Annulated Azuleno[2,1,8-ija]azulenes: Synthesis and Properties

Non-alternant non-benzenoid hydrocarbons exhibit very different optical and electronic properties than their well-studied benzenoid analogues. However, preparing such structures with extended conjugation length, remains challenging. Herein, we report the synthesis and properties of azuleno[2,1,8-ija]azulene derivatives using a two-step sequence involving a four-fold aldol condensation between aromatic dialdehydes and readily available tetrahydropentalene-2,5-(1H,3H)-dione. Molecules with band gap values ranging from 1.69 to 2.14 eV and molar extinction coefficients (ϵ) of nearly 3×10⁵ M⁻¹ cm⁻¹ have been prepared. These annulene-like structures exhibit significant diatropic ring currents (aromatic), as supported by ¹H NMR spectroscopy and DFT calculations. Field-effect transistors (OFETs) using azuleno[2,1,8-ija]azulene derivatives as semiconductors exhibit charge mobility values of up to 0.05 cm² V⁻¹ s⁻¹.     

Estimation of the survival probabilities by adjusting a Cox model to the tail

Within the framework of a survival analysis model with censored life time data and an explanatory covariate, our goal is to predict the survival probability beyond the largest observed time. A Cox model with a constant underlying hazard function is proposed to adjust the tail of the life time distribution. Under some regularity conditions, we prove that the parameter estimators are convergent.     

Geodesics in large planar maps and in the Brownian map

We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we characterize the set S of all points that are connected to the root by more than one geodesic. The set S is dense in the Brownian map and homeomorphic to a non-compact real tree. Furthermore, for every x in S, the number of distinct geodesics from x to the root is equal to the number of connected components of S{x}. In particular, points of the Brownian map can be connected to the root by at most three distinct geodesics. Our results have applications to the behavior of geodesics in large planar maps.     

Barium-Catalysed Dehydrocoupling of Hydrosilanes and Borinic Acids: A Mechanistic Insight

Two very rare cases of barium boryloxides, the homoleptic [Ba(OB{CH(SiMe₃)₂}₂)₂⋅C₇H₈] and the heteroleptic [{LO^NO4}BaOB{CH(SiMe₃)₂}₂] stabilised by the multidentate aminoetherphenolate {LO^NO4}⁻, are presented, and their structural properties are discussed. The electron-deficient [Ba(OB{CH(SiMe₃)₂}₂)₂⋅C₇H₈] shows, in particular, resilient η⁶-coordination of the toluene molecule. Together with its amido parents [Ba{N(SiMe₃)₂}₂⋅thf₂] and [Ba{N(SiMe₃)₂}₂]₂, this complex catalyses the fast and chemoselective dehydrocoupling of borinic acids R₂BOH and hydrosilanes HSiR′₃, yielding borasiloxanes R₂BOSiR′₃ in a controlled fashion. The assessment of substrate scope indicates that, for now, the reaction is limited to bulky borinic acids. Kinetic analysis shows that the rate-limiting step of the catalytic manifold traverses a dinuclear transition state. A detailed mechanistic scenario is proposed on the basis of DFT computations, the results of which are fully consistent with experimental data. It consists of a stepwise process with rate-determining nucleophilic attack of a metal-bound O-atom onto the incoming hydrosilane, involving throughout dinuclear catalytically active species.     

Thiourea-Catalyzed C−F Bond Activation: Amination of Benzylic Fluorides

We describe the first thiourea-catalyzed C−F bond activation. The use of a thiourea catalyst and Ti(OiPr)₄ as a fluoride scavenger allows the amination of benzylic fluorides to proceed in moderate to excellent yields. Preliminary results with S- and O-based nucleophiles are also presented. DFT calculations reveal the importance of hydrogen bonds between the catalyst and the fluorine atom of the substrate to lower the activation energy during the transition state.     

Molecular Bottle Brushes with Positioned Selenols: Extending the Toolbox of Oxidative Single Polymer Chain Folding with Conformation Analysis by Atomic Force Microscopy

A synthesis route to controlled and dynamic single polymer chain folding is reported. Sequence-controlled macromolecules containing precisely located selenol moieties within a polymer chain are synthesized. Oxidation of selenol functionalities lead to diselenide bridges and induces controlled intramolecular crosslinking to generate single chain collapse. The cyclization process is successfully characterized by SEC as well as by ¹H NMR and 2D HSQC NMR spectroscopies. In order to gain insight on the molecular level to reveal the degree of structural control, the folded polymers are transformed into folded molecular brushes that are known to be visualizable as single molecule structures by AFM. The “grafting onto” approach is performed by using triazolinedione−diene reaction to graft the side chain polymers. A series of folded molecular brushes as well as the corresponding linear controls are synthesized. AFM visualization is proving the cyclization of the folded backbone by showing globular objects, where non-folded brushes show typical worm-like structures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 154–162     

Note sur la continuité de la projection dans les facteurs de Host–Kra

B. Host and B. Kra (2005) [5] have introduced the characteristic factors for studying “cubic ergodic means”. These factors allow one to resolve, in particular, multiple recurrence problems introduced by H. Furstenberg (1977) [4]. We show here that the continuity of the projection of the system in its characteristic factors characterises cubic means.