New cyclen-cored dendrimers functionalized with pyrene: Synthesis characterization,optical and photophysical properties

New cyclen (1,4,7,10-teraazacyclododecane) cored dendrimers up to the second generation, functionalized with 4, 8 and 16 pyrene units, respectively, were synthesized following a convergent procedure. All new compounds were characterized by NMR spectroscopies and ESI or MALDI TOF mass spectrometry. The optical and photophysical properties of the new dendrimers were studied in THF solution. Absorption spectra showed the typical absorption bands of pyrene moieties. In the fluorescence spectra, monomer as well as excimer emission were observed for all compounds. An increased proportion of excimer emission was observed in the dendrimer of the highest generation.     

Polyelectrolytes Multilayers to Modulate Cell Adhesion: A Study of the Influence of Film Composition and Polyelectrolyte Interdigitation on the Adhesion of the A549 Cell Line

Polyelectrolyte multilayers (PEMs) with different polycation/polyanion pairs are fabricated by the layer‐by‐layer technique employing synthetic, natural, and both types of polyelectrolytes. The impact of the chemical composition of PEMs on cell adhesion is assessed by studying cell shape, spreading area, focal contacts, and cell proliferation for the A549 cell line. Cells exhibit good adhesion on PEMs containing natural polycations and poly(sodium 4‐styrenesulfonate) (PSS) as polyanion, but limited adhesion is observed on PEMs fabricated from both natural polyelectrolytes. PEMs are then assembled, depositing a block of natural polyelectrolytes on top of a stiffer block with PSS as polyanion. Cell adhesion is enhanced on top of the diblock PEMs compared to purely natural PEMs. This fact could be explained by the interdigitation between polyelectrolytes from the two blocks. Diblock PEM assembly provides a simple means to tune cell adhesion on biocompatible PEMs.

     

A Cahn‐Hilliard–type equation with application to tumor growth dynamics

We consider a Cahn‐Hilliard–type equation with degenerate mobility and single‐well potential of Lennard‐Jones type. This equation models the evolution and growth of biological cells such as solid tumors. The degeneracy set of the mobility and the singularity set of the cellular potential do not coincide, and the absence of cells is an unstable equilibrium configuration of the potential. This feature introduces a nontrivial difference with respect to the Cahn‐Hilliard equation analyzed in the literature. We give existence results for different classes of weak solutions. Moreover, we formulate a continuous finite element approximation of the problem, where the positivity of the solution is enforced through a discrete variational inequality. We prove the existence and uniqueness of the discrete solution for any spatial dimension together with the convergence to the weak solution for spatial dimension d=1. We present simulation results in 1 and 2 space dimensions. We also study the dynamics of the spinodal decomposition and the growth and scaling laws of phase ordering dynamics. In this case, we find similar results to the ones obtained in standard phase ordering dynamics and we highlight the fact that the asymptotic behavior of the solution is dominated by the mechanism of growth by bulk diffusion.     

Polyethylene waxes by metallocenes

The syntheses of low‐molecular‐weight polyethylene (PE), in the presence of catalysts based on five different metallocene frameworks, have been compared. High yields and low molecular masses, typical of industrially relevant PE waxes, can be easily achieved by using overpressure of hydrogen. Particularly suitable for the production of PE waxes are catalytic systems based on the C₂ symmetric rac‐dimethyl‐silyl‐bis‐(2‐methyl‐4‐phenyl‐1‐indenyl)‐zirconium dichloride ( 1 ) and the C_2v symmetric bis‐cyclopentadienyl‐zirconium dichloride ( 5 ). The wax yields can be substantially increased by increasing the MAO/Zr molar ratio. The control of the PE molecular weight allows an easy control of physical properties. In fact, as M_n increases in the range 10³–10⁴ g/mol, the degree of crystallinity decreases from nearly 85 to 60% while the melting temperature increases from 125°C up to 135°C. Copyright © 2010 John Wiley & Sons, Ltd.     

Some isoperimetric inequalities in a special case of the problem of torsional creep

We deal with the problem of torsional creep in multiply connected domains. By symmetrization techniques we derive some isoperimetric inequalities