Convergence and Error Bound for Perturbation of Linear Programs

In various penalty/smoothing approaches to solving a linear program, one regularizes the problem by adding to the linear cost function a separable nonlinear function multiplied by a small positive parameter. Popular choices of this nonlinear function include the quadratic function, the logarithm function, and the x ln(x)-entropy function. Furthermore, the solutions generated by such approaches may satisfy the linear constraints only inexactly and thus are optimal solutions of the regularized problem with a perturbed right-hand side. We give a general condition for such an optimal solution to converge to an optimal solution of the original problem as the perturbation parameter tends to zero. In the case where the nonlinear function is strictly convex, we further derive a local (error) bound on the distance from such an optimal solution to the limiting optimal solution of the original problem, expressed in terms of the perturbation parameter.     

Phase studies and thermal stability of binary systems of cholesteric liquid crystals

The binary mixture of cholesteryl oleyl carbonate (COC) and cholesteryl nonanoate (CN) with different ratios has been characterized by differential scanning calorimetry (DSC) to determine the phase diagrams. Their normal shelf-life and accelerated stability studies were also examined. A novel microscopic Fourier-transform infrared (FT-IR) spectrometer equipped with DSC was also used to measure simultaneously the chemical structural variation and the thermal response of these liquid crystals. The results indicate that the binary mixture might transform from smectic to cholesteric and then to isotropic liquid (CN composition <50%); from solid to cholesteric and then to isotropic liquid (CN composition >50%). Therefore, the 50% CN composition might play a critical role in the phase transition of the binary COC-CN mixture. The microscopic FT-IR/DSCsystem could also confirm the phase transition, but could measure the phase trasition temperature of liquid crystals more easily and sharply than the DSC method. The long-term accelerated thermal stability of the COC-CN mixture seemed to be more constant when stored at 4 °C than in any other temperature conditions.     

Synthesis and characterization of novel poly(amide-imide)s containing hexafluoroisopropylidene linkage

A series of novel soluble poly(amide-imide)s were prepared from the diimide-dicarboxylic acid, 2,2-bis[N-(4-carboxyphenyl)-phthalimidyl]hexafluoropropane, with various diamines by the direct polycondensation in N-methyl-2-pyrrolidinone containing CaCl₂ using triphenyl phosphite and pyridine as condensing agents. All the polymers were obtained in quantitative yields with inherent viscosities of 0.78–1.63 dL g⁻¹. The polymers were amorphous and readily soluble in aprotic polar solvents such as N-methyl-2-pyrrolidinone, N,N-dimethylacetamide, N,N-dimethylformamide, and dimethyl sulfoxide as well as in less polar solvents such as pyridine and γ-butyrolactone, and also in tetrahydrofuran. The polymer films had tensile strength of 84–129 MPa, an elongation at break range of 6–22%, and a tensile modulus range of 2.0–2.7 GPa. The glass transition temperatures of the polymers were determined by DSC method and they were in the range of 240–282°C. These polymers were fairly stable up to a temperature around or above 400°C, and lose 10% weight in the range of 450–514°C and 440–506°C in nitrogen and air, respectively. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2629–2635, 1999     

Glass transition and miscibility in blends of two semicrystalline polymers: Poly(aryl ether ketone) and poly(ether ether ketone)

Binary melt‐blended mixtures of two aryl ether ketone polymers (i.e., a new poly(aryl ether ketone) (code name PK99) and poly(ether ether ketone) (PEEK), have been studied. Polymer miscibility in glassy amorphous (or melt) domains has been demonstrated for the binary blend comprising of two aryl‐ether‐ketone‐type semicrystalline polymers. Composition‐dependent, single T_g was observed within full composition range in the PK99/PEEK blends, and the narrow T_g breadth also suggests that the scale of mixing was fine and uniform. To better resolve any possible overlapping T_g's, physical aging was imposed on a comparison set of blend samples for the purpose of improving detectability of overlapped multiple transitions if existing. The result still showed one single T_g. The relative sharp T_g and lack of cloud point transition suggest that the scale of molecular intermixing is good. Phase homogeneity was further confirmed using optical and scanning electron microscopy. The X‐ray diffractograms suggest that isomorphism does not exist in the PK99/PEEK blends and that the crystal forms of the respective polymers remain distinct and unchanged by the miscibility in the amorphous region. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1485–1494, 1999     

On-Line Coupling of Separation Techniques to NMR

The hyphenation of chromatographic separation techniques with NMR spectroscopy is one of the most powerful and time-saving methods for the separation and structural elucidation of unknown compounds and molecular compositions of mixtures. Most of the routinely used NMR flow-cells have detection volumes between 40–180 μL for conventional separations with analytical columns, and the newest designs employ detection volumes in the order of 200 nL for capillary separations. The low flow rates used in capillary chromatography permit the use of deuterated solvents. Unequivocal structural assignment of unknown chromatographic peaks is possible by two-dimensional stopped-flow capillary HPLC-NMR experiments.     

