Shedding Light on the Interactions of Hydrocarbon Ester Substituents upon Formation of Dimeric Titanium(IV) Triscatecholates in DMSO Solution

The dissociation of hierarchically formed dimeric triple lithium bridged triscatecholate titanium(IV) helicates with hydrocarbyl esters as side groups is systematically investigated in DMSO. Primary alkyl, alkenyl, alkynyl as well as benzyl esters are studied in order to minimize steric effects close to the helicate core. The ¹H NMR dimerization constants for the monomer–dimer equilibrium show some solvent dependent influence of the side chains on the dimer stability. In the dimer, the ability of the hydrocarbyl ester groups to aggregate minimizes their contacts with the solvent molecules. Due to this, most solvophobic alkyl groups show the highest dimerization tendency followed by alkenyls, alkynyls and finally benzyls. Furthermore, trends within the different groups of compounds can be observed. For example, the dimer is destabilized by internal double or triple bonds due to π–π repulsion. A strong indication for solvent supported London dispersion interaction between the ester side groups is found by observation of an even/odd alternation of dimerization constants within the series of n-alkyls, n-Ω-alkenyls or n-Ω-alkynyls. This corresponds to the interaction of the parent hydrocarbons, as documented by an even/odd melting point alternation.     

Characterizing Polyoxovanadate-Alkoxide Clusters Using Vanadium K-Edge X-Ray Absorption Spectroscopy

A number of technologies would benefit from developing inorganic compounds and materials with specific electronic and magnetic exchange properties. Unfortunately, designing compounds with these properties is difficult because metal⋅⋅⋅metal coupling schemes are hard to predict and control. Fully characterizing communication between metals in existing compounds that exhibit interesting properties could provide valuable insight and advance those predictive capabilities. One such class of molecules are the series of Lindqvist iron-functionalized and hexavanadium polyoxovanadate-alkoxide clusters, which we characterized here using V K-edge X-ray absorption spectroscopy. Substantial changes in the pre-edge peak intensities were observed that tracked with the V 3d-electron count. The data also suggested substantial delocalization between the vanadium cations. Meanwhile, the Fe^III cations were electronically isolated from the polyoxovanadate core.     

Synthesis and Characterisation of Hierarchically Structured Titanium Silicalite-1 Zeolites with Large Intracrystalline Macropores

The successful synthesis of hierarchically structured titanium silicalite-1 (TS-1) with large intracrystalline macropores by steam-assisted crystallisation of mesoporous silica particles is reported. The macropore topology was imaged in 3D by using electron tomography and synchrotron radiation-based ptychographic X-ray computed tomography, revealing interconnected macropores within the crystals accounting for about 30 % of the particle volume. The study of the macropore formation mechanism revealed that the mesoporous silica particles act as a sacrificial macropore template during the synthesis. Silicon-to-titanium ratio of the macroporous TS-1 samples was successfully tuned from 100 to 44. The hierarchically structured TS-1 exhibited high activity in the liquid phase epoxidation of 2-octene with hydrogen peroxide. The hierarchically structured TS-1 surpassed a conventional nano-sized TS-1 sample in terms of alkene conversion and showed comparable selectivity to the epoxide. The flexible synthesis route described here can be used to prepare hierarchical zeolites with improved mass transport properties for other selective oxidation reactions.     

The Poincaré–Bendixson theorem for a class of delay equations with state-dependent delay and monotonic feedback

We consider the real-valued differential equation

$x^{\prime }(t)=f(x(t),x(t?d(x_t)))$

with state-dependent delay, where f is strictly monotonic in its second argument. We describe a class of such equations for which a version of the Poincaré–Bendixson theorem holds.     

p-Substituted Tris(2-pyridylmethyl)amines as Ligands for Highly Active ATRP Catalysts: Facile Synthesis and Characterization

A facile and efficient two-step synthesis of p-substituted tris(2-pyridylmethyl)amine (TPMA) ligands to form Cu complexes with the highest activity to date in atom transfer radical polymerization (ATRP) is presented. In the divergent synthesis, p-Cl substituents in tris(4-chloro-2-pyridylmethyl)amine (TPMA^3Cl) were replaced in one step and high yield by electron-donating cyclic amines (pyrrolidine (TPMA^PYR), piperidine (TPMA^PIP), and morpholine (TPMA^MOR)) by nucleophilic aromatic substitution. The [Cu^II(TPMA^NR2)Br]⁺ complexes exhibited larger energy gaps between frontier molecular orbitals and >0.2 V more negative reduction potentials than [Cu^II(TPMA)Br]⁺, indicating >3 orders of magnitude higher ATRP activity. [Cu^I(TPMA^PYR)]⁺ exhibited the highest reported activity for Br-capped acrylate chain ends in DMF, and moderate activity toward C−F bonds at room temperature. ATRP of n-butyl acrylate using only 10–25 part per million loadings of [Cu^II(TPMA^NR2)Br]⁺ exhibited excellent control.     

Strain-Enhanced Metallic Intermixing in Shape-Controlled Multilayered Core–Shell Nanostructures: Toward Shaped Intermetallics

Controlling the surface composition of shaped bimetallic nanoparticles could offer precise tunability of geometric and electronic surface structure for new nanocatalysts. To achieve this goal, a platform for studying the intermixing process in a shaped nanoparticle was designed, using multilayered Pd-Ni-Pt core–shell nanocubes as precursors. Under mild conditions, the intermixing between Ni and Pt could be tuned by changing layer thickness and number, triggering intermixing while preserving nanoparticle shape. Intermixing of the two metals is monitored using transmission electron microscopy. The surface structure evolution is characterized using electrochemical methanol oxidation. DFT calculations suggest that the low-temperature mixing is enhanced by shorter diffusion lengths and strain introduced by the layered structure. The platform and insights presented are an advance toward the realization of shape-controlled multimetallic nanoparticles tailored to each potential application.     

A note on smooth toral reductions of spheres

In this paper we show that there exist mod 2 obstructions to the smoothness of 3-Sasakian reductions of spheres. Specifically, ifS is a smooth 3-Sasakian manifold obtained by reduction of the 3-Sasakian sphereS ⁴ⁿ⁻¹ by a torus, and if the second Betti numberb ₂(S)≥2 then dimS=7, 11, 15, whereas, ifb ₂ (S)≥5 then dimS=7. We also show that the above bounds are sharp, in that we construct explicit examples of 3-Sasakian manifolds in the cases not excluded by these bounds. During the preparation of this work the authors were partially supported by an NSF grant. This article was processed by the author using the L^AT_EX style file from Springer-Verlag.     

The trace anomaly and low energy phenomenological implications of wormholes

In Coleman's wormhole scenario it is the trace anomaly on S₄ that controls the behavior of fundamental coupling constants, particle masses, mixing angles, etc. We indicate how low energy phenomenology may be derivable from very general properties of wormhole physics and calculable β-functions, etc.     

A general method for the synthesis of 1-substituted (or unsubstituted)-4-carbomethoxy-2-imidazolin-5-ones

A general method for the synthesis of the title compounds by employing the reagent methyl $\text{N}$-(dicarbomethoxymethyl)methanimidate is described. The preparation, properties and reactions of the reagent are also reported.