Design of universal supersonic nozzles with conical flow

The problem of designing the supersonic part of nozzles creating source type flows self-similar with respect to the isentropic exponent is solved. A function that approximates the geometry of nozzle channels with cone angles up to 15° is derived. The results of solving the direct nozzle problem, which confirm the accuracy of the approximation obtained, are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–186, July–August, 1989.The authors are grateful to A. N. Ganzhelo for supplying the supersonic flow calculation programs.     

Synthesis and Crystal Structures of Bis(tetraethylammonium)(2-oxo-1,3-dithiole-4,5-dithiolato)zincate(II) and Bis(tetra-n-butylammonium)(2-oxo-1,3-dithiole-4,5-dithiolato)zincate(II)

The title compounds were prepared from 1,3,4,6-tetrathiapentalene-2,5-dione ( 1 ) in one step via the in situ generated intermediate 2-oxo-1,3-dithiole-4,5-dithiolate (dmid; 2 ). The X-ray single crystal structure of (Et₄N)₂[Zn(dmid)₂] ( 3 a ) gave the tetragonal space group P4₃2₁2 with a = b = 13.810(2) Å, c = 16.480(3) Å, and Z = 4. (n-Bu₄N)₂[Zn(dmid)₂] ( 3 b ) gave the triclinic space group P 1 with a = 11.947(4) Å, b = 14.665(5) Å, c = 16.662(8) Å, α = 100.21(3)°, β = 104.46(3)°, γ = 110.73(3)°, and Z = 2.     

[MII(H2dapsc)]-[Cr(CN)6] (M = Mn,Co) Chain and Trimer Complexes: Synthesis,Crystal Structure,Non-Covalent Interactions and Magnetic Properties

Four new heterometallic complexes combining [M^II(H₂dapsc)]²⁺ cations with the chelating H₂dapsc {2,6-diacetylpyridine-bis(semicarbazone)} Schiff base ligand and [Cr(CN)₆]³⁻ anion were synthesized: {[M^II(H₂dapsc)]Cr^III(CN)₆K(H₂O)_2.5(EtOH)_0.5}_n·1.2n(H₂O), M = Mn (1) and Co (2), {[Mn(H₂dapsc)]₂Cr(CN)₆(H₂O)₂}Cl·H₂O (3) and {[Co(H₂dapsc)]₂Cr(CN)₆(H₂O)₂}Cl·2EtOH·3H₂O (4). In all the compounds, M(II) centers are seven-coordinated by N₃O₂ atoms of H₂dapsc in the equatorial plane and N or O atoms of two apical –CN/water ligands. Crystals 1 and 2 are isostructural and contain infinite negatively charged chains of alternating [M^II(H₂dapsc)]²⁺ and [Cr^III(CN)₆]³⁻ units linked by CN-bridges. Compounds 3 and 4 consist of centrosymmetric positively charged trimers in which two [M^II(H₂dapsc)]²⁺ cations are bound through one [Cr^III(CN)₆]³⁻ anion. All structures are regulated by π-stacking of coplanar H₂dapsc moieties as well as by an extensive net of hydrogen bonding. Adjacent chains in 1 and 2 interact also by coordination bonds via a pair of K⁺ ions. The compounds containing Mn^II (1, 3) and Co^II (2, 4) show a significant difference in magnetic properties. The ac magnetic measurements revealed that complexes 1 and 3 behave as a spin glass and a field-induced single-molecule magnet, respectively, while 2 and 4 do not exhibit slow magnetic relaxation in zero and non-zero dc fields. The relationship between magnetic properties and non-covalent interactions in the structures 1–4 was traced.     

New framework hydrous silicate K3Sc[Si3O9] · H2O related to the high-temperature anhydrous silicate K3Ho[Si3O9] and symmetry analysis of a phase transition with prediction of structures

Crystals of a new framework silicate K₃Sc[Si₃O₉] · H₂O, space group Pm2₁ n (nonstandard setting of space group Pmn2₁ = C _2v ⁷), are obtained under hydrothermal conditions. The structure is determined without preliminary knowledge of the chemical formula. The absolute configuration is determined. The structure is close to that of the high-temperature K₃Ho[Si₃O₉] phase, which was obtained upon the heating of K₃HoSi₃O₈(OH)₂. This structural similarity is due to the specific conditions of synthesis and an analogous formula, where holmium is replaced by scandium. A symmetry analysis shows that the high local symmetry of a block (rod) is responsible for the first-order phase transition of both the order-disorder (OD) and displacement type. The number of structures in which the simplest and high-symmetry layers are multiplied by different symmetry elements are predicted.     

