Synthesis, characterization and properties of naphthoxazine-functional poly(propyleneoxide)s

Thermally curable naphthoxazine-functionalized polymers were synthesized by the reaction of linear (diamines) and branched (triamines) poly(propyleneoxide)s (Jeffamine series) having various molecular weights, with p-formaldehyde, and 2-naphthol. The structures of the resulting polymers were characterized by using FT-IR and ¹H-NMR. In addition, curing behavior of these polymers was studied using differential scanning calorimeter (DSC). Hydrophilicity of these polymers, both in cured and non-cured states, was investigated by water contact angle measurements. The surface topographies of the polymers were also examined by atomic force microscope (AFM).     

A low-band gap conductive copolymer of bis-3-hexylthiophene substituted 4-tert-butylphenyl quinoxaline and 3,4-ethylenedioxythiophene

Electrochemical copolymerization of 2,3-bis(4-tert-butylphenyl)-5,8-bis(4-hexylthiophen-2-yl)quinoxaline (HTQ) and 3,4-ethylenedioxythiophene (EDOT) was performed to fulfill a strategy in achieving fine-tuned electrochromic properties. The copolymer, P(HTQ-co-EDOT) was characterized via detailed studies of cyclic voltammetry and spectroelectrochemistry. Copolymer film has many superior properties compared to the parent homopolymer. E _g of the copolymer was calculated as 1.4 eV, which is substantially lower than the homopolymer’s (PHTQ) band gap, which was reported as 1.75 eV. Optical contrast of the resultant copolymer was shown to be 34%, which is nearly 10% higher than the PHTQ. The most striking achievement in the electrochromic properties was in switching times. The copolymer switches very rapidly between its neutral and the oxidized states and achieves a 34% optical contrast in less than 1 s, half of the value for the pristine polymer.     

Electrochemical polymerization of 1-(4-nitrophenyl)-2,5-di(2-thienyl)-1 H-pyrrole as a novel immobilization platform for microbial sensing

Two types of bacterial biosensor were constructed by immobilization of Gluconobacter oxydans and Pseudomonas fluorescens cells on graphite electrodes modified with the conducting polymer; poly(1-(4-nitrophenyl)-2,5-di(2-thienyl)-1 H-pyrrole) [SNS(NO₂)]. The measurement was based on the respiratory activity of cells estimated by the oxygen consumption at − 0.7 V due to the metabolic activity in the presence of substrate. As well as analytical characterization, the linear detection ranges, effects of electropolymerization time, pH and cell amount were examined by using glucose as the substrate. The linear relationships were observed in the range of 0.25–4.0 mM and 0.2–1.0 mM for G. oxydans and P. fluorescens based sensors, respectively.     

On the polyhedral lift-and-project methods and the fractional stable set polytope

We study two polyhedral lift-and-project operators (originally proposed by Lovász and Schrijver in 1991) applied to the fractional stable set polytopes. First, we provide characterizations of all valid inequalities generated by these operators. Then, we present some seven-node graphs on which the operator enforcing the symmetry of the matrix variable is strictly stronger on the odd-cycle polytope of these graphs than the operator without this symmetry requirement. This disproves a conjecture of Lipták and Tunçel from 2003.     

High-performance flow-focusing geometry for spontaneous generation of monodispersed droplets

A high-performance flow-focusing geometry for spontaneous generation of monodispersed droplets is demonstrated. In this geometry, a two-phase flow is forced through a circular orifice integrated inside a silicon-based microchannel. The orifice with its cusp-like edge exerts a ring of maximized stress around the flow and ensures controlled breakup of droplets for a wide range of flow rates, forming highly periodic and reproducible dispersions. The droplet generation can be remarkably rapid, exceeding 10(4) s(-1) for water-in-oil droplets and reaching 10(3) s(-1) for oil-in-water droplets, being largely controlled by flow rate of the continuous phase. The droplet diameter and generation frequency are compared against a quasi-equilibrium model based on the critical Capillary number. The droplets are obtained despite the low Capillary number, below the critical value identified by the ratio of viscosities between the two phases and simple shear-flow.     

