Well‐posedness of a parabolic free boundary problem driven by diffusion and surface tension

Well‐posedness and regularity results are shown for a class of free boundary problems consisting of diffusion on a free domain where the boundary movement depends on its mean curvature of the boundary and the diffusion on the boundary, and initial conditions are radially symmetric. Short‐time existence and uniqueness of solutions in a suitable Sobolev space are shown using a fixed‐point argument. Higher regularity is a posteriori. Finally, it is shown that solutions exist globally in time and converge to equilibrium if the boundary movement depends on the mean curvature of the boundary and diffusion in a specific way. A mathematical model describing the swelling of a cell due to osmosis is treated as an example. Copyright © 2014 John Wiley & Sons, Ltd.     

Water Oxidation with Cobalt-Loaded Linear Conjugated Polymer Photocatalysts

The first examples of linear conjugated organic polymer photocatalysts that produce oxygen from water after loading with cobalt and in the presence of an electron scavenger are reported. The oxygen evolution rates, which are higher than for related organic materials, can be rationalized by a combination of the thermodynamic driving force for water oxidation, the light absorption of the polymer, and the aqueous dispersibility of the relatively hydrophilic polymer particles. We also used transient absorption spectroscopy to study the best performing system and we found that fast oxidative quenching of the exciton occurs (picoseconds) in the presence of an electron scavenger, minimizing recombination.     

Frequency shift of sources embedded in finite two-dimensional photonic clusters

The frequency (Lamb) shift and local density of states (LDOS) in two-dimensional photonic crystals composed of a cluster of infinitely long circular cylinders is calculated classically using the radiation reaction mechanism. We investigate the frequency shift and LDOS as a function of the size of the cluster and show that, at the edges of the band gap, both quantities can be large and increase in magnitude with cluster size. We explain this in terms of poles of a scattering operator and also show that both the Lamb shift and LDOS are sensitive functions of the shape of the cluster.     

Periodic projector augmented wave density functional calculations on the hexachlorobenzene crystal and comparison with the experimental multipolar charge density model

The projector augmented wave (PAW) methodology has been used to calculate a high precision electron density distribution ρ(r) for the hexachlorobenzene crystal phase. Implementing the calculation of the crystallographic structure factors in the VASP code has permitted one to obtain the theoretical multipolar ρ(r). This electron density is compared with both the DFT electron density and the experimental multipolar model obtained from high-resolution X-ray diffraction data. This comparison has been carried out in intra- and intermolecular regions within the framework of the quantum theory of atoms-in-molecules (QTAIM) developed by Bader and co-workers. The characterization of the electron density in both C-Cl and Cl···Cl regions, as well as within the atomic basins, shows similar features for the three models. As a consequence, the observation of charge depletion and charge concentration regions around the halogen nuclei (along the C-Cl bonding axis and in the perpendicular plane, respectively) underlines the nature of halogen bonding in terms of electrophilic and nucleophilic interactions.     

Hydrogen bonding and chemical shift assignments in carbazole functionalized isocyanides from solid-state NMR and first-principles calculations

Carbazole functionalized polyisocyanides are known to exhibit excellent electronic properties (E. Schwartz, et al., Chemistry of Materials, 2010, 22, 2597). The functionalities and properties of such materials crucially depend on the organization and stability of the polymer structure. We combine solid-state Nuclear Magnetic Resonance (NMR) experiments with first-principles calculations of isotropic chemical shifts, within the recently developed converse approach, to rationalize the origin of isotropic chemical shifts in the crystalline monomer l-isocyanoalanine 2-(9H-carbazol-9-yl) ethyl amide (monomer 1) and thereby gain insight into the structural organization of its polymer (polymer 2). The use of state-of-the-art solid-state NMR experiments combined with Density Functional Theory (DFT) based calculations allows an unambiguous assignment of all proton and carbon resonances of the monomer. We were able to identify the structure stabilising interactions in the crystal and understand the influence of the molecular packing in the crystal structure on the chemical shift data observed in the NMR spectra. Here the Nuclear Independent Chemical Shift (NICS) approach allows discriminating between 'physical' interactions amongst neighboring molecules such as ring-current effects and 'chemical' interactions such as hydrogen bonding. This analysis reveals that the isocyanide monomer is stabilized by multiple hydrogen bonds such as a bifurcated hydrogen bond involving -N-H, -C-H and O=C- moieties and Ar-H···C≡N- hydrogen bonding (Ar = aromatic group). Based on the geometrical arrangement it is postulated that the carbazole units are involved in the weak σ-π interactions giving rise to a Herringbone packing of the molecules. The chemical shift analysis of the polymer spectra readily establishes the existence of N-H···O=C hydrogen bonds despite the limited resolution exhibited by the polymer spectra. It is also elucidated that the relative arrangement of the carbazole units in the polymer differs significantly from that of the monomer.     

Single-chain folding of polymers for catalytic systems in water

Enzymes are a source of inspiration for chemists attempting to create versatile synthetic catalysts. In order to arrive at a polymeric chain carrying catalytic units separated spatially, it is a prerequisite to fold these polymers in water into well-defined compartmentalized architectures thus creating a catalytic core. Herein, we report the synthesis, physical properties, and catalytic activity of a water-soluble segmented terpolymer in which a helical structure in the apolar core is created around a ruthenium-based catalyst. The supramolecular chirality of this catalytic system is the result of the self-assembly of benzene-1,3,5-tricarboxamide side chains, while the catalyst arises from the sequential ruthenium-catalyzed living radical polymerization of the different monomers followed by ligand exchange. The polymers exhibit a two-state folding process and show transfer hydrogenation in water.     

Bid and ask prices as non-linear continuous time G-expectations based on distortions

Probability distortions for constructing nonlinear G-expectations for the bid and ask or lower and upper prices in continuous time are here extended to the direct use of measure distortions. Fairly generally measure distortions can be constructed as probability distortions applied to an exponential distribution function on the half line. The valuation methodologies are extended beyond contract valuation to the valuation of economic activities with infinite lives. Explicit computations illustrate the procedures for stock indices and insurance loss processes.