Unusual Bonding and Properties in Main Group Element Chemistry: Rational Synthesis,Characterization, and Experimental Electron Density Determination of Mixed‐Valent Tetraphosphetes

Five dispirocyclic λ³,λ⁵‐tetraphosphetes [{R₂Si(NR¹)(NR²)P₂}₂] (R¹ = R² and R¹ ≠ R²) are easily prepared in almost quantitative yields via photolysis of the respective bis(trimethylsilyl)phosphanyldiazaphosphasiletidines with intense visible light. These deep‐yellow low‐coordinate phosphorus compounds can be considered as the first higher congeners of the well‐known cyclodiphosphazenes. The tetraphosphetes are remarkably stable in air and show unexpected molecular properties related to the unique bonding situation of the central four‐π‐electron four‐membered phosphorus ring. The extent of rhombic distortion of the central P₄ ring is remarkable due to an unusually acute angle at the σ²‐phosphorus atoms. All of the P?P bonds are approximately equal in length. The distances are in the middle of the range given by phosphorus single and double bonds. The anisotropic absorption of visible light that can easily be observed in the case of the yellow/colorless dichroic crystals of [{Me₂Si(NtBu)(NtBu)P₂}₂] and the exceptional ³¹P NMR chemical shift of the σ²‐phosphorus atoms are the most remarkable features of the λ³,λ⁵‐tetraphosphetes. In the case of [{Me₂Si(NtBu)(NtBu)P₂}₂], the Hansen–Coppens multipole model is applied to extract the electron density from high‐resolution X‐ray diffraction data obtained at 100 K. Static deformation density and topological analysis reveal a unique bonding situation in the central unsaturated P₄ fragment characterized by polar σ‐bonding, pronounced out‐of‐ring non‐bonding lone pair density on the σ²‐phosphorus atoms, and an additional non‐classical three‐center back‐bonding contribution.     

Solvent Influence on Cellulose 1,4‐β‐Glycosidic Bond Cleavage: A Molecular Dynamics and Metadynamics Study

We explore the influence of two solvents, namely water and the ionic liquid 1‐ethyl‐3‐methylimidazolium acetate (EmimAc), on the conformations of two cellulose models (cellobiose and a chain of 40 glucose units) and the solvent impact on glycosidic bond cleavage by acid hydrolysis by using molecular dynamics and metadynamics simulations. We investigate the rotation around the glycosidic bond and ring puckering, as well as the anomeric effect and hydrogen bonds, in order to gauge the effect on the hydrolysis mechanism. We find that EmimAc eases hydrolysis through stronger solvent–cellulose interactions, which break structural and electronic barriers to hydrolysis. Our results indicate that hydrolysis in cellulose chains should start from the ends and not in the centre of the chain, which is less accessible to solvent.     

Control of reaction mechanisms in cationically polymerized epoxy resins facilitates the adjustment of morphology and mechanical properties

Structure–property relations of cationically polymerized epoxy thermosets with different morphologies are examined. The morphology adjustment of amorphous epoxy based copolymers and partially crystalline polymer alloys is carried out with star‐shaped poly(ε‐caprolactone) (SPCL) bearing various numbers of hydroxyl end groups. These hydroxyl groups are known for their reactivity toward epoxides following the activated monomer (AM) mechanism. For this reason, four‐armed SPCL was synthesized with four hydroxyl end groups (SPCL‐tetraol) and, in addition, with successively esterified ones down to a SPCL with four ester end groups (SPCL‐tetraester). SPCL species bearing fewer or no hydroxyl end groups segregate into needle‐like nanodomains within the epoxy networks and, if the concentration is high enough, also into crystalline domains. The stronger phase separation of SPCL‐tetraester within the epoxy network compared with SPCL‐tetraol is due to a reduction of the AM mechanism. The mechanical properties resulting from different morphologies lead to a trade‐off between higher storage moduli and T_g values in the case of the more phase separated (and partially crystalline) polymer alloys and higher strain at break in the case of the amorphous copolymers. Nevertheless, in both cases toughness is improved or at least kept on the same level as for the pure epoxy resin. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2188–2199     

On the Differential Polynomial of a Graph

We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x~(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.