UV–visible spectroscopy for zirconocene activation by MAO in olefin polymerization: activity versus wavenumber

Activation of ansa‐zirconocenes of the type Rac [Zr{1‐Me₂Si(3‐R‐(η⁵‐C₉H₅))(3‐R′‐(η⁵‐C₉H₅))}Cl₂] [R = Et, R′ = H ( 1 ); R = Pr, R′ = H ( 2 ); and R = Et, R′ = Pr ( 3 ), R, R′ = Me ( 4 ) and R, R′ = Bu ( 5 )] by MAO has been studied by UV–visible spectroscopy. Compounds 1–3 have been tested in the polymerization of ethylene at different Al:Zr ratios. UV–vis spectroscopy was used to determine a correlation between the electronic structures of ( 1–5 ) and their polymerization activity. Copyright © 2009 John Wiley & Sons, Ltd.     

Nanorod near-field radiative heat exchange analysis

A theoretical method for cylinder-to-cylinder radiative heat exchange is formulated. The method utilized was a modified version of a previously published numerical method for near-field sphere-to-sphere radiative exchange. Modifications were made to the numerical procedure to make it applicable to cylindrical geometry of nanorods. Nanorods investigated had length to diameter ratios of 3:1 and 7:1. The heat exchange of nanorods is plotted vs. gap to assess the impact of near-field radiative transfer as gap decreases. Graphical results of energy vs. nanorod radii are also presented. A nanorod-to-plane configuration is estimated utilizing a nanorod asymptotic method. The nanorod-to-nanorod method approximates a nanorod-to-plane geometric configuration when one nanorod radii is held constant, and the second nanorod radii is iteratively increased until the corresponding radiative exchange converges.     

A multicomponent approach to the synthesis of 1,3-dicarbonylic compounds

A general synthesis of 1,3-dicarbonylic compounds using multicomponent reactions of isocyanides is described. The process involves a Passerini three-component condensation of glyoxal derivatives, isocyanides and acetic acid, followed by metal mediated reductive or solvolytic removal of the acid component. Noteworthy, reductive deacetoxylation of Passerini glyoxylamide adducts was successfully achieved using photochemically activated SmI₂. This procedure constitutes a novel convenient method for the direct synthesis of malonic retro-peptidic subunits.     

Chains are more flexible under tension

The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely-jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility. In many experimental situations the choice is not clear and a model describing the crossover between these two limiting classes is therefore in high demand. We are proposing a unified chain deformation model which describes the force-deformation curve in terms of the chain bending constant K and bond length b. This model demonstrates that the worm-like and freely-jointed chain models correspond to two different regimes of polymer deformation and the crossover between these two regimes depends on the chain bending rigidity and the magnitude of the applied force. Polymer chains with bending constant K>1 behave as a worm-like chain under tension in the interval of the applied forces f ≤ Kk(B)T/b and as a freely-jointed chain for f ≥ Kk(B)T/b (k(B) is the Boltzmann constant and T is the absolute temperature). The proposed crossover expression for chain deformation is in excellent agreement with the results of the molecular dynamics simulations of chain deformation and single-molecule deformation experiments of biological and synthetic macromolecules.     

Entropy Solutions for Nonlinear Degenerate Problems

We consider a class of elliptic-hyperbolic degenerate equations g(u)-Db(u) +\divgf(u) = fg(u)-\Delta b(u) +\divg\phi (u) =f with Dirichlet homogeneous boundary conditions and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)_t-Db(u) +\divgf(u) = fg(u)_t-\Delta b(u) +\divg\phi (u) =f with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function J satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for J continuous.     

Conservation laws with discontinuous flux functions and boundary condition

In a bounded domain we study the existence and uniqueness of entropy solutions of , where is allowed to have some discontinuities of first type.     

Asymptotic Complexity in Filtration Equations

We show that the solutions of nonlinear diffusion equations of the form u _t = ΔΦ(u) appearing in filtration theory may present complicated asymptotics as t → ∞ whenever we alternate infinitely many times in a suitable manner the behavior of the nonlinearity Φ. Oscillatory behaviour is demonstrated for finite-mass solutions defined in the whole space when they are renormalized at each time t > 0 with respect to their own second moment, as proposed in [Tos05, CDT05]; they are measured in the L ¹ norm and also in the Euclidean Wasserstein distance W ₂. This complicated asymptotic pattern formation can be constructed in such a way that even a chaotic behavior may arise depending on the form of Φ. In the opposite direction, we prove that the assumption that the asymptotic normalized profile does not depend on time implies that Φ must be a power-law function on the appropriate range of values. In other words, the simplest asymptotic behavior implies a homogeneous nonlinearity.