Incommensurate modulations in Ba2TiSi2O8, Sr2TiSi2O8, and Ba2TiGe2O8

Incommensurate modulations in Ba₂TiSi₂O₈, Sr₂TiSi₂O₈, and Ba₂TiGe₂O₈ are compared based on their corresponding electron diffraction patterns. The dependence of the modulations on chemical composition provides a suitable model system for the investigation of incommensurations in framework structures using high-resolution transmission electron microscopy (HRTEM). A widening of quantitative HRTEM utilising the concept of rigid units is proposed allowing for a determination of atomistic displacements responsible for the formation of incommensurately modulated structures.     

A conditional dilatation equation

Summary The following theorem holds true. Theorem. Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k.     

Neutron powder diffraction of metal-organic frameworks for hydrogen storage

We review recent structural studies that we have undertaken aimed at elucidating the fundamental properties of metal-organic framework materials and their interactions with hydrogen. We have shown that exposing coordinatively unsaturated metal centers can greatly enhance the hydrogen binding energy and that they result in a significant increase of the surface packing density of adsorbed hydrogen molecules on materials’ surface. We will review some of the structural aspects of these materials, especially the adsorbed hydrogen molecule surface packing density in one type of metal-organic framework, MOF-74, which can be packed even denser than that in solid hydrogen.      

Actinide Organometallic Complexes with π-Ligands

Recent developments and results from the organometallic chemistry of the actinides are reviewed. In the last one and a half years the structural data of about 15 organometallic complexes of transuranium actinides (Np or Pu) have been published, all involving π-ligands in the coordination sphere of the metal ion. On the basis of these data, a comparison of these molecules is presented. Depending on the steric demands of the ligands, effects like the actinide contraction seem to be stronger or weaker in the structural features. This indicates that the interplay between the actinide ion and the π-ligand is rather flexible, enabling the formation of stable bonds over a broad range of actinide ion oxidation states.     

Synthesis of Polymers Containing Potassium Acyltrifluoroborates (KATs) and Post-polymerization Ligation and Conjugation

We report the synthesis of monomers for atom-transfer radical polymerization (ATRP) and a reversible addition-fragmentation chain transfer (RAFT) agent bearing trifluoroborate iminiums (TIMs), which are quantitatively converted into potassium acyltrifluoroborates (KATs) after polymerization. The resulting KAT-containing polymers are suitable for rapid amide-forming ligations for both post-polymerization modification and polymer conjugation. The polymer conjugation occurs rapidly, even under dilute (micromolar) aqueous conditions at ambient temperatures, thereby enabling the synthesis of a variety of linear and star-shaped block copolymers. In addition, we applied post-polymerization modification to the covalent linking of a photocaged cyclic antibiotic (gramicidin S) to the side chains of the KAT-containing copolymer. Cellular assays revealed that the polymer–antibiotic conjugate is biocompatible and provides efficient light-controlled release of the antibiotic on demand.     

Cumulants and moments

We introduce a ¹-algebra of terminating sequences. The set of normalized linear functionals on this algebra is then equipped with a quasi-multiplication and thus with a multiplication. A state corresponds to a sequence of moments. With it we associate its sequence of cumulants. The quasi-multiplication relates cumulants and moments in a very easy way. We give necessary and sufficient conditions for a sequence to be a sequence of moments and necessary and sufficient conditions for a sequence to be a sequence of cumulants.     

Ultraviolet reflectivity spectra of CuInSe2, CuInTe2 and CuGaTe2

Reflectivity spectra of CuInSe₂, CuInTe₂ and CuGaTe₂ are measured in the photon energy range from 2 to 9 eV. All compounds exhibit nearly the same reflectivity structures, and a comparison with measurements on the other Cu-III-VI₂ semiconductors shows that the band structures of all Cu-III-VI₂ compounds should be very similar except the energy range near the fundamental edge.