Alternative method for measuring the phase retardation and fast axis of a wave plate

Optical Review - An alternative method is proposed for simultaneously measuring the phase retardation and fast axis angle of a wave plate by utilizing a radially polarized symmetric light beam. A...     

Micellar electrokinetic biofluid analysis of biogenic amines using on-line sample concentration and UV laser-induced native fluorescence detection

A simple and sensitive sweeping micellar electrokinetic chromatography method coupled with UV laser-induced native fluorescence detection has been developed for quantitative analysis of biogenic amines in biofluids. The background electrolyte comprised 30 mmol L⁻¹ phosphoric acid and 20 mmol L⁻¹ sodium dodecyl sulfate. The concentration limits of detection of analytes using sweeping-micellar electrokinetic chromatography (sweeping-MEKC) were in the range 7–100 nmol L⁻¹, which were 250–3600-fold improvement for dopamine, DOPA and epinephrine compared with conventional capillary zone electrophoresis. An improvement of approximately 20-fold was observed for all analytes compared with typical micellar electrokinetic chromatography conditions. Baseline separation was achieved for the all analytes within 12 min and migration-time and peak-area repeatability were better than RSD 0.35% and 5.68%, respectively. The developed method was applied to measure the biogenic amines in biofluids extracted from wheat phloem sap, human plasma and human urine.     

Thermal runaway evaluation of α-methylstyrene and trans-β-methylstyrene with benzaldehyde

Styrene is an important chemical in the petrochemical industry. In recent years, there have been sporadic releases, runaway reactions, fires, and thermal explosion accidents incurred by styrene and its derivatives worldwide. The purpose of this study was to estimate the impact of styrene and its derivatives of α-methylstyrene (AMS) and trans-β-methylstyrene (TBMS) contacting with benzaldehyde. Experiments were carried out to evaluate the thermokinetic parameters estimated by differential scanning calorimetry (DSC) and thermal activity monitor III (TAM III). TAM III was used to determine the fundamental thermokinetics under various isothermal temperatures, 80, 90 and 100°C. This autocatalytic reaction was demonstrated in thermal curves. After styrene was contacted with benzaldehyde, the exothermic onset temperature (T ₀) and the total heat of reaction (Q _total) were altered by DSC tests. When benzaldehyde is mixed with AMS and TBMS, the reaction time will be shorter but the enthalpy reduced, as revealed by TAM III tests. As AMS and TBMS, respectively, were contacted with benzaldehyde, both exothermic phenomena were changed during the reaction excursion. According to the results of this research, an operator should dictate the oxygen concentration in order to avoid any potential hazards during handling and transportation.     

Thermal hazard evaluation of carbon nanotubes with sulfuric acid by DSC

Many concerns over unsafe or unknown properties of multi-walled carbon nanotubes (MWNTs) have been raised. The thermal characteristics regarding stability would represent potential hazards during the production or utilization stage and could be determined by calorimetric tests for various thermokinetic parameters. Differential scanning calorimetry (DSC) was employed to evaluate the thermokinetic parameters for MWNTs at various compositions. Thermoanalytical curves showed that the average heat of decomposition (ΔH _d) of the MWNTs samples in a manufacturing process was about 31,723 J g⁻¹, by identifying them as an inherently hazardous material. In this study, significant thermal analysis appeared in the presence of sulfuric acid (H₂SO₄). From the DSC experiments, the purification process of MWNTs could induce an unexpected reaction in the condition of batch addition with reactants of H₂SO₄. The results can be applied for designing emergency relief system and emergency rescue strategies during a perturbed situation or accident.     

A Supramolecular Approach for Preparation of Size‐Controlled Nanoparticles

A supramolecular approach has been developed for the preparation of supramolecular nanoparticles (SNPs) with variable sizes (30–450 nm) from three different molecular building blocks using a cyclodextrin/adamantane recognition system. Positron emission tomography (PET) was employed to study the biodistribution and lymph node drainage of the SNPs in mice. The sizes of the SNPs affect their in vivo characteristics (see picture).