Disorder effects in Mn12–acetate at 83 K

The structure of hexadeca‐μ‐acetato‐tetra­aqua­dodeca‐μ₃‐oxo‐dodecamanganese bis(acetic acid) tetrahydrate, [Mn₁₂O₁₂(CH₃COO)₁₆(H₂O)₄]·2CH₃COOH·4H₂O, known as Mn₁₂–acetate, has been determined at 83 (2) K by X‐ray diffraction methods. The fourfold (S₄) molecular symmetry is disrupted by a strong hydrogen‐bonding interaction with the disordered acetic acid mol­ecule of solvation, which displaces one of the acetate ligands in the cluster. Up to six Mn₁₂ isomers are potentially present in the crystal lattice, which differ in the number and arrangement of hydrogen‐bonded acetic acid mol­ecules. These results considerably improve the structural information available on this molecular nanomagnet, which was first synthesized and characterized by Lis [Acta Cryst. (1980), B 36 , 2042–2046].     

Localization of a multiblock copolymer at a selective interface: scaling predictions and Monte Carlo verification

We investigate the localization of a hydrophobic-polar regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length M on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter chi. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D( parallel) is also derived. We implement a dynamic off-lattice Monte Carlo model to verify these scaling predictions. For chain lengths in a wide range (32相似文献   

Reaction of N,N'-dialkyldithiodianilines with β-ketoesters. A new synthesis of N-alkyl-2-acyl-3-oxo-3,4-dihydro-1,4-benzothiazines

The title compounds 3a-j together with the N-alkylacylketene S,N-acetals 12a-j were obtained by reaction of N,N'-dialkyldithiodianilines with β-ketoesters compounds. A possible reaction pathway is suggested.     

Wavy graphene sheets from electrochemical sewing of corannulene

The presence of non-hexagonal rings in the honeycomb carbon arrangement of graphene produces rippled graphene layers with valuable chemical and physical properties. In principle, a bottom-up approach to introducing distortion from planarity of a graphene sheet can be achieved by careful insertion of curved polyaromatic hydrocarbons during the growth of the lattice. Corannulene, the archetype of such non-planar polyaromatic hydrocarbons, can act as an ideal wrinkling motif in 2D carbon nanostructures. Herein we report an electrochemical bottom-up method to obtain egg-box shaped nanographene structures through a polycondensation of corannulene that produces a new conducting layered material. Characterization of this new polymeric material by electrochemistry, spectroscopy, electron microscopy (SEM and TEM), scanning probe microscopy, and laser desorption-ionization time of flight mass spectrometry provides strong evidence that the anodic polymerization of corannulene, combined with electrochemically induced oxidative cyclodehydrogenations (Scholl reactions), leads to polycorannulene with a wavy graphene-like structure.

A bottom-up synthesis of wavy graphene structures obtained through an anodic polymerization process, combined with an electrochemically triggered oxidative cyclodehydrogenation, of the bowl-shaped polyaromatic hydrocarbon corannulene.     

Synthesis of new polycyclic systems containing the pyrimido[2,1-a]phthalazine skeleton

The synthesis of new polyheterocycles containing the pyrimido[2,1-a]phthalazine system 5, 6 and 7 , obtained by condensation of phthalic anhydride with the appropriate hydrazides 2, 3 and 4 , respectively, are reported. It was also synthesized the 14H-[1]Benzothieno[3′,2′:4,5]pyrimido[2,1-a][1,2,4]triazolo[4,3-c]phthalazin-14-one (16).     

Template evaporation method for controlling anatase nanocrystal size in ordered macroporous TiO2

The importance of pure-phase titanium oxide materials as catalysts, sensors, and photonic band-gap materials has been growing steadily. Recently, more attention has been focused on nanostructured titanium oxide showing controlled and periodic porosity on a nanometric scale. The nanocrystal size control of porous nanostructured titanium oxide in an anatase form is a crucial step for the organic template method. Simple template removal by evaporation in an inert atmosphere is reported in this article and compared with the calcination technique usually reported in the literature. The proposed method allows the formation of a double-porous (macro and meso) anatase phase. We demonstrate that it highly preserves the macropore order into a titanium oxide material and induces narrowly dispersed mesopores by controlling the nano-crystal size that is kept around 6 nm. For the proposed method, polystyrene beads are particularly suitable as templates, being evaporated in the temperature range of anatase existence. The final high surface area makes the materials appealing for applications as photocatalysts or sensors.     

Asymmetric Information in a Capital Accumulation Differential Game with Spillover and Learning Effects

Journal of Optimization Theory and Applications - This paper considers a capital accumulation game where the installation costs of investments are lowered by the firm’s own capital stock...     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Fractal relaxed Dirichlet problems

Given aself similar fractal K ? ? ⁿ of Hausdorff dimension α>n?2, andc ₁>0, we give an easy and explicit construction, using the self similarity properties ofK, of a sequence of closed sets? _h such that for every bounded open setΩ?? ⁿ and for everyf ∈ L²(Ω) the solutions to $$\left\{ \begin{gathered} - \Delta u_h = f in \Omega \backslash \varepsilon _h \hfill \\ u_h = 0 on \partial (\Omega \backslash \varepsilon _h ) \hfill \\ \end{gathered} \right.$$ converge to the solution of the relaxed Dirichlet boundary value problem $$\left\{ \begin{gathered} - \Delta u + uc_1 \mathcal{H}_{\left| K \right.}^\alpha = f in \Omega \hfill \\ u = 0 on \partial \Omega \hfill \\ \end{gathered} \right.$$ (H _∣ ^α denotes the restriction of the α-dimensional Hausdorff measure toK). The condition α>n?2 is strict.