accessible aspartate residues was observed. Mechanistic experiments suggest that the hydrolytic activity is likely derived from the actuation of Hf^IV Lewis acidic sites and the Brønsted acidic surface of Hf₁₈ . X-ray scattering and ESI-MS revealed that Hf₁₈ is completely insoluble in these conditions, confirming the HHM hydrolysis is caused by a heterogeneous reaction of the solid Hf₁₈ cluster, and not from smaller, soluble Hf species that could leach into solution.     

Evolution of Actinyl Peroxide Clusters U28 in Dilute Electrolyte Solution: Exploring the Transition from Simple Ions to Macroionic Assemblies

Actinyl peroxide clusters, a unique class of uranyl‐containing nanoclusters discovered in recent years, are crucial intermediates between the (UO₂)²⁺ aqua‐ion monomer and bulk uranyl minerals. Herein, two actinyl polyoxometalate nanoclusters of Cs₁₅[(Ta(O₂)₄)Cs₄K₁₂(UO₂(O₂)_1.5)₂₈] ? 20 H₂O (CsK U₂₈ ) and Na₆K₉[(Ta(O₂)₄)Rb₄Na₁₂(UO₂(O₂)_1.5)₂₈] ? 20 H₂O (RbNa U₂₈ ) were synthesized by incorporating a central Ta(O₂)₄^3? anion that templates a hollow shell of 28 uranyl peroxide polyhedra. When dissolved in aqueous solutions with additional electrolytes, those 1.8 nm‐size macroanions self‐assembled into spherical, hollow, blackberry‐type supramolecular structures, as was characterized by laser‐light scattering (LLS) and TEM techniques. These clusters are the smallest macroions reported to date that form blackberry structures in solution, therefore, can be treated as valuable models for investigating the transition from simple ions to macroions. Kinetic studies showed an unusually long lag phase in the initial self‐assembly process, which is followed by a rapid formation of the blackberry structures in solution. The small cluster size and high surface‐charge density are essential in regulating the supramolecular structure formation, as was shown from the high activation energy barrier of 51.2±2 kJ mol^?1. Different countercations were introduced into the system to investigate the effect of ion binding to the length of the lag phase. The current research provides yet another scale of self‐assembly of uranyl peroxide complexes in aqueous media.     

Witt’s Theorem for Noncommutative Conic Curves

Let k be a field. We extend the main result in Nyman (J. Algebra 434, 90–114, 2015) to show that all homogeneous noncommutative curves of genus zero over k are noncommutative \(\mathbb {P}^{1}\)-bundles over a (possibly) noncommutative base. Using this result, we compute complete isomorphism invariants of homogeneous noncommutative curves of genus zero, allowing us to generalize a theorem of Witt.