Polyferrocenylenes by oxidative coupling of 1,1′-dilithioferrocene with Cu2+ Ion(1)

Summary The oxidative coupling of 1,1 -dilithioferrocene (chelated withN,N,N,N-tetramethylethylenediamine) in the presence of Cu^II halide (Cu²⁺Li=1–1.5) in ether solvents at –70 to 110° gives 30–45% yields of polyferrocenylene. Still higher yields of coupling products result from reactions in which oxidative coupling is paired with thermal coupling,i. e. C-C bond formation through thermal decomposition of organocopper(I) intermediates in the absence of external oxidant (Cu²⁺Li=0.5). Number-average molecular masses of the highest fractions of linear products (2) as separated in the primary work-up process are in the 1500–3400 range, and fractionating precipitation results in subfractions with M_n as high as 5000. Cyclization of dinuclear intermediates, producting up to 10% of [0,0] ferrocenophane (bisfulvalenediiron), competes in all experiments with linear propagation. Experiments conducted with Cu^I halides under conditions leading exclusively to thermal coupling provide even higher conversion to the ferrocenophane (up to 25% yields) at the expense of linear condensation products. Spectroscopic features of the polyferrocenylenes are discussed. In the linear compounds with ¯M_n>800, i.r. absorptions and p.m.r.'s are remarkably invariant with the degree of polymerization, as are the electronic absorption maxima. This shows, in confirmation of earlier reports, that there is insignificant resonance interaction between the cyclopentadienyl rings in the ferrocene system and hence little, if any, electronic delocalization along the polymer chain of heteroannularly interlinked polyferrocenylene structures.     

Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability

The well-posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by Birkhoff in two dimensions and is shown here to hold both in two and three dimensions. Incompressible, inviscid and irrotational flow with a velocity jump across an interface is assumed. In two dimensions, global existence of a weak solution to the Euler equation with such initial conditions is established. In three dimensions, a Lagrangian representation of the vortex sheet analogous to the Birkhoff equation in two dimensions is presented.This work was performed while C.B. was visiting the Dept. de Mathématiques, Nice     

ВЛИЯНИЕ СТАРЕНИЯ НА Э ЛЕКТРИЧЕСКИЕ СВОЙСТ ВА ПОЛУПРОВОДНИКОВОЙ С ИСТЕМЫ Bi2Te3-Bi2Se3

, Bi₂Te₃-Bi₂Se₃. , , , . .

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Influence of ageing on change in electrical properties of semiconducting systems of Bi₂Te₃-Bi₂Se₃

The paper describes the effect of ageing observed on a semiconducting system Bi₂Te₃ — Bi₂Se₃. It is shown that the change in electrical conductivity and thermoelectric force, which takes place during ageing, is caused by the change in concentration of the free electrons. The influence of this process on the efficiency of equipment employing the Peltier effect is analyzed.

     

The energy of periodic surface structures in ferromagnetism

The periodic domain structures on unfavourably oriented surface layers of ferromagnetic materials were studied both experimentally and theoretically. The connection between the surface structure and the crystallographic orientation of the crystals was confirmed. All the terms contributing to the total energy of the surface layer were calculated. A general solution of the potential problem is given for arbitrary periodic distribution of the charges.

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A note on a generalization of Diliberto’s Theorem for certain differential equations of higher dimension

In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.This research was supported by Grant No. 201/99/0295 of the Grant Agency of the Czech Republic.This revised version was published online in April 2005 with a corrected missing date string.     

Some sufficient conditions for the existence of a 1-factor

The following theorem is proved: Let G be a graph of even order. Assume that there exists a connected spanning subgraph F of G such that for every set U of four vertices in G, if the subgraph of F induced by U is a star, then the subgraph of G induced by U is complete. Then G has a 1-factor. The above theorem is derived from another sufficient condition for the existence of a 1-factor, which is also proved in this paper (Lemma 1).     

Kinetic study of dissolution of poly(vinyl chloride) in cyclohexanone

The kinetics of dissolution of five fractions of commercial poly(vinyl chloride) in cyclohexanone was studied at temperatures from 20 to 70°C. Good agreement was observed between the experimental results and equations expressing the dependence of the induction periods and the rates of dissolution on temperature and molecular weight. It was found that the apparent activation energy for the swelling process lies in the range 9–14 kcal/mole and the apparent activation energy for the dissolution diffusion process in the range 8–12 kcal/mole. The apparent dependence of activation energies on number-average molecular weight indicates that the chain ends are more important in determining the dissolution rate than the centers of the polymer chains.