Hypercube subgraphs with minimal detours

Define a minimal detour subgraph of the n-dimensional cube to be a spanning subgraph G of Q_n having the property that for vertices x, y of Q_n, distances are related by d_G(x, y) ≤ d_Qn(x, y) + 2. Let f(n) be the minimum number of edges of such a subgraph of Q_n. After preliminary work on distances in subgraphs of product graphs, we show that The subgraphs we construct to establish this bound have the property that the longest distances are the same as in Q_n, and thus the diameter does not increase. We establish a lower bound for f(n), show that vertices of high degree must be distributed throughout a minimal detour subgraph of Q_n, and end with conjectures and questions. © 1996 John Wiley & Sons, Inc.     

Development and evaluation of a detailed mechanism for the atmospheric reactions of isoprene and NOx

A detailed photochemical mechanism for the atmospheric reactions of isoprene and its major oxidation products in the presence of NO_x, which incorporates the most recent laboratory results and our current understanding of the system, is described. It is evaluated by comparing its predictions against results of NO_x-air irradiations of isoprene and its two major products, methacrolein, and methyl vinyl ketone (MVK), in five different types of environmental chambers at two different laboratories. In most cases it simulated experimental results within the uncertainty of the data and the chamber and run characterization model. However, the photodecomposition quantum yields of methacrolein and MVK and the organic nitrate yield from the OH + isoprene reaction had to be adjusted to obtain satisfactory simulations of the data. The major discrepancy observed was that the model tended to underpredict PAN by ca. 40% in the isoprene experiments, despite the fact that the model predicted PAN from methacrolein and MVK reasonably well. The uncertainties and additional data needed to completely characterize the isoprene atmospheric photooxidation system are discussed. © 1996 John Wiley & Sons, Inc.     

Synthesis,characterization and properties of a soluble polymer with a poly(phenylenevinylene) structure

Soluble poly(2,5-dialkoxy-1,4-phenylenevinylene) has been prepared via Stille coupling reaction between 2,5-dialkoxy-1,4-diiodobenzene and E-1,2-bis(tributylstannyl)-ethene in the presence of palladium complexes. Characterization of this material by means of ¹H and ¹³C nuclear magnetic resonance (NMR), ultraviolet/visible (UV/VIS) and infrared (IR) spectra is described. Molecular weights, determined by means of gelpermeation chromatography (GPC) analysis and referred to standard polystyrene, were in the range number-average molecular weights M _n = 2061–2544 and weight-average molecular weights M _w = 3347–3878. X-ray diffraction (XRD) analysis of the polymer showed semicrystalline structure. T_g = 57°C, transition to a stable smectic mesophase at 115°C and clearing point at 210°C were revealed by differential scanning calorimetry analysis, optical microscopy observation and XRD of the annealed polymer.     

Arsenic biomethylation by the microorganism apiotrichum humicola in the presence of l-methionine-methyl-d3

The microorganism Apiotrichum humicola (previously known as Candida humicola) grown in the presence of either arsenate, arsenite, methylarsonic acid or dimethylarsinic acid, produces arsenic-containing metabolites in the growth medium. When L-methionine-methyl-d₃ is added to the cultures, the CD₃ label is incorporated intact into the metabolites to a considerable extent to form deuterated dimethylarsenic and trimethyl-arsenic species, indicating that S-adenosylmethionine, or some related sulphonium compound, is involved in the biological methylation. Conclusive evidence of CD₃ incorporation in the arsenicals found in the growth medium was provided by using a specially developed hydride generation-gas chromatography-mass spectrometry system (HG–GC–MS).     

Constrained Dipeptide Surrogates: 5- and 7-Hydroxy Indolizidin-2-one Amino Acid Synthesis from Iodolactonization of Dehydro-2,8-diamino Azelates

The constrained dipeptide surrogates 5- and 7-hydroxy indolizidin-2-one N-(Boc)amino acids have been synthesized from L-serine as a chiral educt. A linear precursor ∆⁴-unsaturated (2S,8S)-2,8-bis[N-(Boc)amino]azelic acid was prepared in five steps from L-serine. Although epoxidation and dihydroxylation pathways gave mixtures of hydroxy indolizidin-2-one diastereomers, iodolactonization of the ∆⁴-azelate stereoselectively delivered a lactone iodide from which separable (5S)- and (7S)-hydroxy indolizidin-2-one N-(Boc)amino esters were synthesized by sequences featuring intramolecular iodide displacement and lactam formation. X-ray analysis of the (7S)-hydroxy indolizidin-2-one N-(Boc)amino ester indicated that the backbone dihedral angles embedded in the bicyclic ring system resembled those of the central residues of an ideal type II’ β-turn indicating the potential for peptide mimicry.     

Arene–perfluoroarene interactions confer enhanced mechanical properties to synthetic nanotubes

Supramolecular nanotubes prepared through macrocycle assembly offer unique properties that stem from their long-range order, structural predictability, and tunable microenvironments. However, assemblies that rely on weak non-covalent interactions often have limited aspect ratios and poor mechanical integrity, which diminish their utility. Here pentagonal imine-linked macrocycles are prepared by condensing a pyridine-containing diamine and either terephthalaldehyde or 2,3,5,6-tetrafluoroterephthalaldehyde. Atomic force microscopy and synchrotron in solvo X-ray diffraction demonstrate that protonation of the pyridine groups drives assembly into high-aspect ratio nanotube assemblies. A 1 : 1 mixture of each macrocycle yielded nanotubes with enhanced crystallinity upon protonation. UV-Vis and fluorescence spectroscopy indicate that nanotubes containing both arene and perfluoroarene subunits display spectroscopic signatures of arene–perfluoroarene interactions. Touch-spun polymeric fibers containing assembled nanotubes prepared from the perhydro- or perfluorinated macrocycles exhibited Young''s moduli of 1.09 and 0.49 GPa, respectively. Fibers containing nanotube assemblies reinforced by arene–perfluoroarene interactions yielded a 93% increase in the Young''s modulus over the perhydro derivative, up to 2.1 GPa. These findings demonstrate that tuning the chemical composition of the monomeric macrocycles can have profound effects on the mechanical strength of the resulting assemblies. More broadly, these results will inspire future studies into tuning orthogonal non-covalent interactions between macrocycles to yield nanotubes with emergent functions and technological potential.

Arene–perfluoroarene interactions resulted in enhanced crystallinity between analogous perhydro- and perfluoro macrocycles in a supramolecular nanotube assembly.