Determination of freezable water content of beef semimembranous muscle DSC study

The freezable water contents of samples obtained from previously chilled semimembranous muscle of middle-aged beef carcasses after a 24 h cooling period a room at in 5±1C were determined by differential scanning calorimetry (DSC) at –5, –10, –15, –20, –30, –40, –50 and –65C. This was accomplished by freezing the samples at the above-mentioned temperatures, followed by thawing to 35C, and measuring the melting peaks of freezable water. The areas of these peaks were determined by using the peak integration method programs through a computer linked to the DSC, and they were then used to determine the latent heat of melting (H _m) in kJ kg^–1 at each freezing temperature. The resultant latent heat of melting per sample was divided by the latent heat for pure water to determine the amount of freezable water present in these samples. This amount of freezable water was divided by the total water content of the meat sample to determine the percentage of freezable water in the sample. The percentage of freezable water was subtracted from 100 to determine the percentage of bound water present in the sample.     

A pyrolysis mass spectrometry study of polythiophene copolymers

The thermal behaviour of copolymers of thiophene with decanedioic acid bis-(2-thiophen-3-yl-ethyl)ester (DATE) and terephthalic acid bis-(2-thiophen-3-yl-ethyl)ester (TATE) prepared by potentiostatic polymerization was studied via pyrolysis mass spectrometry. It was determined that the electrolytic films correspond to the related homopolymers. The increase in thermal stability of ester linkages, and evolution of characteristic degradation products of TATE and DATE together with thiophene based products above 400 °C confirmed copolymer formation.     

Approximating the complexity measure of Vavasis-Ye algorithm is NP-hard

Given an m×n integer matrix A of full row rank, we consider the problem of computing the maximum of ∥B ^-1 A∥₂ where B varies over all bases of A. This quantity appears in various places in the mathematical programming literature. More recently, logarithm of this number was the determining factor in the complexity bound of Vavasis and Ye’s primal-dual interior-point algorithm. We prove that the problem of approximating this maximum norm, even within an exponential (in the dimension of A) factor, is NP-hard. Our proof is based on a closely related result of L. Khachiyan [1]. Received November 13, 1998 / Revised version received January 20, 1999? Published online May 12, 1999     

Synthesis of conducting block and graft copolymers with polyether segments

Synthesis of block and graft copolymers containing polyether and conducting polypyrrole sequences were described. Pyrrole moieties were incorporated at the chain ends of polytetrahydrofuran and polysiloxane and at the side chains of polyethyl vinylether by ionic polymerization and appropriate chemical reactions. Subsequent electropolymerization with pyrrole through these moities yielded free standing films of the corresponding block and graft copolymers. The formation copolymers was evidenced by FTIR spectroscopy and extraction with solvent of the precursor homopolymers. The thermal and morphological properties were also characterized. The two surface of the copolymer films generally differ in appearance, the surface at the solution side being cauliflowerlike or wrinkled, whereas the surface at the electrode side smooth. Conductivies of the copolymers were comparable with that of the pure polypyrrole.     

Invariance and efficiency of convex representations

We consider two notions for the representations of convex cones G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation. We first study the basic properties of these representations. We show that some basic properties of convex cones are invariant under one notion of representation but not the other. In particular, we prove that lifted-G-representation is closed under duality when the representing cone is self-dual. We also prove that strict complementarity of a convex optimization problem in conic form is preserved under G-representations. Then we move to study efficiency measures for representations. We evaluate the representations of homogeneous convex cones based on the “smoothness” of the transformations mapping the central path of the representation to the central path of the represented optimization problem. Research of the first author was supported in part by a grant from the Faculty of Mathematics, University of Waterloo and by a Discovery Grant from NSERC. Research of the second author was supported in part by a Discovery Grant from NSERC and a PREA from Ontario, Canada.