Metamorphosis of a Commodity Plastic like PVC to Efficient Catalytic Single-Chain Nanoparticles

We perform the conversion of a commodity plastic of common use in pipes, window frames, medical devices, flexible hoses, etc. like polyvinyl chloride (PVC) to single-chain nanoparticles (SCNPs). SCNPs are versatile, protein-mimetic soft nano-objects of growing interest for catalysis, sensing, and nanomedicine, among other uses. We demonstrate that the metamorphosis process -as induced through metal-free click chemistry- leads to well-defined, uniform SCNPs that are stable during storage in the solid state for months. All the conversion process (from PVC isolation to PVC-SCNPs synthesis) can be run in a green, dipolar aprotic solvent and involving, when required, a simple mixture of ethanol and water (1/1 vol.) as non-solvent. The resulting PVC-SCNPs are investigated as recyclable, metalloenzyme-mimetic catalysts for several representative Cu(II)-catalyzed organic reactions. The method could be valid for the metamorphosis and valorization of other commodity plastics in which it is feasible to install azide functional groups in their linear polymer chains.     

Stereospecific Photoredox-Catalyzed Vinylations to Functionalized Alkenes and C-Glycosides**

We report an efficient radical-mediated C−C coupling through photoredox-catalyzed reactions of 4-alkyl-dihydropyridines (DHPs) and vinylbenziodoxol(on)es (VBX, VBO). This transition-metal-free and mild photocatalytic method has excellent functional group tolerance and affords vinylated products in good yields, with complete retention of the alkene configuration. The utility of the methodology is demonstrated by the diastereoselective synthesis of C-vinyl glycosides. Preliminary mechanistic studies suggest that the C−C bond formation is stereospecific and proceeds through a concerted radical coupling transition state.     

Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals

We consider the highly oscillatory integral $F(w):={\int }_{-\infty }^{\infty }{e}^{iw(t^{K+2}+e^{i\theta }{t}^p)}g(t)dt$ for large positive values of w, , K and p positive integers with $1\le p\le K$, and $g(t)$ an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when $w\to +\infty$ for general values of K and p in terms of elementary functions, and determine the Stokes lines. For $p\ne 1$, the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters K and p; the special case $p=1$ requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals ${\mathrm{\Psi }}_K(x_1,x_2,\text{…},x_K)$ for large values of one of its variables, say $x_p$, and bounded values of the remaining ones. This family of integrals may be written in the form $F(w)$ for appropriate values of the parameters w, θ and the function $g(t)$. Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large $|x_p|$. The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al.