Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Negatively charged hyperbranched polyether-based polyelectrolytes

The preparation of carboxylated hyperbranched polyglycerols of narrow polydispersity was achieved by modification (78–90%) of the hydroxyl end groups via Michael addition of acrylonitrile, followed by hydrolysis. High conversion could only be achieved for low molecular weight starting materials (520 and 1,030 g mol⁻¹). The solution properties of the resulting materials were investigated by dynamic light scattering (DLS), showing the formation of large aggregates with size depending on the pH value. After deposition on a negatively charged mica surface, the structures observed by atomic force microscope (AFM) show the coexistence of aggregates and single macromolecules. Most interesting, in the case of the lower molecular weight sample (PG 520 g mol⁻¹), extended and ordered terrace structures were formed, which are unprecedented for hyperbranched polymers and are of interest for surface modification in general.     

First organophosphorus radical-mediated cyclisations to afford medium-sized rings: eight-membered lactones and seven- and eight-membered lactams

The phosphorus based radical precursors N-ethylpiperidine hypophosphite (EPHP) and diethylphosphine oxide (DEPO) are efficient reagents for carrying out the formation of seven- and eight-membered rings. Esters and amides were successfully converted into the corresponding eight-membered lactones and seven- and eight-membered lactams in good to excellent yields.     

Die Undecaarsenide A3As11 (A = Rb,Cs) — Synthesen und Kristallstrukturen

Alkaline Metal Arsenides A₃As₁₁ (A = Rb, Cs): Preparation and Crystal Structures Rb₃As₁₁ and Cs₃As₁₁ were synthesized from the elements and the crystal structures of the ordered room temperature form were characterized via single crystal x‐ray studies. In the Zintl phases the As atoms form chiral ufosan‐anions As with As‐As distances ranging from 238 to 248 pm. Like K₃As₁₁ Rb₃As₁₁ crystallizes with the Na₃P₁₁ structure type (orthorhombic, space group Pbcn, a = 1108.2(2), b = 1533.5(3), c = 1060.1(2) pm, Z = 4), whereas the Cs compound (monoclinic, space group C2/c, a = 1324.5(7), b = 1524.5(9), c = 1937.2(11) pm, β = 95.29(1)°, Z = 8) forms a new structure type. The crystallographic relationship between the two structure types and the anion packings in the plastic crystalline high temperature forms are discussed.     

Recent advances of group 14 dimetallenes and dimetallynes in bond activation and catalysis

Since the first heavy alkene analogues of germanium and tin were isolated in 1976, followed by West''s disilene in 1981, the chemistry of stable group 14 dimetallenes and dimetallynes has advanced immensely. Recent developments in this field veered the focus from the isolation of novel bonding motifs to mimicking transition metals in their ability to activate small molecules and perform catalysis. The potential of these homonuclear multiply bonded compounds has been demonstrated numerous times in the activation of H₂, NH₃, CO₂ and other small molecules. Hereby, the strong relationship between structure and reactivity warrants close attention towards rational ligand design. This minireview provides an overview on recent developments in regard to bond activation with group 14 dimetallenes and dimetallynes with the perspective of potential catalytic applications of these compounds.

This minireview highlights the recent advances in small molecule activation and catalytic applications of homonuclear dimetallenes, dimetallynes and interconnected bismetallylenes of heavier group 14 elements.     

Mechanochemical Synthesis of 3d Transition‐Metal–1,2,4‐Triazole Complexes as Precursors for Microwave‐Assisted and Thermal Conversion to Coordination Polymers with a High Influence on the Dielectric Properties

The complexes [MCl₂(TzH)₄] (M=Mn ( 1 ), Fe ( 2 ); TzH=1,2,4‐1H‐triazole) and [ZnCl₂(TzH)₂] ( 3 ) have been obtained by mechanochemical reactions of the corresponding divalent metal chloride and 1,2,4‐1H‐triazole. They were successfully used as precursors for the formation of coordination polymers either by a microwave‐assisted reaction or by thermal conversion. For manganese, the conversion directly yielded [MnCl₂TzH] ( 4 ), whereas for the iron‐containing precursor, [FeCl₂TzH] ( 6 ), was formed via the intermediate coordination polymer [FeCl(TzH)₂]Cl ( 5 ). For cobalt, the isotypic polymer [CoCl(TzH)₂]Cl ( 7 ) was obtained, but exclusively by a microwave‐induced reaction directly from CoCl₂. The crystal structures were resolved from single crystals and powders. The dielectric properties were determined and revealed large differences in permittivity between the precursor complexes and the rigid chain‐like coordination polymers. Whereas the monomeric complexes exhibit very different dielectric behaviour, depending on the transition metal, from “low‐k” to “high‐k” with the permittivity ranging from 4.3 to >100 for frequencies of up to 1000 Hz, the coordination polymers and complexes with strong intermolecular interactions are all close to “low‐k” materials with very low dielectric constants up to 50 °C. Therefore, the conversion procedures can be used to deliberately influence the dielectric properties from complex to polymer and for different 3d transition‐metal ions.     

