Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

Micro-composites based on polylactic acid with kaolinite or rice husk particles and their performance on water vapor permeability

In this work, the effect of addition of kaolinite and rice husk microparticles on the water vapor permeability of polylactic acid (PLA) was evaluated. The PLA-composites materials were characterized by X-ray diffraction, differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and optical microscopy. For the composite preparation, an experimental design was established using two factors: additive type and concentration. When evaluating the water vapor permeability of the composites, it was found that the incorporation of kaolinite at 1% and 5% reduced the permeability coefficient of PLA. Furthermore, the inclusion of 5% kaolinite showed an increase on the tensile strength of the material. By contrast, the addition of rice husk produced an increase on water vapor permeability of the material and a decrease of both the tensile strength and ductility (percent of elongation at fracture). The higher dispersion and more regular morphology of the kaolinite particles could explain the enhancement of the gas barrier. A similar thermal behavior was observed for both PLA and composite materials, confirming that no damage of these properties was caused with the incorporation of the filler particles.     

Butylated hydroxytoluene enediyne: access to diradical and electrophilic quinone methide intermediates

A theoretical study was carried out on the unimolecular reaction of an enediyne with a fused butylated hydroxytoluene to internally scavenge the p‐benzyne diradical sites formed after the Bergman cyclization. The calculations revealed that the conversion of the p‐benzyne diradical (2‐tert‐butyl‐4‐methyl‐5,8‐didehydro‐1‐naphthalenol) to p‐quinone methide is favored over the conversion to a phenoxy/benzene diradical 4 in an approximate 95:5 ratio. Based on this model, the Bergman cyclization leads in a bifunctional manner to intermediates for competing reactivity with intermolecular H‐atom abstraction. Copyright © 2015 John Wiley & Sons, Ltd.     

An unexpected formation of pyrazolopyrimidines during the attempted to obtain 5-substituted tetrazoles from carbonitriles

In this Letter, we described the synthesis of new 5-(5-amino-1-aryl-1H-pyrazole-4-yl)-1H-tetrazoles 2a–c from 5-amino-1-aryl-1H-pyrazole-4-carbonitriles 1a–c as well as the unexpected 1H-pyrazolo[3,4-d]pyrimidine derivatives 6a–c from 5-amino-1-aryl-3-methyl-1H-pyrazole-4-carbonitriles 4a–c, instead of 5-(5-amino-1-aryl-3-methyl-1H-pyrazole-4-yl)-1H-tetrazoles 5a–c as desired. In an attempt to obtain these tetrazole derivatives containing the methyl group at C3-position in the pyrazole ring, the amino group in 5-amino-1-(4-methoxyphenyl)-3-methyl-1H-pyrazole-4-carbonitrile 4c was protected by the reaction with sodium hydride and di-tert-butyl-dicarbonate (Boc). The tetrazole derivative 5c was synthesized from the protected compound 7c using analogue methodology to obtain 2a–c and 6a–c.     

Phase modulation and ellipticity of the light transmitted through a smectic C* layer with short helix pitch

A chiral ferroelectric smectic C* liquid crystal (FLC) with the helix pitch p ₀?=?330 nm was developed to avoid any scattering of visible light when the helix is not unwound over a certain limit. Planar cells with different FLC layer thickness (16 and 44 μm) have been assembled with helix axis parallel to the glass plates and aligned along the rubbing direction. The ellipticity of the light passing through the cells vs. the electric field was investigated, and a method for evaluating the electrically controlled birefringence via ellipticity measurements has been established. We have found that the FLC cell is an optical retardation layer driven by the electric field, the effective birefringence being proportional to the square electric field. The physical origin of the electrically controlled phase shift of the light passing through the FLC layer has been analysed.     

Hydroformylation and hydroalkylcarbonylation of 3,4-dihydro[2H]pyran catalysed by Co2(CO)8 under syngas conditions

In the cobalt-catalysed hydroformylation of 3,4-dihydro[2H]pyran, the influence of different reaction parameters such as time, pressure, triphenylphosphine addition, catalyst and substrate concentration has been investigated. 2-formyl-tetrahydropyran, tetrahydropyran and a hydroalkylcarbonylation product were the main reaction products. The selectivity towards 2-formyl-tetrahydropyran formation is favoured at constant catalyst and substrate concentration. The coordination of the pyran’s oxygen to the cobalt atom seems to be an important intermediate for the formation of 2-formyl-tetrahydropyran. Different substrate or catalyst concentrations promote the formation of other reduced products. The addition of triphenylphosphine to the catalyst leads to a less active species, which decreases the yield and promotes the hydroalkylcarbonylation reaction.     

Supermolecular Columnar Liquid‐Crystalline Phosphorus Dendrimers Decorated with Sulfonamide Derivatives

A series of supermolecular liquid crystals has been synthesized by combining phosphorus dendrimers of the zero, first, and fourth generations with sulfonamide derivatives, thus generating dendromesogens bearing 6, 12, and 96 mesogenic units on their surfaces. The relevant reactions could be monitored by ¹H, ¹⁹F, and ³¹P{¹H} NMR spectroscopies. The thermal and mesomorphic properties of the products have been studied by optical microscopy, differential scanning calorimetry, and X‐ray diffraction. All of the new macromolecules prepared in this work have been found to show mesomorphic properties over a wide temperature range; moreover, for all of the compounds, the columnar mesophases observed were maintained or vitrified at room temperature. On increasing the generation of these dendromesogens, mesophases appear at lower temperatures and remain stable over a wider temperature interval. In all cases, on the basis of X‐ray analysis, a cylindrical symmetry of the molecules can be proposed to promote the supramolecular columnar arrangement observed in the mesophases. In this type of model, the height of the dendrimer clearly increases with increasing dendrimer generation, whereas its cross‐ sectional area increases only slightly, probably due to compression of the highly hyperbranched structures as a consequence of their progressive steric constraints. The mesomorphic arrangement is governed by the peripheral sulfonamide units.     

Hierarchical Structure of NiMo Hydrodesulfurization Catalysts Determined by Ptychographic X‐Ray Computed Tomography

Hydrodesulphurization, the removal of sulphur from crude oils, is an essential catalytic process in the petroleum industry safeguarding the production of clean hydrocarbons. Sulphur removal is critical for the functionality of downstream processes and vital to the elimination of environmental pollutants. The effectiveness of such an endeavour is among other factors determined by the structural arrangement of the heterogeneous catalyst. Namely, the accessibility of the catalytically active molybdenum disulphide (MoS₂) slabs located on the surfaces of a porous alumina carrier. Here, we examined a series of pristine sulfided Mo and NiMo hydrodesulphurization catalysts of increasing metal loading prepared on commercial alumina carriers using ptychographic X‐ray computed nanotomography. Structural analysis revealed a build consisting of two interwoven support matrix elements differing in nanoporosity. With increasing metal loading, approaching that of industrial catalysts, these matrix elements exhibit a progressively dissimilar MoS₂ surface coverage as well as MoS₂ cluster formation at the matrix element boundaries. This is suggestive of metal deposition limitations and/ or catalyst activation and following prohibitive of optimal catalytic utilization. These results will allow for diffusivity calculations, a better rationale of current generation catalyst performance as well as a better distribution of the active phase in next‐generation hydrodesulphurization catalysts.