Kekulé structure counts for some classes of all-benzenoid and all-coronoid hydrocarbons

Summary A general formula for the Kekulé structure count (K) is deduced for the class of catacondensed all-benzenoids with unbranched backbones. The formula is extended to thin pericondensed all-benzenoids, where allowance is made for pyrene units. In this treatment the fragmentation matrices are employed. A generalization of these matrices is furnished. Next some generalK formulas for classes of catacondensed and thin pericondensed all-coronoids are deduced. Again the fragmentation matrices are employed, but the problem is also studied in terms of certain polynomials.Dedicated to the memory of Professor Oskar E. Polansky, who died in January 1989. He was the one who coined the term all-benzenoid.     

The simplest coronoids: Hollow hexagons

Hollow hexagons form a subclass of primitive coronoid systems. The macrocyclic aromatic hydrocarbon kekulene corresponds to a hollow hexagon. The hollow hexagons for given numbers of hexagonal units (h) were enumerated by computer aid, but also an analytical solution for the numbers of hollow hexagons was achieved. For the Kekulé structure counts (k) of a hollow hexagon a general formula is reported. Also the maximum and minimumK numbers are considered.This article is Part VI of the series Enumeration and Classification of Coronoid Hydrocarbons. For Part V, see ref. [36].     

Evolution of synthetic routes towards homochiral Tapentadol

Analysis of the literature shows that the development of synthetic approaches to Tapentadol, an agonist of the μ-opioid receptor and norepinephrine reuptake inhibitor, has followed four, partially overlapping, phases. The most advanced approaches, based on stereoselective syntheses, appeared only after 2010. The majority of the chemistry examples presented in this review come from patent applications and as such have not been subjected to rigorous peer review, but may serve well as an inspiration to organic chemists for solving analogous synthetic problems.     

Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

Slight Structural Disorder in Bithiophene-based Random Terpolymers with Improved Power Conversion Efficiency for Polymer Solar Cells

A series of random terpolymers P2-P5 were designed and synthesized by randomly embedding 5 mol%, 10 mol%, 15 mol%and 25 mol% feed ratios of low cost 2,2-bithiophene as the third monomer to the famous donor-acceptor(D-A) type copolymer PTB7-Th(P1). All polymers showed similar molecular weight with number-average molecular weight(Mn) and weight-average molecular weight(Mw) in the range of(59-74) and(93-114) kg·mol~(-1), respectively, to ensure a fair comparison on the structure-property relationships.Compared with the control copolymer PTB7-Th, the random terpolymers exhibited enhanced absorption intensity in a wide range from400 nm to 650 nm in both solution and film as well as in polymer/PC71 BM blends. From grazing incident wide-angle X-ray diffraction(GIWAXS), compared with the regularly alternated copolymer PTB7-Th, the random terpolymers demonstrated mild structural disorder with reduced(100) lamellar stacking and slightly weakened(010) π-π stacking for the polymers as well as slightly reduced PC71 BM aggregation in polymer/PC71 BM blends. However, the measured hole mobility for terpolymers((1.20-3.73) × 104-cm2·V-1·s~(-1)) was evaluated to be comparable or even higher than 1.35 × 10~(-4) cm~2·V~(-1)·s-1 of the alternative copolymer. Enhanced average power conversion efficiency(PCE) from 7.35% to 8.11% and 7.79% to 8.37% was observed in both conventional and inverted device architectures from copolymer P1 to terpolymers P4, while further increasing the 2,2-bithiophene feed ratio decreased the PCE.     

Phase equilibria and excess properties for binary systems in reactive distillation processes Part I. Methyl acetate synthesis

Isothermal vapor–liquid equilibrium (VLE) and excess enthalpy (H^E) data were measured for binary systems required for the design of reactive distillation processes for the methyl acetate production. The isothermal P–x data were measured with the help of a computer-operated static apparatus. A commercial isothermal flow calorimeter was used for the determination of the heats of mixing. Temperature-dependent interaction parameters for the UNIQUAC model were fitted simultaneously to the experimental data from this work and other authors.     

2,3,5,6-Tetramethylmorpholine: II—1H n.m.r. structural studies of the isomers of 2,3,5,6-tetramethylmorpholine

The structures of the six isomers of 2,3,5,6-tetramethyl-morpholine have been determined by means of proton nuclear magnetic resonance studies at 100 MHz. The spectra have been analysed in terms of spin–spin coupling constants and population distributions of the possible conformers at low temperatures. Also included in this paper are results from n.m.r. studies on the six 4-benzyl-2,3,5,6-tetramethylmorpholine derivatives, which give information about the stereochemistry of the methyl groups α to the amine group.     

Indications about the shape of the universe from the Wilkinson microwave anisotropy probe data

It is shown that the recent observations of NASA's Explorer mission, "Wilkinson Microwave Anisotropy Probe," hint that our Universe may possess a nontrivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.