Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Study of spatial inhomogeneity in inverted all‐polymer solar cells: Effect of solvent and annealing

The efficiency optimization of bulk heterojunction solar cells requires the control of the local active materials arrangement in order to obtain the best compromise between efficient charge generation and charge collection. Here, we investigate the large scale (10–100 μm) inhomogeneity of the photoluminescence (PL) and the external quantum efficiency (EQE) in inverted all‐polymer solar cells (APSC) with regioregular poly(3‐hexylthiophene) (P3HT):poly(9,9‐dioctylfluorene‐co‐benzothiadiazole) (F8BT) active blends. The morphology and the local active polymer mixing are changed by depositing the active layer from four different solvents and by thermal annealing. The simultaneous PL and EQE mapping allowed us to inspect the effects of local irregularities of active layer thickness, polymer mixing, polymer aggregation on the charge generation and collection efficiencies. In particular, we show that the increase of the solvent boiling point affects the EQE non‐uniformity due to thickness fluctuations, the density non‐uniformity of rrP3HT aggregate phase, and the blend components clustering. The thermal annealing leads to a general improvement of EQE and to an F8BT clustering in all the samples with locally decrease of the EQE. We estimate that the film uniformity optimization can lead to a total EQE improvement between 2.7 and 6.3 times. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 804–813     

Highly Conjugated π-Systems Arising from Cannibalistic Hexadehydro-Diels–Alder Couplings: Cleavage of C−C Single and Triple Bonds

We have investigated the cannibalistic self-trapping reaction of an ortho-benzyne derivative generated from 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne in an HDDA reaction. Without adding any specific trapping agent, the highly reactive benzyne is trapped by another bisdiyne molecule in at least three different modes. We have isolated and characterized the resulting products and performed high-level calculations concerning the reaction mechanism. During the cannibalistic self-trapping process, either a C≡C triple bond or an sp–sp³ C−C single bond is cleaved. Up to seven rings and nine C−C bonds are formed starting from two 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne molecules. Our experiments and calculations provide considerable insight into the variety of reaction pathways which the ortho-benzyne derivative, generated from a bisdiyne, can take when reacting with another bisdiyne molecule.     

Nonclassical Recrystallization

Applications in the fields of materials science and nanotechnology increasingly demand monodisperse nanoparticles in size and shape. Up to now, no general purification procedure exists to thoroughly narrow the size and shape distributions of nanoparticles. Here, we show by analytical ultracentrifugation (AUC) as an absolute and quantitative high-resolution method that multiple recrystallizations of nanocrystals to mesocrystals is a very efficient tool to generate nanocrystals with an excellent and so-far unsurpassed size-distribution (PDI_c=1.0001) and shape. Similar to the crystallization of molecular building blocks, nonclassical recrystallization removes “colloidal” impurities (i.e., nanoparticles, which are different in shape and size from the majority) by assembling them into a mesocrystal. In the case of nanocrystals, this assembly can be size- and shape-selective, since mesocrystals show both long-range packing ordering and preferable crystallographic orientation of nanocrystals. Besides the generation of highly monodisperse nanoparticles, these findings provide highly relevant insights into the crystallization of mesocrystals.     

Photochemical Bromination of 2,5-Dimethylbenzoic Acid as Key Step of an Improved Alkyne-Functionalized Blue Box Synthesis**

Cyclobis(paraquat-p-phenylene), also known as “blue box”, is a highly electron-deficient macrocycle, widely used as a molecular receptor for small electron-rich molecules. Inserting a reactive functional group onto the molecular structure of this cyclophane is paramount for its inclusion into complex architectures. To this aim, including an alkyne moiety would be ideal, because it can participate in click reactions. However, the synthesis of such alkyne-functionalized cyclophane suffers from several drawbacks: the use of toxic and expensive CCl₄, the need for high-pressure reactors, and overall low yield. We have revised the existing synthesis of this cyclophane derivative bearing an alkyne moiety, to overcome all these limitations. In particular, photochemical radical bromination is adopted to obtain a sensitive intermediate. We demonstrated that the synthesized host molecule can be functionalized via click reactions and take part in radical-radical interactions. Our work makes a key functionalized paraquat macrocycle more accessible, facilitating the development of novel redox-responsive systems.     

