Influence of the order parameter on the anchoring energy of liquid crystals

No theory of the polar and azimuthal anchoring energies of liquid crystals (LCs) has been developed on a molecular level, despite the scientific and practical topicality of the problem. The interaction energies of mesogenic molecules with graphite and polyethylene surfaces calculated previously by the method of atom-atom potentials are in good agreement with the experimental data, but, at the same time, the calculated polar and azimuthal anchoring energies are larger than their experimental values by one and two orders of magnitude, respectively. To explain these values, the anchoring energy has been assumed to depend not only on the interaction with the surface but also on the interaction between the LC molecules arranged in the model in the form of quasi-layers. The mesogenic molecules have been modeled by rods with virtual C’ atoms (carbon atoms with hydrogen atoms attached to them) “threaded” on them. The molecule orientation has been specified by the polar and azimuthal angles θ _i , φ _i and θ _j , φ _j relative to the directors of the ith and jth layers. The derived polar and azimuthal anchoring energies as well as their dependences on the order parameter have turned out to be close to the experimental data.     

Deactivation mechanism of the green fluorescent chromophore

We report time-resolved fluorescence data for the anion of p-hydroxybenzylidene dimethylimidazolinone (p-HBDI), a model chromophore of the green fluorescence protein, in viscous glycerol-water mixtures over a range of temperatures, T. The markedly nonexponential decay of the excited electronic state is interpreted with the aid of an inhomogeneous model possessing a Gaussian coordinate-dependent sink term. A nonlinear least-squares fitting routine enables us to achieve quantitative fits by adjusting a single activation parameter, which is found to depend linearly on 1/T. We derive an analytic expression for the absolute quantum yield, which is compared with the integrated steady-state fluorescence spectra. The microscopic origins of the model are discussed in terms of two-dimensional dynamics, coupling the phenyl-ring rotation to a swinging mode that brings this flexible molecule to the proximity of a conical intersection on its multidimensional potential energy surface.     

Nanocomposites through copolymerization of a polyhedral oligomeric silsesquioxane and methyl methacrylate

The mechanical properties and thermal stability of polymers can be enhanced through the formation of nanocomposites. Nanocomposites consisting of hybrid copolymers of methacrylcyclohexyl polyhedral oligomeric silsesquioxane (POSS‐1) and methyl methacrylate (MMA) with up to 92 wt % (51 mol %) POSS‐1 and with superior thermal properties were synthesized using solution polymerization. The POSS‐1 contents of the copolymers were similar to or slightly higher than those in the feeds, the polydispersity indices were relatively low, and the degree of polymerization decreased with increasing POSS‐1 content. POSS‐1 enhanced the thermal stability, increasing the degradation temperature, reducing the mass loss, and preventing PMMA‐like degradation from propagating along the chain. The mass loss was reduced in a high POSS‐1 content copolymer since the polymerization of POSS‐1 with itself reduced sublimation. Exposure to 450 °C produced cyclohexyl‐POSS‐like remnants in the POSS‐1 monomer and in all the copolymers. The degradation of these remnants, for the copolymers and for the POSS‐1 monomer, yielded 75% SiO₂ and an oxidized carbonaceous residue. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4264–4275, 2007     

Apparent stoichiometry of water in proton hydration and proton dehydration reactions in CH3CN/H2O solutions

Gradual solvation of protons by water is observed in liquids by mixing strong mineral acids with various amounts of water in acetonitrile solutions, a process which promotes rapid dissociation of the acids in these solutions. The stoichiometry of the reaction XH(+) + n(H(2)O) = X + (H(2)O)(n)H(+) was studied for strong mineral acids (negatively charged X, X = ClO(4)ˉ, Clˉ, Brˉ, Iˉ, CF(3)SO(3)ˉ) and for strong cationic acids (uncharged X, X = R*NH(2), H(2)O). We have found by direct quantitative analysis preference of n = 2 over n = 1 for both groups of proton transfer reactions at relatively low water concentrations in acetonitrile. At high water concentrations, we have found that larger water solvates must also be involved in the solvation of the proton while the spectral features already observed for n = 2, H(+)(H(2)O)(2), remain almost unchanged at large n values up to at least 10 M of water.     

Persistence of embedded eigenvalues

We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m<∞ we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension m. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.     

Resolving sets and integer programs for recommender systems

Recommender systems make use of different sources of information for providing users with recommendations of items. Such systems are often based on either collaborative filtering methods which make automatic predictions about the interests of a user, using preferences of similar users, or content based filtering that matches the user’s personal preferences with item characteristics. We adopt the content-based approach and propose to use the concept of resolving set that allows to determine the preferences of the users with a very limited number of ratings. We also show how to make recommendations when user ratings are imprecise or inconsistent, and we indicate how to take into account situations where users possibly don’t care about the attribute values of some items. All recommendations are obtained in a few seconds by solving integer programs.