Infrared spectral changes with crystallization in poly(vinylchloride): Correlations with X-ray and density data

The influence of crystallinity and stereoregularity on the infrared (IR) spectrum of atactic PVC in the solid state has been studied by many researchers [1-12]. Although the molecules in commercial PVC consist of both syndiotactic and isotactic sequences, the bulk polymer is not highly stereoregular, having approximately 50% syndiotacticity. Its infrared spectrum is different from that of highly syndiotactic PVC [3,5,7,9,10-12], particularly in the carbon-to-chlorine stretching region where there are three bands located at 610(615), 635, and 690 cm^?1. These three bands are known to be of complex origin, since each band consists of more than one absorption frequency and its relative intensity depends on the physical state or history of the specimen [3,5,7,9,10-12]. The spectrum in this region is most rigorously interpreted in terms of chain conformational structure, the spatial arrangement of the atoms around the C-C1 bond. Thus, while changes in absorbance intensities for the bands with history do not necessarily reflect changes in crystallinity, their history dependence renders these bands potentially useful as crystallinity indicators.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.     

Mechanism of white phosphorus activation by three-coordinate molybdenum(III) complexes: a thermochemical, kinetic, and quantum chemical investigation

White phosphorus (P(4)) reacts with three-coordinate molybdenum(III) trisamides or molybdaziridine hydride complexes to produce either bridging or terminal phosphide (P(3)(-)) species, depending upon the ancillary ligand steric demands. Thermochemical measurements have been made that place the MoP triple bond dissociation enthalpy at 92.2 kcal.mol(-)(1). Thermochemical measurements together with computational analysis rule out simple P-atom abstraction from P(4) as a step in the phosphorus activation mechanism. Kinetic measurements made by the stopped-flow method show that the reaction between the monomeric molybdenum complexes and P(4) is first-order both in metal complex and in P(4). Cyclo-P(3) complexes can be obtained when ancillary ligand steric demands are small, but kinetic measurements rule them out as monometallic intermediates in the P(4) activation mechanism. Also studied by calorimetric, kinetic, and in one case variable-temperature NMR methods is the process of mu-phosphide bridge formation. Post-rate-determining steps of the P(4) activation process were examined in a search for minima on the reaction's potential energy surface, leading to the proposal of two plausible, parallel, bimetallic reaction channels.     

Characterization of the aggregates of N-alkyl-N-methylpyrrolidinium bromide surfactants in aqueous solution

We have characterized a new class of surfactant molecules using fluorescence spectroscopic and light-scattering techniques. Our results suggest that this homologous series of N-alkyl-N-methlypyrrolidinium bromide (CnMPB) surfactants with n = 10, 12, 14, 16, and 18 represents a bridge between the well-characterized alkyltrimethylammonium bromide (CnTAB) and dialkyldimethylammonium bromide (di-CnDAB) surfactant series. For the smaller members of the CnMPB series with n = 10, 12, and 14, our results are consistent with the formation of spherical micelles as the surfactant concentration is increased. With increasing alkyl chain length, we observe that the critical micelle concentration decreases and the aggregation number increases, typical of single-tail surfactants. For C16MPB, the formation of micelles at dilute concentrations (0.10 mM) is likely, followed by the coexistence of micelles and small unilamellar vesicles at higher concentrations up to 0.82 mM where only vesicles are present. For C18MPB, our data are consistent with the formation of vesicles only. We demonstrate in this study that the combination of spectroscopic and light-scattering methods is a powerful approach to reveal aspects of aggregate structure and morphology in aqueous CnMPB surfactant systems. In particular, the sensitivity of the fluorescence probe prodan to the polarity of its microenvironment enables the rich complexity of surfactant aggregates exhibited by this series of amphiphilic molecules to be detected.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Quasi-Symmetric Designs with Good Blocks

The article is concerned with a characterization of quasi-symmetric (QS) designs with intersection numbers 0 and y. It uses the idea of a good block. Such a block G has the property that for any block B with |G ∩ B| = y, every point is on a block containing G ∩ B. It is proved that if a QS design II with intersection numbers 0 and y has a good block, then II must (i) be affine, symmetric, a linear space or (ii) have one of two possible exceptional parameter sets. Only one example is known in case (ii). If all blocks of II are good and II is not a linear space, then it is a projective or affine geometry or it is an extension (in a more general sense than usual) of a projective plane of order y² or y³+ y. © 1995 John Wiley & Sons, Inc.     

Breakdown of stabilization of atoms interacting with intense, high-frequency laser pulses

An analysis of the influence of the magnetic field of an intense, high-frequency laser pulse on the stabilization of an atomic system is presented. We demonstrate that at relatively modest intensities the magnetic field can significantly alter the dynamics of the system. In particular, a breakdown of stabilization occurs, thereby restricting the intensity regime in which the atom is relatively stable against ionization. Counterpropagating pulses do not negate the detrimental effects of the magnetic field. We compare our quantum mechanical results with classical Monte Carlo simulations.