Synthesis and Reactivity of the First Isolated Hydrogen‐Bridged Silanol–Silanolate Anions

We report on the first examples of isolated silanol–silanolate anions, obtained by utilizing weakly coordinating phosphazenium counterions. The silanolate anions were synthesized from the recently published phosphazenium hydroxide hydrate salt with siloxanes. The silanol–silanolate anions are postulated intermediates in the hydroxide‐mediated polymerization of aryl and alkyl siloxanes. The silanolate anions are strong nucleophiles because of the weakly coordinating character of the phosphazenium cation, which is perceptible in their activity in polysiloxane depolymerization.     

Triphilic pentablock copolymers with perfluoroalkyl segment in central position

Adding perfluoroalkyl (PF) segments to amphiphilic copolymers yields triphilic copolymers with new application profiles. Usually, PF segments are attached as terminal blocks via Cu(I) catalyzed azide-alkyne cycloaddition (CuAAC). The purpose of the current study is to design new triphilic architectures with a PF segment in central position. The PF segment bearing bifunctional atom transfer radical polymerization (ATRP) initiator is employed for the fabrication of triphilic poly(propylene oxide)-b-poly(glycerol monomethacrylate)-b-PF-b-poly(glycerol monomethacrylate)-b-poly(propylene oxide) PPO-b-PGMA-b-PF-b-PGMA-b-PPO pentablock copolymers by a combined ATRP and CuAAC reaction approach. Differential scanning calorimetry indicates the PF-initiator to undergo a solid–solid phase transition at 63°C before the final crystal melting at 95°C. This is further corroborated by polarized optical microscopy and X-ray diffraction studies. The PF-initiator could successfully polymerize solketal methacrylate (SMA) under typical ATRP conditions producing well-defined Br-PSMA-b-PF-b-PSMA-Br triblock copolymers that are then converted into PPO-b-PSMA-b-PF-b-PSMA-b-PPO pentablock copolymer via CuAAC reaction. Subsequently, acid hydrolysis of the PSMA blocks afforded water soluble well-defined triphilic pentablock copolymers PPO-b-PGMA-b-PF-b-PGMA-b-PPO with fluorophilic central segment, hydrophilic middle blocks, and lipophilic outer blocks. The triphilic block copolymers could self-assemble, depending upon the preparatory protocol, into spherical and filament-like phase-separated nanostructures as revealed by transmission electron microscopy.     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

Conceptual continuity as a mode of understanding complex systems: Applications to the dynamics sociopolitical systems

In complex biological systems, entities that are conceptually distinct but empirically related—such as sunlight and plant growth or antigene and immune response—are being explicitly linked through the identification of highly specific uninterrupted interaction sequences that take place between their macromolecular system components. These uninterrupted sequences of causation include common elements that are shared by the empirically related but conceptually distinct entities. Through the identification of specific shared elements, “conceptual continuity” is established between these entities. Examples are introduced to suggest that in sociopolitical systems, an analogous conceptual continuity can be established between distinct sociopolitical entities. The identification of specific shared elements, essential for the well being of each of the entities, can play a significant role in resolving conflicts between those separated by seemingly insurmountable obstacles such as race or religion or ideology. © 2006 Wiley Periodicals, Inc. Complexity 11:20–24, 2006     

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