The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Benzodifuran‐containing well‐defined π‐conjugated polymers for photovoltaic cells

Two well‐defined alternating π‐conjugated polymers containing a soluble electroactive benzo[1,2‐b:4,5‐b′]difuran (BDF) chromophore, poly(BDF‐(9‐phenylcarbazole)) (PBDFC), and poly(BDF‐benzothiadiazole) (PBDFBTD) were synthesized via Sonogashira copolymerizations. Their optical, electrochemical, and field‐effect charge transport properties were characterized and compared with those of the corresponding homopolymer PBDF and random copolymers of the same overall composition. All these polymers cover broad optical absorption ranges from 250 to 750 nm with narrow optical band gaps of 1.78–2.35 eV. Both PBDF and PBDFBTD show ambipolar redox properties with HOMO levels of ?5.38 and ?5.09 eV, respectively. The field‐effect mobility of holes varies from 2.9 × 10^?8 cm² V^?1 s^?1 in PBDF to 1.0 × 10^?5 cm² V^?1 s^?1 in PBDFBTD. Bulk heterojunction solar cell devices were fabricated using the polymers as the electron donor and [6,6]‐phenyl‐C₆₁‐butyric acid methyl ester as the electron acceptor, leading to power conversion efficiencies of 0.24–0.57% under air mass 1.5 illumination (100 mW cm^?2). These results indicate that their band gaps, molecular electronic energy levels, charge mobilities, and molecular weights are readily tuned by copolymerizing the BDF core with different π‐conjugated units. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Platanus acerifolia’s buds: additional non-polar metabolites and structure revision of two previous dihydrochalcone-like metabolites

In addition to the methylated and prenylated flavonoids previously reported from Platanus acerifolia, the multistep chromatographic processing of the n-hexane extract of the fresh unripe buds resulted in the isolation of 11 metabolites. Besides six common wax constituents, the n-hexane portion led to the isolation of four gem-dimethylpyrano flavanones. They corresponded to two pairs of angular and linear isomers derived only from pinocembrin (5,7-dihydroxyflavanone). Additionally, a novel β-decadione was split into the major keto-enol tautomer as shown by the detailed NMR and EIMS analyses. Moreover, the structures of grenoblone and 4-hydroxygrenoblone, two previously reported dihydrochalcone-like metabolites, were revised according to the EIMS spectra.     

METHYLTHIODITHIOLYLIUM REACTIONS WITH 2-BUTENE NITRILES DERIVATIVES

Abstract

The 3-methylthio-1. 2-dithiolylium including at 5 position a donor substituent, in acetic acid in the presence of pyridine, the 2-methylthio-1. 3-dithiolylium ions in methylene chloride-triethylamine, react with the 2-butene nitrile derivatives and lead to the (A) and (B) corresponding 4-dithiolylidene-2-butene nitriles. In contrast ring opening reaction of the 1, 2-dithiole is observed when 2-cyano-3-phenyl-2-butene nitrile reacts with the 3-methylthio-4-aryl-1. 2-dithiolylium ions in 3 and 5 positions, in methylene chloride-triethylamine. The nucleophilic attack on the 5 position of the dithiolylium ion leads to a 2-cyano-3-phenyl-3 (4-aryl-5-methylthio-2-thienyl) propene nitrile (C), meanwhile the attack on the 3 position leads to a 2-cyano-3-phenyl-3-(4-aryl-3-mercapto-2-thienyl) propene nitrile (D). The proposed structures are established by means of physical methods (IR, NMR, and Mass Spectrometry) and by non ambiguous synthesis. The reactivities of the various sites are explained in function of the electronic and steric effects, furthermore the reaction conditions and the intermediary isolation allow to propose the mecanisms of these reactions.     

On the Strategy of NMR Spectral Analysis. The 1H-NMR Spectrum of Amphetamine

The successive steps of the computer analysis of a NMR spectrum are examined. Better results can be obtained by direct simulation of tentative model spectra. As an example the ¹H-NMR spectrum of amphetamine is analysed.     

Quaterthiophene-based dimers containing an ethylene bridge: molecular design,synthesis, and optoelectronic properties

Two quaterthiophene-based dimers including an ethylene bridge have been designed and efficiently prepared; experimental and computational studies show a promising potential as semiconducting material with a charge transport of higher dimensionality compared to quaterthiophene.