Long‐chain‐branched polyethene by the copolymerization of ethene and nonconjugated α,ω‐dienes

Ethene was copolymerized (1) with 1,5‐hexadiene with rac‐ethylenebis(indenyl)zirconium dichloride/methylaluminoxane (MAO) used as a catalyst and (2) with 1,7‐octadiene with bis(n‐butylcyclopentadienyl)zirconium dichloride/MAO and rac‐ethylenebis(indenyl)hafnium dichloride (Et[Ind]₂HfCl₂)/MAO used as catalysts at 80 °C in toluene. The copolymer microstructure and the influence of diene incorporation on the rheological properties were examined. Ethene and 1,5‐hexadiene formed a copolymer in which a major fraction of the 1,5‐hexadiene was incorporated into rings and a small fraction formed 1‐butenyl branches. The copolymerization of ethene with 1,7‐octadiene resulted in a higher selectivity toward branch formation. Some of the branches formed long‐chain‐branching (LCB) structures. The ring formation selectivity increased with decreasing ethene concentration in the polymerization reactor. Melt rheological properties of the diene copolymers resembled those of metallocene‐catalyzed LCB homopolyethenes and depended on the vinyl content, the catalyst, and the polymerization conditions. At high diene contents, all three catalysts produced crosslinked polyethene. This was especially pronounced with Et[Ind]₂HfCl₂, where only 0.2 mol % 1,7‐octadiene in the copolymer was required to achieve significantly modified rheological properties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3805–3817, 2001     

Fractal characteristics of critical and localized states in incommensurate quantum systems

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.     

A special method of deformational correction in N.M.R. of molecules dissolved in liquid crystals

A simple method of deformational correction for the N.M.R. spectral parameters of molecules dissolved in liquid crystals is described. The method is applicable to the different isotopically substituted derivatives of the molecules belonging to the cubic point groups. Its validity is verified for the dipolar and quadrupolar couplings observed in the molecules CH₄, CD₄ and CH₃D dissolved in the liquid crystals Merck Phase IV, Merck ZLI 1167 and their mixtures.     

Entropy,limit theorems,and variational principles for disordered lattice systems

We study infinite volume limits and Gibbs states of disordered lattice systems with bounded and continuous potentials. Our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes. We find that many familiar results of invariant potentials, such as large deviation theorems, variational principles, and equivalence of ensembles, continue to hold for disordered models, with suitably modified statements.     

Growth, percolation, and correlations in disordered fiber networks

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameterp which controls the degree of clustering. Forp=1 the deposited network is uniformly random, while forp=0 only a single connected cluster can grow. Forp=0 we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. Forp>0 we carry out extensive simulations on fibers, and also needles and disks, to study the dependence of the percolation threshold onp. We also derive a mean-field theory for the threshold nearp=0 andp=1 and find good qualitative agreement with the simulations. The fiber networks produced by the model display nontrivial density correlations forp<1. We study these by deriving an approximate expression for the pair distribution function of the model that reduces to the exactly known case of a uniformly random network. We also show that the two-point mass density correlation function of the model has a nontrivial form, and discuss our results in view of recent experimental data on mss density correlations in paper sheets.     

Bayesian graphical model determination using decision theory

Bayesian model determination in the complete class of graphical models is considered using a decision theoretic framework within the regular exponential family. The complete class contains both decomposable and non-decomposable graphical models. A utility measure based on a logarithmic score function is introduced under reference priors for the model parameters. The logarithmic utility of a model is decomposed into predictive performance and relative complexity. Axioms of decision theory lead to the judgement of the plausibility of a model in terms of the posterior expected utility. This quantity has an analytic expression for decomposable models when certain reference priors are used and the exponential family is closed under marginalization. For non-decomposable models, a simulation consistent estimate of the expectation can be obtained. Both real and simulated data sets are used to illustrate the introduced methodology.     

Addition of tert-butylcuprate to (2S)-N-acyl-Δ-dehydroprolinates as a diastereoselective synthetic procedure for obtaining (2S,5S)-5-tert-butylproline

The synthesis of (2S,5S)-Boc-5-tert-butylproline ethyl ester via the addition of tert-butylcuprate to (2S)-N-Boc-Δ⁵-dehydroproline ethyl ester, formed from (2S)-N-Boc-5-methoxyproline ethyl ester, gives an excellent yield of 94% and a high diastereoselectivity (2S,5S):(2S,5R) 78:22. This synthesis opens up a new synthetic route to (2S,5S)-5-tert-butylproline, which is a useful, conformationally rigid, analogue of l-proline.     

Über neue olefin-dicarbonyl-isonitril-eisen(0)-komplexe

The reactions of [R₃O]BF₄ or R₃ECl (R = Me, Et; E = Si, Ge, Sn, Pb) with various olefincyanodicarbonyl ferrates(0) [olenFe(CO)₂CN]^?] (olen  C₄H₆, C₅H₈, C₆H₈, C₆H₁₀, C₇H₁₀, C₈H₈, C₈H₁₄), which can be easily synthesized from olenFe(CO)₃ and NaN(SiMe₃)₂, lead to the neutral isonitrile derivatives olenFe(CO)₂CNR or olenFe(CO)₂CNER₃. The 31 new complexes are characterized by their analyses, IR and ¹H NMR spectra.