Biology‐Oriented Synthesis of a Withanolide‐Inspired Compound Collection Reveals Novel Modulators of Hedgehog Signaling

Biology‐oriented synthesis employs the structural information encoded in complex natural products to guide the synthesis of compound collections enriched in bioactivity. The trans‐hydrindane dehydro‐δ‐lactone motif defines the characteristic scaffold of the steroid‐like withanolides, a plant‐derived natural product class with a diverse pattern of bioactivity. A withanolide‐inspired compound collection was synthesized by making use of three key intermediates that contain this characteristic framework derivatized with different reactive functional groups. Biological evaluation of the compound collection in cell‐based assays that monitored biological signal‐transduction processes revealed a novel class of Hedgehog signaling inhibitors that target the protein Smoothened.     

Enantiomeric separation of 1,3‐dimethylamylamine by capillary electrophoresis with indirect UV detection using a dual‐selector system

The CE method employing an indirect UV detection for the enantioseparation of 1,3‐dimethylamylamine (DMAA), widely used in various preworkout and dietary supplements labeled as a constituent of geranium extract has been developed. The dual‐selector system consisting of negatively charged sulfated α‐CD (1.1% w/v) and sulfated β‐CD (0.2% w/v) in 5 mM phosphate/Tris buffer (pH 3.0) containing the addition of 10 mM benzyltriethylammonium chloride (BTEAC) as the chromophoric additive was used for the enantiomeric separation of DMAA stereoisomers with the LODs in the range of 7.82–9.24 μg/mL. The method was partly validated and applied for the determination of the stereoisomeric composition of DMAA in commercial dietary supplements to verify the potential natural origin of DMAA.     

Di-tert-butyldiphosphatetrahedrane as a Source of 1,2-Diphosphacyclobutadiene Ligands

Reactions of di-tert-butyldiphosphatetrahedrane ( 1 ) with cycloocta-1,5-diene- or anthracene-stabilised metalate anions of iron and cobalt consistently afford complexes of the rarely encountered 1,2-diphosphacyclobutadiene ligand, which have previously been very challenging synthetic targets. The subsequent reactivity of 1,2-diphosphacyclobutadiene cobaltates toward various electrophiles has also been investigated and is compared to reactions of related 1,3-diphosphacyclobutadiene complexes. The results highlight the distinct reactivity of such isomeric species, showing that the 1,2-isomers can act as precursors for previously unknown triphospholium ligands. The electronic structures of the new complexes were investigated by several methods, including NMR, EPR and Mößbauer spectroscopies as well as quantum chemical calculations.     

On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet

By formally invoking the Wiener–Hopf method, we explicitly solve a one‐dimensional, singular integral equation for the excitation of a slowly decaying electromagnetic wave, called surface plasmon‐polariton (SPP), of small wavelength on a semiinfinite, flat conducting sheet irradiated by a plane wave in two spatial dimensions. This setting is germane to wave diffraction by edges of large sheets of single‐layer graphene. Our analytical approach includes (i) formulation of a functional equation in the Fourier domain; (ii) evaluation of a split function, which is expressed by a contour integral and is a key ingredient of the Wiener–Hopf factorization; and (iii) extraction of the SPP as a simple‐pole residue of a Fourier integral. Our analytical solution is in good agreement with a finite‐element numerical computation.     

Generalised continuation by means of right limits

Several theories have been proposed to generalise the concept of analytic continuation to holomorphic functions of the disc for which the circle is a natural boundary. Elaborating on Breuer-Simon’s work on right limits of power series, Baladi-Marmi-Sauzin recently introduced the notion of renascent right limit and rrl-continuation. We discuss a few examples and consider particularly the classical example of Poincaré simple pole series in this light. These functions are represented in the disc as series of infinitely many simple poles located on the circle; they appear, for instance, in small divisor problems in dynamics. We prove that any such function admits a unique rrl-continuation, which coincides with the function obtained outside the disc by summing the simple pole expansion. We also discuss the relation with monogenic regularity in the sense of Borel.