Nuclear magnetic resonance relaxometry as a spectroscopic probe of the coordination sphere of a paramagnetic metal bound to a humic acid mixture

Protons on water molecules are strongly affected by paramagnetic ions. Since the acid-base properties of water facilitate rapid proton exchange, a single proton nuclear magnetic resonance (NMR) signal is seen in aqueous solutions of paramagnetic ions. Proton relaxation times are significantly affected by paramagnetic species and the readily detectable single signal serves as a powerful amplifier of the information contained concerning the protons in the paramagnetic environment. Where water molecules coordinated to free paramagnetic ions and to metal complexes of ligands that form non-labile (on the NMR time scale) complexes, the effects on water in the two environments can be distinguished. This can provide information on the nature of the ligand binding sites. The example of Cu²⁺ bound to the Laurentian humic acid mixture reported here using convenient low field NMR relaxometers shows that the information can enrich our understanding of complexation and speciation in the presence of complex mixture ligands characteristic of natural water systems. In this case, the data underline the role of aggregation and conformation in defining the complexation sites.     

Dynamic Optimization of Molecular Weight Distribution Using Orthogonal Collocation on Finite Elements and Fixed Pivot Methods: An Experimental and Theoretical Investigation

In the present study, two numerical methods, namely the orthogonal collocation on finite elements and the fixed pivot technique, are employed to calculate the MWD in an MMA free‐radical batch suspension polymerization reactor operating up to very high conversions (e.g., ≥95%). The theoretical MWD predictions are directly compared with experimentally measured MWDs, obtained from a pilot‐scale batch MMA suspension polymerization reactor. It is shown that there is a very good agreement between model predictions and experimental measurements on both monomer conversion and MWD. Subsequently, two different time‐optimal temperature trajectories are calculated to obtain a polymer having either a narrow or a bimodal MWD in minimum batch time. The calculated time optimal trajectories are then applied, as set point temperature changes, to a pilot plant batch polymerization reactor. It is shown that the measured MWDs are in very good agreement with the off‐line calculated optimal MWDs.

     

31P NMR spectroscopy in the quality control and authentication of extra-virgin olive oil: a review of recent progress

This review is a brief account on the application of a novel methodology to the quality control and authentication of extra-virgin olive oil. This methodology is based on the derivatization of the labile hydrogens of functional groups, such as hydroxyl and carboxyl groups, of olive oil constituents with the phosphorus reagent 2-chloro-4,4,5,5-tetramethyldioxaphospholane, and the use of the (31)P chemical shifts to identify the phosphitylated compounds. Various experimental aspects such as pertinent instrumentation, sample preparation, acquisition parameters and properties of the phosphorus reagent are reviewed. The strategy to assign the (31)P signals of the phosphitylated model compounds and olive oil constituents by employing 1D and 2D NMR experiments is presented. Finally, the capability of this technique to assess the quality and the genuineness of extra-virgin olive oil and to detect fraud is discussed.     

Model block copolymers with complex architecture

The synthesis of non linear block copolymers of the type (BA)₂B (3-miktoarm star copolymer), (BA)₃B (4-miktoarm star copolymer), (BA)₃B(AB)₃ (super H-shaped), B₂AB₂ (H-shaped) and (B,A)A(B,A) (π-shaped), where A is polyisoprene 1,4 and B is polystyrene was performed using anionic polymerization techniques and suitable chlorosilane chemistry. Characterization data showed that the samples are molecularly and compositionally homogeneous. TEM, SAXS and SANS were used to study the microphase behavior of the copolymers. For all samples, the results were analyzed in the frame of the theoretical predictions given by Milner and taking into account the results from previous studies on the A₂B and A₃B miktoarm star copolymers.     

Prediction of the Bivariate Molecular Weight‐Long Chain Branching Distribution in High‐Pressure Low‐Density Polyethylene Autoclaves

In the present study a population balance approach is described to follow the time evolution of bivariate molecular weight‐long chain branching (MW‐LCB) distributions in high pressure low density polyethylene autoclaves. The model formulation is based on a sectional grid method, the so‐called fixed pivot technique (FPT). According to this method, the ‘live’ and ‘dead’ polymer chain populations are assigned to a selected number of discrete points. Then, the resulting dynamic discrete‐continuous molar species equations for ‘live’ and ‘dead’ polymer chains are solved at the specified grid points. It is shown that a very good agreement exists between theoretical results and experimental data which proves the capability of the FPT method in calculating the joint MW‐LCB distribution for branched polymers.

     

Nanohybrids based on polymeric ionic liquid prepared from functionalized MWCNTs by modification of anionically synthesized poly(4‐vinylpyridine)

We report the synthesis of a composite material comprised of poly(4‐vinylpyridine) (P4VP) grafted on multiwall carbon nanotubes (MWCNTs) and the preparation of a nanohybrid via quaternization of the nitrogen atom per monomeric unit of the polymer chains. 4‐Vinylpyridine was polymerized anionically using high vacuum techniques and was reacted with MWCNTs under vacuum to be grafted on the polymer segments. The composite material was soluble in common solvents and the dispersion of the carbon nanotubes was improved after quaternization due to the formation of polymeric ionic liquid (PIL) of the MWCNTs‐g‐[P4VP‐r‐poly(4ViEtPy⁺Br^‐)] type. The successful synthesis was confirmed with Fourier‐transform infrared and Raman spectroscopies, whereas differential scanning calorimetry was adopted to verify the stability of the polymer's glass transition temperature before and after grafting on the MWCNTs. Moreover, thermogravimetric analysis was used for examining the thermal stability and the PIL formation of the composite. Energy dispersive spectroscopy measurements confirm the precipitation of silver bromide when the MWCNTs‐g‐[P4VP‐r‐poly(4ViEtPy⁺Br^‐)] is reacted with silver nitrite indicating the successful quaternization and formation of the appropriate PIL. High temperature size exclusion chromatography was used for the determination of the molecular characteristics (average molecular weight by number $\overline M _n$ , polydispersity I) of the homopolymer obtained from the filtration of the composite material. Finally, field‐emission scanning electron microscopy was used to verify the successful grafting of the polymer to the MWCNTs. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

On the arithmetically cohen-macaulay property for monomial curves

Let C be a monomial curve in three dimensional projective space over a field of characteristic zero . We give a necessary criterion for a monomial curve to be set theoretic complete intersection on bihomogeneous surfaces. Using this criterion we prove several results concerning the arithmetically Cohen-Macaulay property for monomial curves.     

Robust risk management

Estimating the probabilities by which different events might occur is usually a delicate task, subject to many sources of inaccuracies. Moreover, these probabilities can change over time, leading to a very difficult evaluation of the risk induced by any particular decision. Given a set of probability measures and a set of nominal risk measures, we define in this paper the concept of robust risk measure as the worst possible of our risks when each of our probability measures is likely to occur. We study how some properties of this new object can be related with those of our nominal risk measures, such as convexity or coherence. We introduce a robust version of the Conditional Value-at-Risk (CVaR) and of entropy-based risk measures. We show how to compute and optimize the Robust CVaR using convex duality methods and illustrate its behavior using data from the New York Stock Exchange and from the NASDAQ between 2005 and 2010.