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.     

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.     

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.     

Kinetic Analysis of the Reactions between GG-Containing Oligonucleotides and Platinum Complexes. 1. Reactions of Single-Stranded Oligonucleotides with cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) and [Pt(NH(3))(3)(H(2)O)](2+)

Using concentration measurements based on high performance liquid chromatography, we have investigated the kinetics of reaction between single-stranded oligonucleotides containing a d(GpG) sequence, i.e., d(GG), d(TGG), d(TTGG), and d(CTGGCTCA), and the platinum complexes cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) (1) and [Pt(NH(3))(3)(H(2)O)](2+) (2). The rate constants for the substitution of one aqua ligand of platinum in 1 or 2 by each guanine of the oligonucleotides were individually measured, as well as, for 1, those for the subsequent conversion of the monoadducts to the diadduct. For the platination of d(GG) and d(TGG), the rate constants are similar for the 5'- and 3'-guanines. The longer oligonucleotides d(TTGG) and d(CTGGCTCA) are platinated slightly faster on the 5'-G than on the 3'-G. 2 shows a similar slight preference for the 5'-guanine, but it reacts by a factor of 4-10 more slowly than 1. For both complexes, the platination rate constants increase with increasing oligonucleotide length. Platination of the 5'-G by 1 is 1 order of magnitude faster on d(CTGGCTCA) than on d(GG). Concerning the chelation step giving the GG diadduct of 1, the longer the oligonucleotide, the larger is the ratio between the rates of the cyclization of the 3'- and 5'-monoadducts k(3)(')(c) and k(5)(')(c): k(3)(')(c)/k(5)(')(c) equals 1.4 for d(GG) and 3.3 for d(CTGGCTCA).     

Dialumenes – aryl vs. silyl stabilisation for small molecule activation and catalysis

Main group multiple bonds have proven their ability to act as transition metal mimics in the last few decades. However, catalytic application of these species is still in its infancy. Herein we report the second neutral NHC-stabilised dialumene species by use of a supporting aryl ligand (3). Different to the trans-planar silyl-substituted dialumene (3Si), compound 3 features a trans-bent and twisted geometry. The differences between the two dialumenes are explored computationally (using B3LYP-D3/6-311G(d)) as well as experimentally. A high influence of the ligand''s steric demand on the structural motif is revealed, giving rise to enhanced reactivity of 3 enabled by a higher flexibility in addition to different polarisation of the aluminium centres. As such, facile activation of dihydrogen is now achievable. The influence of ligand choice is further implicated in two different catalytic reactions; not only is the aryl-stabilised dialumene more catalytically active but the resulting product distributions also differ, thus indicating the likelihood of alternate mechanisms simply through a change of supporting ligand.

Ligand controlled reactivity: a trans-bent and twisted geometry enables dihydrogen activation and enhanced catalytic activity for NHC-stabilised dialumenes.     

2,2‐Dichloro‐1,3‐bis(trimethylsilyl)‐1,3‐diaza‐2‐silacyclopentane

In the title compound, C₈H₂₂Cl₂N₂Si₃, the central Si atom is tetrahedrally coordinated by two Cl and two N atoms in a molecule that has crystallographically imposed C₂ symmetry. Comparison is made with the isomorphous structure having titanium instead of silicon at the central position in the diazacyclopentane ring [Tinkler, Deeth, Duncalf & McCamley (1996). Chem. Commun. pp. 2623–2624].     

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.     

Dynamisch-mechanische Untersuchungen an Polyisobutylenschmelzen

Zusammenfassung Zur Untersuchung des Einflusses von Molekulargewicht und Molekulargewichtsverteilung auf das viskoelastische Verhalten hochpolymerer Schmelzen wurde der dynamische Schubmodul von zwei Serien von Polyisobutylenen mit verschiedenen Molekulargewichten bzw. Verteilungen in einem weiten Frequenz- und Temperaturbereich gemessen. Mit wachsendem Molekulargewicht verschiebt sich der niederfrequente Abfall beider Moduln zu tieferen Frequenzen. Durch die Molekulargewichtsverteilung wird der gesamte Verlauf der Modulkurven beeinflußt.Das viskoelastische Verhalten bei tiefen Frequenzen wird durch zwei Größen bestimmt: die Nullviskosität ₀ und die Gleichgewichtsnachgiebigkeit J_e ⁰. ₀ ist proportional zu M^3,8 und hängt von der Verteilung nur wenig ab. J_e ⁰ ist dagegen fürM>ca. 10⁵ vom Molekulargewicht unabhängig, wird aber durch geringe hochmolekulare Anteile in der Verteilung außerordentlich stark beeinflußt. Die experimentellen Ergebnisse werden mit Aussagen der vonFerry erweiterten Theorie vonRouse verglichen. Es ergeben sich Diskrepanzen zwischen Theorie und Experiment, insbesondere was den Einfluß der Molekulargewichtsverteilung auf das viskoelastische Verhalten betrifft.

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Summary In order to investigate the influence of the molecular weight and the molecular weight distribution on the linear viscoelastic behaviour of high polymer melts, the dynamic shear modulus of two series of polyisobutylenes with different molecular weights or distributions respectively was measured in a wide frequency and temperature range. With increasing molecular weight the terminal zone of the two moduli is shifted to lower frequencies. The total shape of the modulus curves is influenced by the molecular weight distribution.At low frequencies the viscoelastic behaviour is determined by two quantities, i.e. the zero shear viscosity ₀ and the steady-state compliance J_e ⁰. ₀ is proportional to M^3,8 and depends only little on the distribution. J_e ⁰, however, is independent of the molecular weight forM > about 10⁵, but is strongly influenced by small high molecular components in the distribution. The experimental results are compared with statements of theRouse theory extended byFerry. There are some discrepancies between theory and experiment, mainly with regard to the influence of the molecular weight distribution on the viscoelastic behaviour.

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Herrn Professor Dr.Walter Franke zum 65. Geburtstag gewidmet.

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Ich danke HerrnDoll und HerrnStephan für ihre Hilfe bei den Messungen.     

Supramolecular structures of coronene and alkane acids at the Au(111)-solution interface: a scanning tunneling microscopy study

Scanning tunneling microscopy (STM) is utilized to study the solution-solid interface formed between Au(111) and solutions of coronene in hexanoic, heptanoic, and octanoic acids. In all three cases adsorbed coronene is observed and lays flat on the metal surface. Heptanoic and hexanoic acid solutions produce a hexagonal symmetry monolayer. For the heptanoic and hexanoic cases, dipole-image dipole interactions and H bonding stabilize a surface structure in which 12 acid molecules surround each coronene and produce a coronene spacing of 1.45 nm. In the case of octanoic acid as solvent, the incorporation of the solvent into the monolayer is not as strongly favored. The coronene spacing can range from close-packed (1.2 nm) with no solvent presumed present in the monolayer, to 1.50 nm with up to 12 solvent molecules surrounding each coronene. The close-packed regions have hexagonal symmetry, as do those with the largest (1.5 nm) spacing. Heptanoic acid solutions give the clearest STM images and are associated with the most stable two-component monolayer. The present paper demonstrates that non-covalent interactions at the solution-metal interface can lead to complex multicomponent monolayer structures.