Supramolecular networks through second-sphere coordination based on 1D metal-4,4′-dipyridyldisulfide coordination polymers and hydrogenfumarate or sulfonate anions

Four hydrogen-bonded assemblies of formula [M(dpds)₂(OH₂)₂]A₂·nH₂O (A = anion) are described. These assemblies result from the second-sphere coordination interactions between the 1D coordination polymers [M(dpds)₂(OH₂)₂]²⁺, M = Zn(II) and Cu(II), dpds = 4,4′-dipyridyldisulfide, and the pyridine-3-sulfonate (3pySO₃⁻) or hydrogenfumarate (Hfum⁻) anions. Significantly, supramolecular structural variations are observed depending on the presence of water lattice molecules, which formed discrete aggregates when the Hfum⁻ anion was used. The effects of geometrical variations in the building blocks are also evident on using Jahn-Teller-distorted divalent Cu(II) ions or regular octahedral species based on Zn(II) ions. The second-sphere effects on the stabilization of the compounds are illustrated by TGA experiments.     

Three anilides of 2,2′‐thiodibenzoic acid

The structures of N,N′‐bis(2‐methylphenyl)‐2,2′‐thiodibenzamide, C₂₈H₂₄N₂O₂S, (Ia), N,N′‐bis(2‐ethylphenyl)‐2,2′‐thiodibenzamide, C₃₀H₂₈N₂O₂S, (Ib), and N,N′‐bis(2‐bromophenyl)‐2,2′‐thiodibenzamide, C₂₆H₁₈Br₂N₂O₂S, (Ic), are compared with each other. For the 19 atoms of the consistent thiodibenzamide core, the r.m.s. deviations of the molecules in pairs are 0.29, 0.90 and 0.80 Å for (Ia)/(Ib), (Ia)/(Ic) and (Ib)/(Ic), respectively. The conformations of the central parts of molecules (Ia) and (Ib) are similar due to an intramolecular N—H...O hydrogen‐bonding interaction. The molecules of (Ia) are further linked into infinite chains along the c axis by intermolecular N—H...O interactions, whereas the molecules of (Ib) are linked into chains along b by an intermolecular N—H...π contact. The conformation of (Ic) is quite different from those of (Ia) and (Ib), since there is no intramolecular N—H...O hydrogen bond, but instead there is a possible intramolecular N—H...Br hydrogen bond. The molecules are linked into chains along c by intermolecular N—H...O hydrogen bonds.     

Synthesis, structure, and properties of the new mixed-valent dodecahalogenotrimetallate in(4)ti(3)br(12) and its relation to compounds a(3)ti(2)x(9) (a = k, in; x = cl, br)

Black single crystals of the new dodecahalogenotrimetallate In(4)Ti(3)Br(12) were obtained by reacting InBr(3) with Ti-wire at 450 °C in a silica tube sealed under vacuum. In(4)Ti(3)Br(12) (Pearson symbol hR57, space group R3?m, Z = 3, a = 7.3992(8) ?, c = 36.673(6) ?, 643 refl., 25 param., R(1)(F) = 0.025; wR(2)(F(2)) = 0.046) is a defect variant of a 12 L-perovskite. In(+) cations are 12-fold coordinated in two different ways: In1 as an anticuboctahedron and In2 as a cuboctahedron. In both cases the 5s(2) configuration results in 3 short, 6 medium, and 3 long In-Br distances which might be explained as lone pair effect or second order Jahn-Teller instability. Furthermore there are isolated linear trimers [Ti(3)Br(12)](4-) consisting of facesharing octahedra similar to [Ru(3)Cl(12)](4-). The [Ti(3)Br(12)](4-)-unit has to be described as a mixed-valent d(1)-d(2)-d(1) system. According to magnetic measurements, the Ti-atoms in In(4)Ti(3)Br(12) show strong antiferromagnetic interactions (Θ = -1216(6) K) which might be addressed as weak Ti(3+)-Ti(2+)-Ti(3+) bonds. For comparison, single crystals of K(3)Ti(2)X(9) (X = Cl, Br) were synthesized and their structures refined. The rotation of the Ti(2)X(9)(3-) dimers reduced the symmetry of the well-known Cs(3)Cr(2)Cl(9) type from P6(3)/mmc to P6(3)/m and resulted in the formation of merohedral twins. According to the unit cell volumes In(+) is smaller than K(+) in all cases.     

Large solutions for the Laplacian with a power nonlinearity given by a variable exponent

In this paper we consider positive boundary blow-up solutions to the problem Δu=uq(x)$\mathrm{\Delta }u=u^{q(x)}$ in a smooth bounded domain Ω⊂Rn$\Omega \subset {\mathbb{R}}^n$. The exponent q(x)$q(x)$ is allowed to be a variable positive Hölder continuous function. The issues of existence, asymptotic behavior near the boundary and uniqueness of positive solutions are considered. Furthermore, since q(x)$q(x)$ is also allowed to take values less than one, it is shown that the blow up of solutions on ∂Ω is compatible with the occurrence of dead cores, i.e., nonempty interior regions where solutions vanish.