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Graphical abstract Four-membered metallic quadrangle as a coordination centre, and eight pentazoles as ligands, five new high-energy clusters were built and their properties were theoretically studied. Abstract Metal–metal multiple bonds based polynitrogen complex clusters may become a class of high-energy, insensitive and green primary explosives. Five complexes containing chromium (Cr≡Cr), molybdenum (Mo≡Mo), tungsten (W≡W), technetium (Tc≡Tc) and rhenium (Re≡Re) metal multiple bonds with pentazole ligands were theoretically built. The metal–metal multiple bonds, metal-pentazole coordination bonds, molecular static and dynamic polarizability were investigated with density functional theory M06-L/LanL2DZ, The Wiberg bond order sequence of metal–metal is Mo–Mo > Cr–Cr > W–W > Re–Re > Tc–Tc Bidentate coordination bonds were formed between each metal–metal edge and two pentazole ligands, which strengthen the coordination bonds, and Wiberg bond order sequence of metal-pentazole is Re–N > W–N > Tc–N > Mo–N > Cr–N. The gaseous and solid phase formation enthalpies, enthalpies of sublimation and theoretical density of five complexes were predicted. As candidates for primary explosives, their detonation heats were calculated and the descending order is Re 4 (N 5) 8 > W 4 (N 5) 8 > Tc 4 (N 5) 8 > Mo 4 (N 5) 8 > Cr 4 (N 5) 8. M 4 N 40 clusters may be a class of promising green primary explosives. [ABSTRACT FROM AUTHOR]

We consider the Fisher–KPP equation with Robin boundary conditions on the half line. We show that this problem has even number of nonnegative stationary solutions, which are ordered, a stable one is sandwiched by two unstable ones. Then we construct several types of entire solutions between them, each entire solution connects an unstable stationary solution with a stable one. In particular, we construct two types of entire solutions U c (x , t) and U (x , t) connecting 0 and the smallest positive stationary solution. In addition, U c tend to the traveling wave solution with speed c as t → − ∞ in a moving frame, and U (x , t) enjoys convexity. This paper extends the recent results of Lou, Lu and Morita in Lou et al. (2020) from Dirichlet boundary condition to Robin boundary condition. [ABSTRACT FROM AUTHOR]

Abstract: A fluorinated polyimide (PI) was synthesized by a two-step reaction from 4,4′-(hexafluoroisopropylidene) diphthalic anhydride and 2,2′-bis(trifluoromethyl)-4,4′diaminobiphenyl. A series of PI composites with various mass fractions of multi-walled carbon nanotubes (MWNTs) were prepared by either an in situ polymerization or blending process. To increase the chemical compatibility of carbon nanotubes with the PI matrix, MWNTs were treated with an acid mixture and sulfoxide chloride by turns. Results show that the dispersion of the MWNTs is highly improved in the PI by modification. The modified MWNTs are dispersed homogeneously in the matrix, while the structures of the PI and MWNTs are stable in the preparation process. The thermal stability of the nanocomposites is slightly lower than that of the pure PI. With incorporating MWNTs, the storage modulus and glass transition temperature of the composite films enhanced comparing to that of PI matrix. The dielectric constants of the composites increase sharply, which is favorable to their practical use in anti-static materials and embedded capacitors. [Copyright &y& Elsevier]