Dependence of nonlinear elasticity on filler size in composite polymer systems

Nanosized filler particles enhance the mechanical properties of polymer composites in a size-dependent fashion. This is puzzling, because classical elasticity is inherently scale-free, and models for the elasticity of composite systems never predict a filler-size dependence. Here, we study the industrially important system of silica-filled rubbers, together with a well-characterized model-filled crosslinked gel and show that at high filler content both the linear and nonlinear elastic properties of these systems exhibit a unique scaling proportional to the cube of the volume fraction divided by the particle size. This remarkable behavior makes it possible to predict the full mechanical response of particle-filled rubbers for small but finite deformations based solely on the rheology of the matrix and the size and modulus of the filler particles.     

Expeditious synthesis of TADDOL-derived phosphoramidite and phosphonite ligands

A simple and reliable protocol for the synthesis of TADDOL-derived monodentate ligands is reported. The reaction of the requisite TADDOL with PCl₃ is immediately followed by the treatment of the crude intermediate with both nitrogen and carbon nucleophiles. Several previously unknown or difficult-to-make phosphoramidite and phosphonite ligands L1–L3 and L4–L9 were accessed using this novel procedure.     

Nuclear resonance vibrational spectroscopy reveals the FeS cluster composition and active site vibrational properties of an O2-tolerant NAD+-reducing [NiFe] hydrogenase

Hydrogenases are complex metalloenzymes that catalyze the reversible splitting of molecular hydrogen into protons and electrons essentially without overpotential. The NAD⁺-reducing soluble hydrogenase (SH) from Ralstonia eutropha is capable of H₂ conversion even in the presence of usually toxic dioxygen. The molecular details of the underlying reactions are largely unknown, mainly because of limited knowledge of the structure and function of the various metal cofactors present in the enzyme. Here, all iron-containing cofactors of the SH were investigated by ⁵⁷Fe specific nuclear resonance vibrational spectroscopy (NRVS). Our data provide experimental evidence for one [2Fe2S] center and four [4Fe4S] clusters, which is consistent with the amino acid sequence composition. Only the [2Fe2S] cluster and one of the four [4Fe4S] clusters were reduced upon incubation of the SH with NADH. This finding explains the discrepancy between the large number of FeS clusters and the small amount of FeS cluster-related signals as detected by electron paramagnetic resonance spectroscopic analysis of several NAD⁺-reducing hydrogenases. For the first time, Fe–CO and Fe–CN modes derived from the [NiFe] active site could be distinguished by NRVS through selective ¹³C labeling of the CO ligand. This strategy also revealed the molecular coordinates that dominate the individual Fe–CO modes. The present approach explores the complex vibrational signature of the Fe–S clusters and the hydrogenase active site, thereby showing that NRVS represents a powerful tool for the elucidation of complex biocatalysts containing multiple cofactors.     

Resolvent estimates and smoothing for homogeneous partial differential operators on graded Lie groups

By using commutator methods, we show uniform resolvent estimates and obtain globally smooth operators for self-adjoint injective homogeneous operators H on graded groups, including Rockland operators, sublaplacians, and many others. Left or right invariance is not required. Typically the globally smooth operator has the form T = V|H|^1∕2, where V only depends on the homogeneous structure of the group through Sobolev spaces, the homogeneous dimension and the minimal and maximal dilation weights. For stratified groups improvements are obtained, by using a Hardy-type inequality. Some of the results involve refined estimates in terms of real interpolation spaces and are valid in an abstract setting. Even for the commutative group ?^N some new classes of partial differential operators are treated.     

On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization

The aim of this paper is to address new approaches, in separate ways, to necessary and, respectively, sufficient optimality conditions in constrained vector optimization. In this respect, for the necessary optimality conditions that we derive, we use a kind of vectorial penalization technique, while for the sufficient optimality conditions we make use of an appropriate scalarization method. In both cases, the approaches couple a basic technique (of penalization or scalarization, respectively) with several results in variational analysis and optimization obtained by the authors in the last years. These combinations allow us to arrive to optimality conditions which are, in terms of assumptions made, new.     

NdHO, a novel oxyhydride

A new metal oxyhydride; neodymium oxyhydride, NdHO, has been synthesized from a reactant mixture of metal hydride (CaH₂ or NdH₃) and neodymium oxide (Nd₂O₃). The unit cell dimensions decrease smoothly in the series from LaHO, CeHO, PrHO to NdHO, in line with the lanthanide contraction. The crystal structure of NdHO is described on the basis of Rietveld refinement on neutron powder diffraction data:

Space group: P4/nmm (no. 129, D_4h⁷).

Axis lengths: a=7.8480(5) Å, c=5.5601(8) Å.

Volume: V=342.46(6) Å³.

The tetragonal structure is derived from the fluorite structure, showing complete ordering of hydride and oxide ions over the anion sublatttice. The formation of NdHO was further substantiated by Raman spectroscopy.     

An axially chiral, electron-deficient borane: synthesis, coordination chemistry, Lewis acidity, and reactivity

An axially chiral dihydroborepine with a binaphthyl backbone and a C(6)F(5) substituent at the boron atom was prepared by transmetalation from the corresponding tin precursor. This novel motif was structurally characterized by X-ray diffraction analysis as its THF and its PhCN Lewis acid/base complex. (1)H NMR measurements at variable temperatures of the former adduct revealed a remarkable dynamic behavior in solution. Several more Lewis pairs with oxygen, nitrogen, carbon, and phosphorus σ-donors were synthesized and analyzed by multinuclear NMR spectroscopy. The determination of the borane's Lewis acidity with the Gutmann-Beckett method attests its substantial Lewis acidity [85% with Et(3) PO as well as 74% with Ph(3) PO relative to the parent B(C(6)F(5))(3)]. Representative examples of Si-H bond activation (carbonyl reduction and dehydrogenative Si-O coupling) are included, demonstrating the chemical stability and the synthetic potential of the new chiral boron-based Lewis acid.     

Ruled quartic surfaces,models and classification

New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ‘modern’ treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. The string models of Series XIII of some ruled quartic surfaces (manufactured by L. Brill and by M. Schilling) are based on a result of Rohn concerning curves in \mathbbP¹×\mathbbP¹{\mathbb{P}^1\times \mathbb{P}^1} of bi-degree (2, 2). This is given here a conceptional proof.