Polystyrene-graft-polyglycerol resins: a new type of high-loading hybrid support for organic synthesis

The preparation of a dendritic graft polymer by a very efficient synthesis of polyglycerol directly on a polystyrene resin is presented. This one-step process can be performed on a multigram scale to provide a chemically stable polymeric support. The resulting hybrid polymers were fully characterized by diverse analytical methods (NMR, IR, ESEM, UV detection of cleaved protecting groups, and mass-spectrometric methods). They combine a high loading capacity (up to 4.3 mmol g(-1)) with good swelling properties in a wide range of solvents (including water), which is the major drawback for many existing solid phase supports. In comparison to the widely employed PEGylated resins, these hybrid materials offer a 10-fold higher loading capacity. Their suitability as supports for organic synthesis and for the immobilization of reagents has been demonstrated. These materials also swell in water, and consequently, it should be possible to use these new hybrid materials for synthesis in protic solvents.     

Some Algebraic Features of Z2-graded KK-Theory

We study the relation of Z₂equivariant and Z₂graded KK-theory. The former is the universal stable, split exact and homotopy invariant theory on the category of Z₂graded C^*algebras and graded homomorphisms (Theorem 1). We obtain an abstract characterization for the product of the graded KK-functor (Theorem 2). We give generalizations to Z₂graded C^*algebras of the Universal Coefficent Theorem, Künneth Theorem and Künneth Theorem for tensor products. We prove some results about graded crossed products of Thom isomorphism and Pimsner-Voiculescu type (Theorem 3 and Corollary 2) and compute an example. We obtain a split surjective map KK(A,B) KK(A⁰,B⁰) commuting with products, where A⁰is a canonically defined trivially graded algebra for any Z₂-graded A.     

Editorial note

Communications in Mathematical Physics -     

Secondary and primary relaxations in hyperbranched polyglycerol: a comparative study in the frequency and time domains

The non-Debye relaxation behavior of hyperbranched polyglycerol was investigated by broadband dielectric spectroscopy. A thorough study of the relaxations was carried out paying special attention to truncation effects on deconvolutions of overlapping processes. Hyperbranched polyglycerol exhibits two relaxations in the glassy state named in increasing order of frequency beta and gamma processes. The study of the evolution of these two fast processes with temperature in the time retardation spectra shows that the beta absorption is swallowed by the alpha in the glass-liquid transition, the gamma absorption being the only relaxation that remains operative in the liquid state. In heating, a temperature is reached at which the alpha absorption vanishes appearing the alphagamma relaxation. Two characteristics of alpha absorptions, decrease of the dielectric strength with increasing temperature and rather high activation energy, are displayed by the alphagamma process. Williams' ansatz seems to hold for these topologically complex macromolecules.     

Controlled synthesis of cell-laden microgels by radical-free gelation in droplet microfluidics

Micrometer-sized hydrogel particles that contain living cells can be fabricated with exquisite control through the use of droplet-based microfluidics and bioinert polymers such as polyethyleneglycol (PEG) and hyperbranched polyglycerol (hPG). However, in existing techniques, the microgel gelation is often achieved through harmful reactions with free radicals. This is detrimental for the viability of the encapsulated cells. To overcome this limitation, we present a technique that combines droplet microfluidic templating with bio-orthogonal thiol-ene click reactions to fabricate monodisperse, cell-laden microgel particles. The gelation of these microgels is achieved via the nucleophilic Michael addition of dithiolated PEG macro-cross-linkers to acrylated hPG building blocks and does not require any initiator. We systematically vary the microgel properties through the use of PEG linkers with different molecular weights along with different concentrations of macromonomers to investigate the influence of these parameters on the viability and proliferation of encapsulated yeast cells. We also demonstrate the encapsulation of mammalian cells including fibroblasts and lymphoblasts.     

Stability and equilibrium states

For an infinite dynamical quantum system idealized as aC*-algebra acted upon by time-translations automorphisms in an asymptotically abelian way, we propose to characterize equilibrium states by the three properties of stationarity, stability for local perturbations of the dynamics, and relative purity. We show that a state with these properties either gives rise to a one-sided energy spectrum or is a KMS- (i.e. essentially a limit Gibbs-) state.