Multicyclic polyethers derived from 1,1,1‐tris(4‐hydroxyphenyl)ethane and 2,6‐dihalopyridines

Poly(pyridine ether)s were prepared in two ways: the polycondensation of silylated 1,1,1‐tris(4‐hydroxyphenyl)ethane (THPE) with 2,6‐difluoropyridine (method A) and the polycondensation of free THPE with 2,6‐dichloropyridine (method B). With method A, the THPE/difluoropyridine feed ratio was varied from 1.0:1.0 to 1.0:1.6. Cycles, bicycles, and multicycles were the main reaction products, and crosslinking was never observed. When ideal stoichiometry was used exclusively, multicycles free of functional groups were obtained. These multicycles were detectable in matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectra up to B₃₈C₇₆ with a mass of approximately 32,000 Da. With method B, the reaction conditions were varied at a fixed feed ratio to achieve an optimum for the preparation of multicyclic polyethers, but because of the lower reactivity of 2,6‐dichloropyridine, a quantitative conversion was not achieved. The reaction products were characterized with MALDI‐TOF mass spectrometry, viscosity measurements, and size exclusion chromatography. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5725–5735, 2004     

catena‐Poly[tetra­kis(3‐phenyl­propyl­ammonium) [iodo­plumbate(II)‐tri‐μ‐iodo‐plumbate(II)‐tri‐μ‐iodo‐iodo­plumbate(II)‐di‐μ‐iodo]]

The title compound, {(C₉H₁₄N)₄[Pb₃I₁₀]}_n, crystallizes as an organic–inorganic hybrid. As such, the structure consists of a two‐dimensional inorganic layer of [Pb₃I₁₀]_n⁴ⁿ⁻ ions extending along [100]. The asymmetric unit contains two independent Pb atoms, viz. one in a general position and the other on an inversion centre. Each Pb atom is octa­hedrally coordinated by six iodide ions and exhibits both face‐ and corner‐sharing with adjacent atoms in the inorganic layer. These anionic layers alternate with 3‐phenyl­propyl­ammonium cations, which hydrogen bond to the iodides. Simple face‐to‐edge σ–π stacking inter­actions are observed between the aromatic rings that stabilize the overall three‐dimensional structure. This net structure has only been observed five times previously.     

Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006     

A catalyst-free one-step synthesis of N-pyrimidinyl amidines from endocyclic enamines and 4-azidopyrimidines

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