The matrix version of the truncated Hamburger moment problem is considered. The criterium of its solvability is specified and a matrix version of the scalar Nevanlinna formula describing all possible solutions is established. As a main tool methods of the theory of extensions of symmetric operators and, in particular, the M.G. Krein formula for generalized resolvents are used.
We synthesized a series of hybrid nanomaterials combining organic dyes with polyhedral oligomeric silsesquioxanes (POSS) based on three different azobenzenes: monoazobenzene (4-phenylazophenol), bis-azobenzene (Disperse Yellow 7 and Fast Garnet derivative), and push-pull azobenzene (Disperse Red 1) via hydrosilylation coupling. The azo-functionalized POSS compounds possess high thermal stability, and their branched architecture resulted in effective suppression of molecular aggregation and allowed for direct imaging of individual dye-POSS structures with expected molecular dimensions. Stable, uniform, smooth, and ultrathin nanocomposite films with mixed silica-organic composition and relatively low refractive indices can be fabricated from all azo-POSS branched conjugates. Finally, the photoisomerization behavior of POSS-conjugated 4-phenylazophenol was investigated in solution as well as in ultrathin nanocomposite film. We found that conjugation to POSS core did not affect the kinetics of trans-cis photoisomerization and thermal cis-trans relaxation. Furthermore, rapid and reversible photoisomerization was observed in azo-POSS nanocomposite films. We suggest that the highly stable branched azo-POSS conjugates with high dye grafting density described here can be considered for nanometer-sized photoswitches, active layer material with optical-limiting properties, and a medium with photoinduced anisotropy for optical storage.
We report on the synthesis of novel branched organic-inorganic azo-polyhedral oligomeric silsesquioxane (POSS) conjugates (Azo-POSS) and their use as a stable active medium to induce reversible plasmonic modulations of embedded metal nanostructures. A dense monolayer of silver nanocubes was deposited on a quartz substrate using the Langmuir-Blodgett technique and subsequently coated with an ultrathin Azo-POSS layer. The reversible light-induced photoisomerization between the trans and cis states of the azobenzene-terminated branched POSS material results in significant changes in the refractive index (up to 0.17) at a wavelength of 380 nm. We observed that the pronounced and reversible change in the surrounding refractive index results in a corresponding hypsochromic plasmonic shift of 6 nm in the plasmonic band of the embedded silver nanocubes. The reversible tuning of the plasmonic modes of noble-metal nanostructures using a variable-refractive-index medium opens up the possibility of fabricating photoactive, hybrid, ultrathin coatings with robust, real-time, photoinitiated responses for prospective applications in photoactive materials that can be reversibly tuned by light illumination.
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