Correlation in calculations of density of states in thin films

The density of electronic states and its spatial distribution in thin films are considered including the electron correlations in the coherent phase approximation applied to the intra-atomic interaction. This new approach allows us to derive the line shape for electronic levels which is important from the point of view of the convergency for the density function in the case of systems with restricted dimensions. Detailed calculations are performed for 4s copper film functions with the fcc lattice and various crystallographic orientations of the surfaces.The authors are very grateful to Professor L. Valenta (Prague) for his kind interest in this paper and to Dr. J. Mizia (Cracow) for helpful discussions. We would like to express our gratitude to Professor M. Wonicki and Mrs M. Firszt (Toru) for their help in obtaining the computer program procedure for two-particle interaction integrals calculations.The paper has been done in the framework of the Problem M.R I-11.     

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Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean-field equations are iterated with Anderson mixing. The different methods are tested on the triply periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.     

Polymer fibers as carriers for homogeneous catalysts

This paper describes a polymer fiber-based approach for the immobilization of homogeneous catalysts. The goal is to generate products that are free of catalysts which would be of great importance for the development of optoelectronic or pharmaceutical compounds. Electrospinning was employed to prepare the non-woven fiber assembly composed of polystyrene. The homogeneous catalyst scandium triflate was immobilized on the polystyrene fibers during electrospinning and on corresponding core shell fibers using a fiber template approach. An imino aldol and an aza-Diels-Alder model reaction were carried out with each fibrous catalytic system. This resulted in the immobilization of homogeneous catalysts in a polymer environment without loss of their catalytic activity and may even be enhanced when compared with reactions carried out in homogeneous solutions.     

Predicting Optimal Lengths of Random Knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.