Novel alkoxyanthracene donor and benzothiadiazole acceptor for organic thin film transistor and bulk heterojunction organic photovoltaic cells

Novel alkoxy anthracene (ODA)‐based polymeric semiconductors were designed for polymer solar cell applications. Alkoxyanthracene, which contains many π electrons and electron donating group, was easily synthesized. The copolymers, poly(alkoxy anthracene‐alt‐thiophene benzothiadiazole thiophene) poly(ODA‐TBT) and poly(alkoxy anthracene‐alt‐benzothiadiazole) poly(ODA‐BT), have been obtained by Suzuki coupling polymerization. Both polymers have ODA unit as a donor and benzothiadiazole as an acceptor. ODA‐TBT has thiophene linkages between ODA and benzothiadiazole. The optical, thermal, and electrochemical properties have been investigated by UV–visible absorption, thermal gravimetric analysis, differential scanning calorimetry, and CV. Organic thin‐film transistor using polymers showed that the hole mobility of poly(ODA‐alt‐TBT) was around 3.6 × 10^?3 cm²/Vs with on/off ratio of 9.91 × 10⁵ while that of poly(ODA‐alt‐BT) was around 1.21 × 10^?2 cm²/Vs with on/off ratio of 2.64 × 10⁶. Organic photovoltaic performance based on polymers were evaluated with a configuration of ITO/PEDOT:PSS/active layer/LiF/Al. Poly(ODA‐TBT) exhibits a short circuit current (J_sc) of 3.9 mA/cm² and power conversion efficiency (PCE) of 1.4%, and poly(ODA‐BT) exhibits the J_sc of 6.4 mA/cm² and PCE of 2.2%. The better device performance of poly(ODA‐BT) is attributed to its charge transfer ability and enhanced mobility and crystallinity although poly(ODA‐BT) does not have extended π‐conjugation due to twisted structure compared with poly(ODA‐TBT). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1306–1314     

Dynamic crystallization behavior,morphology, and physical properties of highly concentrated poly(vinylidene fluoride)/silver nanocomposites

The effects of the inclusion of silver (Ag) nanoparticles on the physical properties, the crystallization behavior under shear, and the consequential crystalline morphology of poly(vinylidene fluoride) (PVDF) were investigated. Ag nanoparticles were melt compounded with PVDF in weight fractions of 20, 50, and 90 wt % (15.3 vol %). In the melt rheology, the presence of 20 wt % Ag nanoparticles had little effect on the dynamic viscosity of PVDF, but further addition increased it with the loading level. In Cole–Cole plot, all the melts gave a single master curve independent of the presence of Ag nanoparticles. As Ag loading level was increased, the overall crystallization process under shear was accelerated by reducing both induction time and crystallization time. The degree of acceleration was more notable at higher crystallization temperatures. The induction time and the crystallization time of 90 wt % loaded nanocomposites were promoted by 53.5 and 3.7%, respectively, at 145 °C and by 62 and 26.3%, respectively, at 160 °C, compared with those of pure PVDF. For the isothermal crystallization measured by differential scanning calorimeter, the critical Ag concentration, where overall crystallization was not promoted by further addition, occurred between 50 and 90 wt %. Both wide angle X‐ray diffraction profiles and Fourier transform infrared spectra of the samples crystallized under shear displayed the peaks for only α‐form crystals without new peak or peak shift regardless of the Ag loading and crystallization temperature. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

A combinatorial proof of Andrews' partition functions related to Schur's partition theorem

We construct an involution to show equality between partition functions related to Schur's second partition theorem.

     

Dispersibility of clay and crystallization kinetics for in situ polymerized PET/pristine and modified montmorillonite nanocomposites

Nanocomposite materials composed of poly (ethylene terephthalate) (PET) and montmorillonite (MMT) clays were prepared by in situ polymerization. Samples consisted of PET blended with various quantities of either pristine (Na⁺‐MMT) or organically modified MMT (A10‐MMT). The morphology and thermal and mechanical properties were evaluated for each sample. TEM micrographs, acquired at a 20 nm resolution, provide direct evidence of exfoliation of the clay particles into the PET matrix and show the effect of the alkyl‐modifier on clay dispersibility. The dispersion of PET/A10‐MMT was greater than that observed for the PET/Na⁺‐MMT nanocomposites. The greatest degree of exfoliation occurred for PET/A10‐MMT 0.5 wt %. However, PET/Na⁺‐MMT exhibited higher crystallization temperatures and rates suggesting that Na⁺‐MMT is a more efficient nucleating agent. Both mechanically and thermally, PET/A10‐MMT nanocomposites exhibited superior properties over pure PET. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1022–1035, 2008     

On the Generalized Rogers–Ramanujan Continued Fraction

On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers–Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers–Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are examined. One of them is an identity bearing a superficial resemblance to the generating function for the generalized Rogers–Ramanujan continued fraction. Thus, our third main goal is to establish, with the help of an idea of F. Franklin, a partition bijection to prove this identity.     

