Bernoullian,Terminal, Penultimate or Third Order Markov Statistics?

Summary: A series of 7 homogeneous ethylene‐propylene copolymers is modeled by a Bernoullian, a terminal, a penultimate and a third order Markov model and it is found that the penultimate model describes this series best. The Bernoullian and terminal model prove to be insufficient and the third order Markov model is statistically not justified. Based on these results, a criterion to select the optimal Markovian order of homogeneous, single site catalyst produced copolymers is developed.

Schematic of the [(3‐MePh)(4‐MePh)C(2,7‐di‐tert‐BuFlu)(Cp)]ZrCl₂ metallocene copolymerizing ethene and propene.     

Stable growth of penny-shaped crack in viscoelastic composite material under time-dependent loading

Considered is the long-term cracking of the three-dimensional fiber-reinforced viscoelastic composite with a plane penny-shaped crack under time-dependent loading. The composite has a hexagonal structure and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled by transversally isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. The crack propagation planecoincides with the plane of isotropy. A ring-shaped yield zone in front of the moving crack is modeled as a Dugdale's zone with time-dependent stresses. Crack growth under deformation of the composite occurs by application of a slowly increasing tensile load; it is normal to the plane of crack propagation. A convolution-type time operator describes the viscoelastic properties of the matrix material. Use is made of the Volterra principle and the theory of long-term cracking of viscoelastic bodies. The irrational function of integral operator associated with the viscoelastic crack opening expression is expanded into a continued fraction of operators. The solution is reduced to the nonlinear integral equations of crack growth. Numerical results are obtained for a specific material. Crack growth kinetics is discussed in connection with the onset of stable crack growth and crack border stress intensity factor.     

Initial kinking of an interface crack between two elastic media

The initial kinking of a thin fracture process zone near the crack tip under plane strain is studied using the Wiener-Hopf method. The crack is located at the interface between dissimilar elastic media. The fracture process zone is modeled by a straight line of normal displacement discontinuity emerging from the crack tip at an angle to the interface. The angle between the process zone and the interface is determined from the condition of strain energy maximum in the process zone. The dependences of the length and angle of the process zone on the external load and other parameters of the problem are studied. The results are compared with theoretical and experimental data obtained by other researchers __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 28–41, October 2007.     

Efficient Protocol for Synthesis of Pyrazolo[3,4-a]acridines

A new class of pyrazolo[3,4-a]acridines have been prepared. The synthon acridones were obtained in very good yield by a one-pot reaction of 2-amino-5-chloro or nitro substituted benzophenones with 1,3-cyclic diketones in the presence of freshly prepared Eaton’s reagent without solvent, using Friedländer synthesis. The intermediates were reacted with ethylformate followed by hydrazine hydrate to afford pyrazolo[3,4-a]acridines. All of the compounds were purified by recrystallization only, and no chromatographic workup was required. The structures of the synthesized compounds were deduced by spectroscopic techniques, including single-crystal x-ray diffraction.     

Pseudo‐Fivefold Diffraction Symmetries in Tetrahedral Packing

We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo‐fivefold rotational diffraction symmetry. A unified geometric model involving the 600‐cell is presented: the model accounts for the observed pseudo‐fivefold symmetries among the different Bravais lattice types. The model accounts for vertex‐, edge‐, polygon‐, and cell‐centered fused‐icosahedral clusters. Vertex‐centered and edge‐centered types correspond to the well‐known pseudo‐fivefold symmetries in I_h and D_5h quasicrystalline approximants. The concept of a tetrahedrally‐packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused‐icosahedrally‐packed crystals. This reciprocal‐space cluster is a direct result of the pseudosymmetry and, just as the real‐space clusters, can be rationalized by the 600‐cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally‐packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry‐based Jones model are shown to accord with the observed electron counts for a variety of Group 10–12 tetrahedrally‐packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu₂, Cd₃Cu₄, Cu₅Cd₈, and Cu₃Cd₁₀. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn₁₁Au₁₅Cd₂₃, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10–12 elements is presented. This compound crystallizes in Im$\bar 3$ (space group no. 204) with a=13.842(2) Å. The structure was solved with R₁=3.53 %, I>2σ;=5.33 %, all data with 1282/0/38 data/restraints/parameters.     

Oxygen‐Promoted CH Bond Activation at Palladium

[Pd(P(Ar)(tBu)₂)₂] ( 1 , Ar=naphthyl) reacts with molecular oxygen to form Pd^II hydroxide dimers in which the naphthyl ring is cyclometalated and one equivalent of phosphine per palladium atom is released. This reaction involves the cleavage of both C? H and O? O bonds, two transformations central to catalytic aerobic oxidizations of hydrocarbons. Observations at low temperature suggest the initial formation of a superoxo complex, which then generates a peroxo complex prior to the C? H activation step. A transition state for energetically viable C? H activation across a Pd? peroxo bond was located computationally.