Hybrid polymer sol–gel material for UV-nanoimprint: microstructure and thermal densification

Hybrid polymer solutions suitable for UV-nanoimprint were synthesized by combination of an alkoxysilane binder mixture with silica nanoparticles. Hydrolysis and condensation reactions were monitored by NMR and viscosity measurements. Thereby long-term stable systems were produced as a prerequisite for industrial application. Dip-coating of glass substrates and subsequent UV-curing yielded thin films. Their thermal densification and microstructural evolution resulted in pure glassy porous coatings, which were in detail characterized by N₂-sorption measurements and ellipsometric porosimetry. Results emphasize the importance of the binder-particle interaction within these materials that are destined for the fabrication of microstructured surfaces by cost efficient and industrially feasible UV-based soft lithography. Structured glassy layers with high inorganic content show thermal stability up to >500 °C and have a high structure accuracy >85 %.     

Single-ion magnetism in the extended solid-state: insights from X-ray absorption and emission spectroscopy

Large single-ion magnetic anisotropy is observed in lithium nitride doped with iron. The iron sites are two-coordinate, putting iron doped lithium nitride amongst a growing number of two coordinate transition metal single-ion magnets (SIMs). Uniquely, the relaxation times to magnetisation reversal are over two orders of magnitude longer in iron doped lithium nitride than other 3d-metal SIMs, and comparable with high-performance lanthanide-based SIMs. To understand the origin of these enhanced magnetic properties a detailed characterisation of electronic structure is presented. Access to dopant electronic structure calls for atomic specific techniques, hence a combination of detailed single-crystal X-ray absorption and emission spectroscopies are applied. Together K-edge, L_2,3-edge and Kβ X-ray spectroscopies probe local geometry and electronic structure, identifying iron doped lithium nitride to be a prototype, solid-state SIM, clean of stoichiometric vacancies where Fe lattice sites are geometrically equivalent. Extended X-ray absorption fine structure and angular dependent single-crystal X-ray absorption near edge spectroscopy measurements determine Fe^I dopant ions to be linearly coordinated, occupying a D_6h symmetry pocket. The dopant engages in strong 3dπ-bonding, resulting in an exceptionally short Fe–N bond length (1.873(7) Å) and rigorous linearity. It is proposed that this structure protects dopant sites from Renner–Teller vibronic coupling and pseudo Jahn–Teller distortions, enhancing magnetic properties with respect to molecular-based linear complexes. The Fe ligand field is quantified by L_2,3-edge XAS from which the energy reduction of 3d_z² due to strong 4s mixing is deduced. Quantification of magnetic anisotropy barriers in low concentration dopant sites is inhibited by many established methods, including far-infrared and neutron scattering. We deduce variable temperature L₃-edge XAS can be applied to quantify the J = 7/2 magnetic anisotropy barrier, 34.80 meV (∼280 cm⁻¹), that corresponds with Orbach relaxation via the first excited, M_J = ±5/2 doublet. The results demonstrate that dopant sites within solid-state host lattices could offer a viable alternative to rare-earth bulk magnets and high-performance SIMs, where the host matrix can be tailored to impose high symmetry and control lattice induced relaxation effects.

Taking advantage of synchrotron light source methods, we present the geometric and electronic structure of iron doped in lithium nitride.     

Self-assembly of supramolecular architectures and polymers by orthogonal metal complexation and hydrogen-bonding motifs

A modular construction kit with two orthogonal noncovalent binding sites for self-assembly of supramolecular architectures is presented. The heteroditopic building blocks contain a terpyridine (tpy) unit for coordination of metal ions and a Hamilton receptor for multiple H-bonding of cyanuric acid derivatives. The association constants of ligand binding of M(II) complexes (M=Ru, Zn, Fe, and Pt) with a dendritic end cap were determined to be in the range of 10(2) and 10(4) L mol(-1) in chloroform. The capabilities for binding of metal ions were investigated by (1)H NMR and UV/Vis spectroscopy. The Fe complexes are most appropriate for the generation of discrete and high-ordered architectures due to their strong tendency to form FeL(2) complexes. Superstructures are readily formed in a one-pot procedure at room temperature. No mutual interactions between the orthogonal binding motifs were observed, and this demonstrates the highly specific nature of each binding process. Decomplexation experiments were carried out to examine the reversibility of Fe-tpy coordination. Substitution of the terminal end cap with a homoditopic bis-cyanurate linkage leads to formation of an iron-containing supramolecular strand. Formation of coordination polymers was confirmed by viscosity measurements. The supramolecular polymer strands can be reversibly cleaved by addition of a terminating cyanuric acid building block, and this proves the dynamic nature of this noncovalent polymerization process.