Synthesis and characterisation of selected group 14 derivatives of the 2,5-(CF3)2C6H3 (Ar) ligand

Selected group 14 tetrahalides EX(4) (E = Si, Ge or Sn; X = Cl or Br) have been reacted in various molar ratios with ArLi, where Ar = 2,5-(CF(3))(2)C(6)H(3). The compounds Ar(2)SiCl(2)1, Ar(3)SiF 3, Ar(2)Si(OH)(2)4, Ar(2)GeCl(2)7, Ar(2)Ge(Br)Ge(Br)Ar(2)8, Ar(3)SnCl 10, Ar(4)Sn 11 and Ar(3)SnBr 12 have been isolated, and characterised by single-crystal X-ray diffraction, elemental analysis and (19)F solution-state NMR spectroscopy.     

Formation of μ(2)-hydroxo-bonded (MgPc)2OH- assemblies and (C60(-))2 dimers in ionic fullerene {(MgPc)2OH-}2·(C60(-))2·(cation+)4 complexes

Ionic complexes containing μ(2)-hydroxo-bonded (MgPc)(2)OH(-) phthalocyanine assemblies and C(60)(-) anions: {(MgPc)(2)OH(-)}(2)·(C(60)(-))(2)·(PMDAE(+))(4)·(C(6)H(5)CN)(4) (1); {(MgPc)(2)OH(-)}(2)·(C(60)(-))(2)·(TMP(+))(4)·(C(6)H(5)CN)(3)·(C(6)H(4)Cl(2))(2.5) (2) (where PMDAE(+) is the cation of N,N,N',N',N'-pentamethyldiaminoethane and TMP(+) is the N,N'N'-trimethylpiperazinium cation) have been obtained as single crystals. The ionic ground state of the complexes is justified by the EPR spectra and the spectra in the IR and NIR ranges. The C(60)˙(-) radical anions are dimerized both in 1 and 2 in the 240-220 K range. Dimerization is accompanied by the reversible transition of the complexes from paramagnetic to diamagnetic state. MgPc forms unusual (MgPc)(2)OH(-) assemblies, in which the hydroxo-anion coordinates to two MgPc molecules by a μ(2)-fashion. The length of the Mg-O bonds is 1.936-1.955(2) ?, the Mg-O-Mg angle is 133.37-135.27(4)° and the displacement of the Mg atoms out of the mean 24-atom phthalocyanine plane is 0.77-0.86 ?. The packing of spherical fullerene and planar phthalocyanine molecules is attained in a crystal by the insertion of fullerenes between phenylene groups of phthalocyanines. It has been shown that metal phthalocyanines in ionic complexes with C(60) form M(II)Pc·(L(-)) assemblies, whereas metalloporphyrins form M(II)porphyrin·(C(+)) assemblies.     

Amino acid derivatives of perylenediimide and their N-H···O peptide bond dipoles-templated solid state assembly into stacks

A methodology is proposed to provide direct access in good yields to peptide residues-appended perylenediimides PDI-(Cl(4))-[Gly-Ala(OEt)](2), 2a, PDI-(Cl(4))-[Gly-Val(OEt)](2), 2b and PDI-(Cl(4))-[Gly-Gly(OEt)](2), 2c from a generic perylenediimide (PDI) platform symmetrically functionalized with carboxylic acids at the imide sites, PDI-(Cl(4))-[Gly(OH)](2), 1. The latter is obtained in good purity by a non classical two-steps route avoiding the many, notoriously cumbersome successive chromatography steps typical of PDI chemistry, and including a single final purification allowing to crystallize the water soluble pure diacid 1, of great interest in its own right for further developments in a variety of fields. Then, the synthesis, crystallization and analysis of the crystal structures of 2a and 2b reveal a common pattern of self-assembly of the outer peptide residues based on collections of parallel N-H···O peptidic hydrogen bonds running alongside stacks where the constraints imposed upon on the inner PDI skeletons by long range interaction of these parallel electric dipoles reduce the dihedral angles around the bay regions by as much as 11% down to 32°.