Molecular understanding of alumina supported single-site catalysts by a combination of experiment and theory

The nature and structure of grafted organometallic complexes on gamma-alumina are studied from a combination of experimental data (mass balance analysis, IR, NMR) and density functional theory calculations. The chemisorptive interactions of two complexes are analyzed and compared. The reaction of [Zr(CH2tBu)4] with alumina dehydroxylated at 500 degrees C gives {[(AlsO)2Zr(CH2tBu)]+[(tBuCH2)(Als)]-}, a bisgrafted cationic complex as major surface species. The DFT calculations show that the reaction with surface hydroxyls is very exothermic and that alkyl transfer on Al atoms is favored. In contrast, [W(CtBu)(CH2tBu)3] reacts with an alumina treated under identical conditions to give selectively a monografted neutral surface complex, [(AlsO)W(CtBu)(CH2tBu)2]. This was inferred by the evolution of 1 equiv of tBuCH3 per grafted W and the presence of remaining hydroxyls. The calculations show that the reaction of [W(CtBu)(CH2tBu)3] with surface hydroxyls is in fact less exothermic and has a considerably higher activation barrier than the one of the Zr complex. Additionally, the transfer of an alkyl ligand onto an adjacent Al center is disfavored, and hence cationic species are not formed. Some ligands of this monoaluminoxy surface complex interact with remaining surface hydroxyls, which explains the complexity of the experimental NMR and IR data.     

Minimal Lipschitz Extensions to Differentiable Functions Defined on a Hilbert Space

We generalize the Lipschitz constant to fields of affine jets and prove that such a field extends to a field of total domain \mathbbRⁿ{\mathbb{R}^n} with the same constant. This result may be seen as the analog for fields of the minimal Kirszbraun’s extension theorem for Lipschitz functions and, therefore, establishes a link between Kirszbraun’s theorem and Whitney’s theorem. In fact this result holds not only in Euclidean \mathbbRⁿ{\mathbb{R}^n} but also in general (separable or not) Hilbert space. We apply the result to the functional minimal Lipschitz differentiable extension problem in Euclidean spaces and we show that no Brudnyi–Shvartsman-type theorem holds for this last problem. We conclude with a first approach of the absolutely minimal Lipschitz extension problem in the differentiable case which was originally studied by Aronsson in the continuous case.     

Orthogonal Helmholtz decomposition in arbitrary dimension using divergence-free and curl-free wavelets

We present tensor-product divergence-free and curl-free wavelets, and define associated projectors. These projectors enable the construction of an iterative algorithm to compute the Helmholtz decomposition of any vector field, in wavelet domain. This decomposition is localized in space, in contrast to the Helmholtz decomposition calculated by Fourier transform. Then we prove the convergence of the algorithm in dimension two for any kind of wavelets, and in larger dimension for the particular case of Shannon wavelets. We also present a modification of the algorithm by using quasi-isotropic divergence-free and curl-free wavelets. Finally, numerical tests show the validity of this approach for a large class of wavelets.     

Polaron dynamics in thin polythiophene films studied with time-resolved photoemission

Femtosecond time-resolved two-photon photoemission spectroscopy is employed to study the dynamics of an excited state in a thin regioregular poly(3-hexylthiophene) (RR-P3HT) film deposited on a conducting polymer poly(3,4-ethylene-dioxythiophene): poly-(styrenesulfonate) (PEDT:PSS) electrode following optical excitation at 2.1 eV. We found that the biexponential decay of this excited state has a fast component (2.6 ps) assigned to bound polaron pairs which recombine quickly or separate to be added to the slow component (7.6 ps). The latter is attributed to polarons generated via charge transfer between adjacent polymer chains.     

Moisture Absorption Effects on the Mechanical Properties of Sandwich Biocomposites with Cork Core and Flax/PLA Face Sheets

The aim of this study was to evaluate the moisture absorption behaviour and its influence on the mechanical properties of newly developed sandwich biocomposites with flax fibre-reinforced poly-lactic acid (PLA) face sheets and soft cork as the core material. Three different types of sandwich biocomposite laminates comprised of different layup configurations, namely, non-woven flax/PLA (Sample A), non-woven flax/PLA and cork as core (Sample B) and non-woven flax/paper backing/PLA, cork as core (Sample C), were fabricated. In order to evaluate the influence of moisture ingress on the mechanical properties, the biocomposites were immersed in seawater for a period of 1200 h. The biocomposites (both dry and water immersed) were then subjected to tensile, flexural and low-velocity falling weight impact tests. It was observed from the experimental results that the moisture uptake significantly influenced the mechanical properties of the biocomposites. The presence of the cork and paper in sample C made it more susceptible to water absorption, reaching a value of 34.33%. The presence of cork in the core also has a considerable effect on the mechanical, as well as energy dissipation, behaviours. The results of sample A exhibited improved mechanical performance in both dry and wet conditions compared to samples B and C. Sample A exhibits 32.6% more tensile strength and 81.4% more flexural strength in dry conditions than that in sample C. The scanning electron microscopy (SEM) and X-ray micro-CT images revealed that the failure modes observed are a combination of matrix cracking, core crushing and face core debonding. The results from this study suggest that flax/PLA sandwich biocomposites can be used in various lightweight applications with improved environmental benefits.     

Mannich-Type Reactions of Alkylzinc Reagents

Mannich-type reactions involving alkylzinc reagents have been developed using different strategies. We show that the addition of these organometallic species to sulfonyl imines occurs upon simple heating and affords Mannich products in moderate to excellent yields (14 examples, 30–99 %). Interestingly, N-alkyl imines were also found to be suitable partners after activation as an acyliminium by acetyl chloride (12 examples, 49–86 %) or, more originally, by TMSCl (14 examples, 26–87 %). These methods proved complementary, leading to the preparation of both N-protected secondary or tertiary amines and N-unprotected secondary amines in good yields, with an increased eco-compatibility, and under simple conditions.