Sampling Eulerian orientations of triangular lattice graphs

We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although Mihail and Winkler (1989) showed that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian graphs. We analyse the mixing time of a Markov chain on the Eulerian orientations of a planar graph which moves between orientations by reversing the edges of directed faces. Using path coupling and the comparison method we obtain a polynomial upper bound on the mixing time of this chain for any solid subgraph of the triangular lattice. By considering the conductance of the chain we show that there exist non-solid subgraphs (subgraphs with holes) for which the chain will always take an exponential amount of time to converge. Finally, we show that the problem of counting Eulerian orientations remains #P-complete when restricted to planar graphs (Mihail and Winkler had already established this for general graphs).     

Organic–inorganic nanocomposite films made from polyurethane dispersions and colloidal silica particles

Polyurethane/silica nanocomposites were prepared by solution blending of polyurethane water dispersion (PUD) based on polycarbonate macrodiol with colloidal silica aqueous sol LUDOX TMA. Because of mixing PUDs made from linear polyurethane with the nanofiller, only physical polymer/filler type of interface formed by hydrogen bonds was obtained. As a result the materials were possible to reuse after dissolution in acetone followed by dispersion in water. The effect of colloidal silica content on mechanical, thermal, morphological, and swelling properties of obtained films was tested by tensile test, dynamic mechanical thermal analysis, thermogravimertic analysis, scanning electron microscopy, atomic force microscopy, and swelling analyses. The nanocomposites were classified in three groups differing in the internal structure and functional properties: organic matrix filled with inorganic nanofiller (up to 10 wt% of silica), bicontinous systems (25 and 32 wt% of silica) and inorganic matrix filled with polyurethane (50 and 60 wt% of silica). Only small amount of colloidal silica (up to 10 wt%) improves thermo-mechanical properties, smoothes the materials, and suppresses extent of swelling without changing of the films transparency.     

Organometallic Molecular Wires with Thioacetylene Backbones,trans-{RS-(C≡C)n}2Ru(phosphine)4: High Conductance through Non-Aromatic Bridging Linkers

In this work, the design, synthesis, and single-molecule conductance of ethynyl- and butadiynyl-ruthenium molecular wires with thioether anchor groups [RS=n-C₆H₁₃S, p-tert-Bu−C₆H₄S), trans-{RS−(C≡C)_n}₂Ru(dppe)₂ (n=1 ( 1^R ), 2 ( 2^R ); dppe: 1,2-bis(diphenylphosphino)ethane) and trans-(n-C₆H₁₃S−C≡C)₂Ru{P(OMe)₃}₄ 3^hex ] are reported. Scanning tunneling microscope break-junction study has revealed conductance of the organometallic molecular wires with the thioacetylene backbones higher than that of the related organometallic wires having arylethynylruthenium linkages with the sulfur anchor groups, trans-{p-MeS−C₆H₄-(C≡C)_n}₂Ru(phosphine)₄ 4 ⁿ (n=1, 2) and trans-(Th−C≡C)₂Ru(phosphine)₄ 5 (Th=3-thienyl). It should be noted that the molecular junctions constructed from the butadiynyl wire 2^R , trans-{ Au −RS−(C≡C)₂}₂Ru(dppe)₂ ( Au : gold metal electrode), show conductance comparable to that of the covalently linked polyynyl wire with the similar molecular length, trans-{ Au −(C≡C)₃}₂Ru(dppe)₂ 6³ . The DFT non-equilibrium Green's function (NEGF) study supports the highly conducting nature of the thioacetylene molecular wires through HOMO orbitals.     

Acid-Catalyzed RNA-Oligomerization from 3’,5’-cGMP

The assembly of ancient informational polymers from nucleotide precursors is the central challenge of life's origin on our planet. Among the possible solutions, dry polymerization of 3’,5’-cyclic guanosine monophosphate (3’,5’-cGMP) has been proposed as a candidate to create oligonucleotides of 15–20 units in length. However, the reported sensitivity of the reaction to the presence of cations raised questions of whether this chemistry could be relevant in a geological context. The experiments in this study show that the presence of cations is not restrictive as long as the reaction is conducted in an acidic environment, in contrast to previous reports that suggested optimal conditions at pH 9.