Polymerization kinetics of phosphonic acids and esters using an iodonium initiator

Phosphonic acids are known to be useful monomers in dental restorative materials because of their good potential to provide enhanced adhesion to hydroxyapatite and their high hydrolytic stability. In this study, the photopolymerization of phosphonic acid‐based monomer via the camphorquinone (CQ)/ethyl‐4‐(dimethylaminobenzoate) (EDAB) photoredox system is compared with a ternary system composed of iodonium hexafluorophosphate and CQ/EDAB. Photocalorimetry shows that the ternary system does not provide a significant acceleration of the polymerization with either acrylamide or methacrylate phosphonic acids. The complexation of the iodonium by the phosphonic moiety of the acidic monomers leads to a lowered iodonium reactivity and reduced polarizability of the medium and as a consequence limits the rate enhancement effect normally observed by phosphonic acids on the polymerization rate. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 5046–5055     

Hydrophilic functionalization of syndiotactic polystyrene via a combination of electrophilic bromination and Suzuki–Miyaura reaction

Postfunctionalization of high‐molecular‐weight syndiotactic polystyrene (sPS) was achieved via combination of electrophilic bromination at the para‐position of the polymer aromatic ring and subsequent Suzuki–Miyaura cross‐coupling reactions with functionalized phenylboronic acids. The concentration of brominated styrene repeating unit in sPS was conveniently controlled by changing the ratio of added bromine relative to the polymer repeating unit. Brominated sPS (8.5 mol %) was converted quantitatively to other polar functional groups via Suzuki–Miyaura cross‐coupling reactions with various functional group‐substituted phenylboronic acids. The surface properties of functionalized sPS were studied by measuring water contact angles. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4335–4343, 2010     

A linear wave equation with a nonlinear boundary condition of viscoelastic type

The paper is devoted to the study of a linear wave equation with a nonlinear boundary condition of viscoelastic type. The existence of a weak solution is proved by using the Faedo–Galerkin method. The uniqueness, regularity and asymptotic expansion of the solution are also discussed.     

Determination of four acidic nonsteroidal anti‐inflammatory drugs in wastewater samples by dispersive liquid–liquid microextraction based on solidification of floating organic droplet and high‐performance liquid chromatography

A simple, environmentally friendly, and sensitive dispersive liquid–liquid microextraction based on solidification of floating organic droplet for the extraction of four acidic nonsteroidal anti‐inflammatory drugs (ketoprofen, naproxen, ibuprofen, and diclofenac) from wastewater samples subsequent by high‐performance liquid chromatography analysis was developed. The influence of extraction parameters such as pH, the effect of solution ionic strength, type of extraction solvent, disperser solvent, and extraction solvent volume were studied. High enrichment factors (283–302) were obtained through the developed method. The method provides good linearity (r > 0.999) in a concentration range of 1–100 μg/L, good intra‐ and inter‐day precision (relative standard deviation < 7%) and low limits of quantification. The relative recoveries of the selected compounds were situated over 80% both in synthetic and real water samples. The developed method has been successfully applied for the analysis of the selected compounds in wastewater samples.     

Simple and rapid synthesis of ternary polyaniline/titanium oxide/graphene by simultaneous TiO<Subscript>2</Subscript> generation and aniline oxidation as hybrid materials for supercapacitor applications

This paper reports a simple methodology for the synthesis of a polyaniline/titanium oxide/graphene hybrid (Pani/TiO₂/GN) using a simple methodology, and their application as a supercapacitor electrode material for energy storage. The Pani/TiO₂/GN hybrid was prepared by a simple approach by simultaneous generation of Pani and TiO₂ in situ from aniline and titanium iso-propoxide, respectively, in the presence of GN under ice bath conditions. The incorporation of GN improved the electrical conductivity of Pani and helped to decrease the charge transfer resistance, whereas TiO₂ generation by an in situ method increased the surface area considerably and enhanced the capacitance of the Pani/TiO₂/GN hybrid. TEM showed that Pani and TiO₂ were well incorporated and coated on the GN successfully. The shift of the peaks in the FTIR spectrum and XRD pattern of the Pani/TiO₂/GN hybrid compared to their pure counterparts suggested that TiO₂ and Pani had been perfectly coated on the GN, and there was a strong interaction among Pani, GN, and TiO₂ particles. The electrochemical performance of the as-prepared Pani/TiO₂/GN hybrid electrode showed a high specific capacitance of 403.2 F g^?1 at a current density of 2 A g^?1 and excellent cycling stability for up to 1000 cycles. This suggested that the effective incorporation of GN and TiO₂ into Pani and the high surface area could simultaneously increase the electrochemical capacitance and cyclic stability of the Pani/TiO₂/GN hybrid, leading to superior electrochemical performance.

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Graphical abstract The electrochemical performance of as-prepared Pani/TiO₂/GN hybrid electrode showed a high specific capacitance of 403.2 F g^?-1 at a current density of 2 A g^?-1 and excellent cycling stability for up to 1000 cycles. This suggested that the effective incorporation of GN and TiO₂ into Pani and the high surface area could simultaneously increase the electrochemical capacitance and cycle stability of the Pani/TiO₂/GN hybrid, leading to superior electrochemical performance.

     

On the Stability and Solution Sensitivity of a Consumer Problem

We present a continuous-time generalization of the seminal research and development model of d’Aspremont and Jacquemin (Am Econ Rev 78(5):1133–1137, 1988) to examine the trade-off between the benefits of allowing firms to cooperate in research and the corresponding increased potential for product market collusion. We show the existence of a solution to the optimal investment problem using a combination of results from viscosity theory and the theory of planar dynamical systems. In particular, we show that there is a critical level of marginal cost at which firms are indifferent between doing nothing and starting to develop the technology. We find that colluding firms develop further a wider range of initial technologies, pursue innovations more quickly, and are less likely to abandon a technology. Product market collusion could thus yield higher total surplus.     

On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.