Improved thermal stability of polybenzoxazines by transition metals

The incorporation of various transition metal salts increases the char formation of polybenzoxazines. It is shown that the effect of the transition metal salt is not simply additive and is independent of the amine and phenol structures. While the metal salts have an insignificant effect on the polymerization, their presence in benzoxazine favors the formation of carbonyl functional groups. It is proposed that reduced flammability of polybenzoxazines is achieved through the evolution of CO₂ during thermal degradation.     

A simple phase unwrapping approach based on filtering by windowed Fourier transform

Phase unwrapping is an interesting yet challenging problem in optical interferometry. In this paper, we limit our interest to unwrapping noisy phase maps as it is a common but difficult task. Our aim is to propose a simple solution to phase unwrapping. We first remove the noise by a novel windowed Fourier transform approach and then use sequential line scanning method for phase unwrapping. This simple approach is verified to be very effective.     

Thermomechanical properties and crystallization behavior of layered double hydroxide/poly(ethylene terephthalate) nanocomposites prepared by in‐situ polymerization

Thermomechanical properties and crystallization behavior of poly(ethylene terephthalate) (PET) nanocomposites containing layered double hydroxide (LDH) were investigated. To enhance the compatibility between PET matrix and LDH, dimethyl 5‐sulfoisophthalate (DMSI) anion intercalated LDH (LDH‐DMSI) was synthesized by coprecipitation method, and its structure was confirmed by Fourier transform infrared (FTIR) spectrometer and X‐ray diffraction (XRD) measurements. Then, PET nanocomposites with LDH‐DMSI content of 0, 0.5, 1.0, and 2.0 wt% were prepared by in‐situ polymerization. The dispersion morphologies were observed by transmission electron microscopy (TEM) and XRD, showing that LDH‐DMSI was exfoliated in PET matrix. Thermal and mechanical properties, such as thermal stability, tensile modulus, and tensile yield strength of nanocomposites, were enhanced by exfoliated LDH‐DMSI nanolayers. However, elongation at break was drastically decreased with LDH loading owing to the increased stiffness and microvoids. The effect of exfoliated nanolayers, which acted as a nucleating agent confirmed by differential scanning calorimeter (DSC), on the microstructural parameters during isothermal crystallization, was analyzed by synchrotron small‐angle X‐ray scattering (SAXS). It is believed that nanocomposites could be crystallized more easily owing to the increased nucleation sites, which lead to the decrease of average amorphous region size and the long period with the increase of LDH‐DMSI content. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 28–40, 2007     

Homologous series of alkylsilylphenyl‐substituted poly (p‐phenylenevinylene)s for light‐emitting diodes

Substituent‐induced electroluminescence polymers—poly[2‐(2‐dimethyldodecylsilylphenyl)‐1,4‐phenylenevinylene] [(o‐R₃Si)PhPPV], poly[2‐(3‐dimethyldodecylsilylphenyl)‐1,4‐phenylenevinylene] [(m‐R₃Si)PhPPV], and poly[2‐(4‐dimethyldodecylsilylphenyl)‐1,4‐phenylenevinylene] [(p‐R₃Si)PhPPV]—were synthesized according to the Gilch polymerization method. The band gap and spectroscopic data were tuned by the dimethyldodecylsilyl substituent being changed from the ortho position to the para position in the phenyl side group along the polymer backbone. The weight‐average molecular weights and polydispersities were 8.0–96 × 10⁴ and 3.0–3.4, respectively. The maximum photoluminescence wavelengths for (o‐R₃Si)PhPPV, (m‐R₃Si)PhPPV, and (p‐R₃Si)PhPPV appeared around 500–530 nm in the green emission region. Double‐layer light‐emitting diodes with an indium tin oxide/poly(3,4‐ethylenedioxythiophene)/polymer/Al configuration were fabricated with these polymers. The turn‐on voltages and the maximum brightness of (o‐R₃Si)PhPPV, (m‐R₃Si)PhPPV, and (p‐R₃Si)PhPPV were 6.5–8.7 V and 1986–5895 cd/m², respectively. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2347–2355, 2004