"Oscillating" metallocene catalysts: what stops the oscillation?

The 150 MHz (13)C NMR microstructural analysis of polypropylene samples produced with two representative "oscillating" metallocene catalysts of largely different steric hindrance, namely [(2-(3,5-di-tert-butyl-4-methoxyphenyl)indenyl)(2)ZrP](+) and [(2-phenylindenyl)(2)ZrP](+) (P = polymeryl), and the implications on the origin of the stereocontrol are presented and discussed in detail. The original mechanistic proposal of an "oscillation" between a rac-like (isotactic-selective) and a meso-like (nonstereoselective) conformation cannot explain the observed polymer configuration. The isotactic-stereoblock nature of the polymers obtained with the former catalyst proves unambiguously that the active cation "oscillates" between the two enantiomorphous rac-like conformations at an average frequency that, even at high propene concentration, is only slightly lower than that of monomer insertion. The less-hindered [(2-phenylindenyl)(2)ZrP](+) gives instead a largely stereoirregular polypropylene, which is the logical consequence of a faster ligand rotation; however, depending on the use conditions (in particular, on the nature of the cocatalyst and the polarity of the solvent), the polymerization products may also contain appreciable amounts of a fairly isotactic fraction. The peculiar microstructure of this fraction, with isotactic blocks of the same relative configuration spanned by very short atactic ones, rules out the possibility that the latter are due to an active species in meso-like conformation and points rather to a conformationally "locked" rac-like species with restricted ring mobility. The hypothesis of a stereorigidity induced by the proximity to a counteranion, which would play the role of the interannular bridge in the rac-bis(indenyl) ansa-metallocenes, was tested by computer modeling on a [rac-(2-phenylindenyl)(2)ZrMe(C(3)H(6))][B(C(6)F(5))(4)] ion couple and found viable.     

Three-Dimensional Analytical Solution for an Axisymmetric Biharmonic Problem

In this paper, we propose a method for the solution of the axisymmetric boundary value problem for a finite elastic cylinder with assigned stress and/or displacements acting on the ends and side. The technique utilizes the Love representation, which allows for reduction of the solution of the elastic problem to the search for a biharmonic function on a cylindrical domain. In the solution method suggested here, we write the Love function with a Bessel expansion and analyze in detail the conditions under which it is possible to differentiate the expansion term by term. We show that this is possible only for a restricted class of elastic solutions. In the general case, we introduce two new auxiliary functions of the z-coordinate. In this way, we obtain the general form of the axisymmetric biharmonic function, which is discussed in relation to certain specific boundary conditions applied on the side and ends of the cylinder. We obtain an exact explicit solution of practical interest for a cylinder with free ends and assigned displacements applied to the side.     

Existence of extremals for the Maz’ya and for the Caffarelli–Kohn–Nirenberg inequalities

This paper deals with some Sobolev-type inequalities with weights that were proved by Maz’ya in 1980 and by Caffarelli–Kohn–Nirenberg in 1984.     

Simultaneous Differential Pulse Voltammetric Determination of Ascorbic Acid and Caffeine in Pharmaceutical Formulations Using a Boron‐Doped Diamond Electrode

A cathodically pretreated boron‐doped diamond electrode was used for the simultaneous anodic determination of ascorbic acid (AA) and caffeine (CAF) by differential pulse voltammetry. Linear calibration curves (r=0.999) were obtained from 1.9×10^?5 to 2.1×10^?4 mol L^?1 for AA and from 9.7×10^?6 to 1.1×10^?4 mol L^?1 for CAF, with detection limits of 19 μmol L^?1 and 7.0 μmol L^?1, respectively. This method was successfully applied for the determination of AA and CAF in pharmaceutical formulations, with results equal to those obtained using a HPLC reference method.     

Photodegradation of poly(3-hydroxybutyrate)

The effect of ultraviolet radiation on the properties of poly(3-hydroxybutyrate) (PHB) was studied. The PHB investigated is produced from microbial fermentation using saccharose from sugarcane as the carbon source to the bacteria. The material was exposed to artificial UV-A radiation for 3, 6, 9 and 12 weeks. The photodegradation effect was followed by changes of molecular weight, of chemical and crystalline structures, of thermal, morphological, optical and mechanical properties, as well as of biodegradability. The experimental results showed that PHB undergoes both chain scission and crosslinking reactions, but the continuous decrease in its mechanical properties and the low amount of gel content upon UV exposure indicated that the scission reactions were predominant. Molar mass, melting temperature and crystallinity measurements for two layers of PHB samples with different depth suggested that the material has a strong degradation profile, which was attributed to its dark colour that restricted the transmission of light. Previous photodegradation initially delayed PHB biodegradability, due to the superficial increase in crystallinity seen with UV exposure. The possible reactions taking place during PHB photodegradation were presented and discussed in terms of the infrared and nuclear magnetic resonance spectra. A reference peak (internal standard) in the infrared spectra was proposed for PHB photodegradation.     

Macromolecular Diffusion in Self-Assembling Biodegradable Thermosensitive Hydrogels

Hydrogel formation triggered by a change in temperature is an attractive mechanism for in situ gelling biomaterials for pharmaceutical applications such as the delivery of therapeutic proteins. In this study, hydrogels were prepared from ABA triblock polymers having thermosensitive poly(N-(2-hydroxypropyl) methacrylamide lactate) flanking A-blocks and hydrophilic poly(ethylene glycol) B-blocks. Polymers with fixed length A blocks (~22 kDA) but differing PEG-midblock lengths (2, 4 and 10 kDa) were synthesized and dissolved in water with dilute fluorescein isothiocyanate (FITC)-labeled dextrans (70 and 500 kDA). Hydrogels encapsulating the dextrans were formed by raising the temperature. Fluorescence recovery after photobleaching (FRAP) studies showed that diffusion coefficients and mobile fractions of the dextran dyes decreased upon elevating temperatures above 25 °C. Confocal laser scanning microscopy and cryo-SEM demonstrated that hydrogel structure depended on PEG block length. Phase separation into polymer-rich and water-rich domains occurred to a larger extent for polymers with small PEG blocks compared to polymers with a larger PEG block. By changing the PEG block length and thereby the hydrogel structure, mobility of FITC-dextran could be tailored. At physiological pH the hydrogels degraded over time by ester hydrolysis, resulting in increased mobility of the encapsulated dye. Since diffusion can be controlled according to polymer design and concentration, plus temperature, these biocompatible hydrogels are attractive as potential in situ gelling biodegradable materials for macromolecular drug delivery.     

Beliefs and engagement structures: behind the affective dimension of mathematical learning

Beliefs influencing students’ mathematical learning and problem solving are structured and intertwined with larger affective and cognitive structures. This theoretical article explores a psychological concept we term an engagement structure, with which beliefs are intertwined. Engagement structures are idealized, hypothetical constructs, analogous in many ways to cognitive structures. They describe complex “in the moment” affective and social interactions as students work on conceptually challenging mathematics. We present engagement structures in a self-contained way, paying special attention to their theoretical justification and relation to other constructs. We suggest how beliefs are characteristically woven into their fabric and influence their activation. The research is based on continuing studies of middle school students in inner-city classrooms in the USA.     

Genuine quantum and classical correlations in multipartite systems

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.     

Solvability of the Dirichlet Problem in W~（2,p ）for a Class of Elliptic Equations with Singular Data

We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.