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     

Facile synthesis of poly(ether carbonate)s via copolymerization of CO2 and propylene oxide under combinatorial catalyst of rare earth ternary complex and double metal cyanide complex

Poly(ether carbonate)s (PPCs) with carbonate unit (CU) content ranging from 57.8 to 97.1% and number average molecular weight (M_n) around 100 kg/mol were conveniently prepared via copolymerization of CO₂ and propylene oxide under combinatorial catalyst of rare earth ternary (RET) complex and double metal cyanide (DMC) complex. Enhancement of catalytic activity and reduction of propylene carbonate byproduct were realized due to synergetic effect of the two metal catalysts, where DMC can be activated in the presence of RET. Solubility fractionation confirmed that the obtained PPCs were copolymers, not physical blends of each polymer. Thermal performances of the PPCs were closely related to their CU content, their glass transition temperatures (T_g) were tunable in the range of 6.7–36.3 °C, which decreased with decreasing CU content, while their thermal stabilities were enhanced significantly, an increase of 50.5 °C in 50% weight loss temperature was observed when CU content decreased from 97.1 to 57.8%. Both shear storage modulus and complex viscosity increased with increasing CU content, which became more obvious at lower frequency, featuring well with the CU content in the PPCs. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A two-component geodesic equation on a space of constant positive curvature

We propose a new two-component geodesic equation with the unusual property that the underlying space has constant positive curvature. In the special case of one space dimension, the equation reduces to the two-component Hunter–Saxton equation.     

Output response in orthogonal directions of a He–Ne laser caused by birefringent-external-cavity feedback

The output responses of phase, amplitude, and polarization of light intensity of a He–Ne laser with the birefringent external cavity are presented. All phenomena are observed in two orthogonal directions related to the birefringent element’s orientation, and are studied under weak optical feedback. Experiments are carried out in five available detecting positions. It is found that laser intensities are modulated in the two orthogonal directions simultaneously, with a phase difference dominated by the phase retardation of the birefringence element. The modulation amplitudes are different in the two directions. A special polarization phenomenon is also observed and discussed. This research may provide a potential novel measuring principle for transparent birefringent materials.     

Finite-time H ∞ control for a class of Markovian jump delayed systems with input saturation

This work considers the finite-time control problem for a class Markovian jump delayed systems with partially known transition rates subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov–Krasovkii function, an observer-based state feedback controller is designed to guarantee that the resulted closed-loop constrained system is mean-square locally asymptotically finite-time stabilizable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.     

A one‐pot method for synthesis of reduced graphene oxide‐supported Cu–Cu2O and catalytic application in tandem reaction of halides and sodium azide with terminal alkynes

Reduced graphene oxide (RGO)‐supported Cu–Cu₂O nanocomposite material (Cu‐Cu₂O@RGO) was prepared through a one‐pot reflux synthesis method. The morphology, crystal structure and composition of the prepared Cu‐Cu₂O@RGO were characterized using transmission electron microscopy, X‐ray diffraction, and X‐ray photoelectron, infrared and Raman spectroscopies. Cu‐Cu₂O@RGO as a heterogeneous catalyst was applied to tandem reactions of halides and sodium azide with terminal alkynes to synthesize effectively 1,4‐disubstituted 1,2,3‐triazoles. Moreover, the catalyst showed excellent recyclability performance with very little leaching of the metal. Compared with homogeneous catalysts, Cu‐Cu₂O@RGO as a green and efficient catalyst was recoverable, easy to separate and highly stable in the tandem method for the synthesis of 1,2,3‐triazole compounds.