Copolymerization of vinylcyclohexane with ethene and propene using zirconocene catalysts

Vinylcyclohexane (VCH) was copolymerized with ethene and propene using methylaluminoxane‐activated metallocene catalysts. The catalyst precursor for the ethene copolymerization was rac‐ethylenebis(indenyl)ZrCl₂ ( 1 ). Propene copolymerizations were further studied with C_s‐symmetric isopropylidene(cyclopentadienyl)(fluorenyl)ZrCl₂ ( 2 ), C₁‐symmetric ethylene(1‐indenyl‐2‐phenyl‐2‐fluorenyl)ZrCl₂ ( 3 ), and “meso”‐dimethylsilyl[3‐benzylindenyl)(2‐methylbenz[e]indenyl)]ZrCl₂ ( 4 ). Catalyst 1 produced a random ethene–VCH copolymer with very high activity and moderate VCH incorporation. The highest comonomer content in the copolymer was 3.5 mol %. Catalysts 1 and 4 produced poly(propene‐co‐vinylcyclohexane) with moderate to good activities [up to 4900 and 15,400 kg of polymer/(mol of catalyst × h) for 1 and 4 , respectively] under similar reaction conditions but with fairly low comonomer contents (up to 1.0 and 2.0% for 1 and 4 , respectively). Catalysts 2 and 3 , both bearing a fluorenyl moiety, gave propene–VCH copolymers with only negligible amounts of the comonomer. The homopolymerization of VCH was performed with 1 as a reference, and low‐molar‐mass isotactic polyvinylcyclohexane with a low activity was obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6569–6574, 2006     

Maximum entropy principles for disordered spins

Summary We transform nonstationary independent random fields with exponential Radon-Nikodym factors and study the asymptotics of the transformed processes. As applications we deduce conditional limit theorems for such random fields, and we study a Curie-Weiss-type mean-field model of a quenched mixed magnetic crystal. This model has quenched site disorder and frustration but non-random coupling constants. We find a continuous phase transition with critical exponents equal to those of the classical Curie-Weiss theory.     

From students’ achievement to the development of teaching: requirements for feedback in comparative tests

In November 2004 Germany's largest federal state North-Rhine-Westphalia for the first time carried out central tests in the subjects German, English and Mathematics in grade 9 with about 210.000 students participating. One of the main goals in assessing students' performance was to improve of teaching. This imposed certain requirements on the construction of tasks and on the feedback of results. In this article we present —referring to the specific experience from the development of the mathematics test—concepts and requirements for comparative assessment that is intended to support desirable changes in teaching practice.     

A 13C NMR study of pyridoxal-5′-phosphate oxime

Pyridoxal-5′-phosphate amino-oxy acetate oxime was titrated in water, over the pH range 4–12, and the changes followed using ¹³C NMR. The results were compared to those of analogous Schiff's bases presented in the literature. The chemical shifts and titration curves of the oxime were appreciably different from those of the Schiff's bases, and the differences are explained as being due to the absence of ketoenamine-enolimine tautomerism in the oxime. The low chemical shift value and the large changes of the oxime azomethine carbon during titration, as compared to the Schiff's bases, are discussed. The high stability of the oximes in water makes them suitable as model compounds for some tautomeric forms of the Iess stable Schiff's bases.     

On the solutions of stochastic traveling salesman problems

We consider the n-city traveling salesman problem where the distances between the cities are nondeterministic. Our purpose is to estimate the expectation of the length of the optimal tour. This is done by calculating the expectations of a lower bound and an upper bound for the length of the optimal tour. Because the upper bound is formed by the well-known nearest neighbour rule, we can simultaneously find the cases where this rule is effective in the mean. If we let the number of cities grow, we obtain symptotic results that are totally determined by the behaviour of the distribution of the distance between any two points in the neighbourhood of the distance zero.     

Conformational analysis: XIV—A 1H n.m.r. conformational study of methyl substituted 2-oxo-1,3,2-dioxathians to confirm the predominance of chair forms in the trimethylene sulphite series

Seven isomeric 4,5,6-trimethyl-2-oxo-1,3,2-dioxathians, cis-4-trans-6-dimethyl-r-2-oxo-1,3,2-dioxathian and two isomeric 4,5,5,6-tetramethyl-2-oxo-1,3,2-dioxathians were prepared and their ¹H n.m.r. spectra analysed. The values of the vicinal coupling constants reported earlier for the cis-4-trans-6 compound were shown to be erroneous. In all cases the values of the vicinal coupling constants (and those of the chemical shifts) are indicative of a single chair conformation or a chair-chair equilibrium, in contrast to earlier reports on the significant contribution of twist forms but in agreement with an electron diffraction study. The chair form is ? 31 kJ mol^?1 thermochemically more stable than the twist form.     

Improving solid-state NMR dipolar recoupling by optimal control

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.