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  • 1980-1984  (4)
  • 1970-1974  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1513-1526 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Gauss-Jordan inversion algorithm requires 0(n3) arithmetic operations. In some practical applications, like state estimation or short-circuit calculation in power systems, the given matrix is sparse and only part of the inverse is needed. Most frequently in the diagonal dominant case this is the diagonal. There are two ways to exploit sparsity to determine elements of the inverse: 1Columnwise inversion via the solution of sparse linear systems with columns of the unit matrix as right-hand sides.2Application of the algorithm of Takahashi et al6.The latter algorithm arises very naturally from multiplying the left- and right-hand factors of the Zollenkopf bifactorization in reverse order. We indicate how computing time can be gained in the important symmetric diagonal dominant case if only part of the diagonal is needed and compare computing times of the method of Takahasi et al.6 with several variants of columnwise inversion. Whereas most of the theory holds for general matrices, experiments are performed on the symmetric diagonal dominant case. For band matrices the operation count is 0(n) both for computing a column of the inverse by columnwise inversion and the diagonal by the algorithm of Takahashi et al6.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 169 (1973), S. 163-176 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: This paper deals with the kinetics of the low pressure polymerization of ethylene catalysed by the soluble ZIEGLER-catalyst (C5H5)2Ti(C2H5)Cl/Al(C2H5)Cl2. By a special technique it was possible to study for the first time the kinetics of the initial homogeneous part of the polymerization. The following results were obtained: The active species of this catalyst system is formed extremely rapid and seems to be a very dynamic equilibrium product. Its concentration depends on the ratio Al/Ti. The propagation reaction therefore corresponds to an intermitting process. The propagation rate constant was estimated to 15 dm3 · mol-1 · s-1 for 10°C. An excess of the aluminum component (Al/Ti 〉 1) acts as deactivator. The polymerization of the heterogeneous system is probably diffusion controlled. Therefore, the rate decay of the polymerization cannot be described by simple kinetic laws. For small ratios Al/Ti the polymerization has the character of a “living” system.
    Notes: Es wird die Kinetik der Äthylenpolymerisation mit dem löslichen Katalysatorsystem (C5H5)2Ti(C2H5)Cl/Al(C2H5)Cl2 behandelt. Mit Hilfe einer speziellen Meßmethode konnte erstmals der homogene Anfangsbereich der Polymerisation kinetisch erfaßt werden. Anhand der erzielten Befunde lassen sich folgende Schlußfolgerungen ziehen: Die polymerisationsaktive Spezies wird unmeßbar rasch nach dem Mischen der Katalysatorkomponenten gebildet und ist als ein sehr dynamisches Gleichgewichtsprodukt anzusehen, dessen Konzentration vom Verhältnis der Katalysatorkomponenten abhängt. Kettenwachstum ist demnach ein intermittierender Vorgang. Die Geschwindigkeitskonstante der Wachstumsreaktion wurde zu etwa 15 dm3 · mol-1 · s-1 für 10°C bestimmt. Überschüssiges Aluminium-organyl (Al/Ti 〉 1) wirkt desaktivierend. Die Polymerisation in heterogener Phase ist sehr wahrscheinlich diffusionsbestimmt. Die Abnahme der Polymerisationsgeschwindigkeit mit der Zeit ist komplexer Natur und ist mit einfachen kinetischen Zeitgesetzen nicht zu beschreiben. Die zeitliche Zunahme des Polymerisationsgrades für Verhältnisse Al/Ti = 2 weist darauf hin, daß die Polymerisation den Charakter eines „lebenden“ Systems aufweist.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Angewandte Makromolekulare Chemie 12 (1970), S. 175-183 
    ISSN: 0003-3146
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: The rate of polymerisation of ethylene by the soluble ZIEGLER-NATTA-catalyst (C5H5)2Ti(C2H5)Cl/Al(C2H5)Cl2 was investigated in toluene as solvent. From the dependence of the initial rate of the polymerisation follows, that the primary complex, formed by the catalyst components, is not the active species of this system. The obtained dependences rather suggest, that the active species is to be viewed as an equilibrium product and the location of this equilibrium is determined by the ratio of the catalyst compounds in that manner, that only at high Al/Ti-ratios the charged Ti(IV)-compound is equal to the initial concentration of the active species. The existence of such an equilibrium is also suggested by the increase of the rate, occuring at lower Al/Ti-ratios, when polymer is falling out. The desactivation of propagating chains is of complex nature. Considerable desactivation of the active species by the aluminiumorganic compound is obtained.
    Notes: Es wurde die Geschwindigkeit der Polyreaktion von äthylen mit dem löslichen ZIEGLER-NATTA-Katalysator (C5H5)2Ti(C2H5)Cl/Al(C2H5)Cl2 in Toluol als Lösungsmittel untersucht. Aus der Abhängigkeit der Anfangsgeschwindigkeit der Polyreaktion von der Aluminiumalkylkonzentration ergibt sich, daß der aus den Katalysatorkomponenten sich bildende Primärkomplex nicht die aktive Spezies dieses Systems ist. Vielmehr sprechen die ermittelten Abhängigkeiten dafür, daß die aktive Spezies als Gleichgewichtsprodukt anzusehen ist und die Gleichgewichtslage vom Verhältnis der Katalysatorkomponenten bestimmt wird, derart, daß erst bei sehr hohen Verhältnissen Al/Ti die insgesamt eingesetzte Titan(IV)-Verbindung momemtan als aktive Spezies vorliegt. Für das Vorliegen eines solchen Gleichgewichtes spricht auch der für kleine Verhältnisse Al/Ti stets zu beobachtende Geschwindigkeitsanstieg nach dem Ausfallen des Polymeren. Die Desaktivierung der wachsenden Ketten ist komplexer Natur. Es zeigt sich, daß das Aluminiumorganyl in starkem Maße an der Desaktivierung der aktiven Spezies beteiligt ist.
    Additional Material: 4 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Angewandte Makromolekulare Chemie 94 (1981), S. 1-23 
    ISSN: 0003-3146
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: In this work the mechanism of olefine polymerization with Ziegler-Natta catalysts is presented. The first part is a discussion of the results obtained with soluble catalysts of the (C5H5)2-Ti(IV) type in combination with various aluminiumorganyls. Important analytical results, the characteristics of the yielded polymers and the kinetics of homogeneous and heterogeneous polymerization are discussed. The second part deals with heterogeneous titanium-catalysts, especially so-called carrier-fixed catalysts with Mg-compounds as carrier. The kinetics of ethylene polymerization and the reason for the elevated catalytic activity of such systems is discussed. Finally some mechanisms and their conformity with experimental results are given.
    Notes: In der vorliegenden Arbeit wird der Mechanismus der Olefinpolymerisation mit Ziegler-Natta-Katalysatoren erörtert. Im 1. Teil dieser Arbeit werden Ergebnisse diskutiert, die mit löslichen Katalysatorsystemen auf Basis (C5H5)2Ti(IV)-Verbindungen in Kombination mit verschiedenen Aluminiumorganylen erzielt wurden. Angesprochen werden wichtige analytische Befunde, charakteristische Eigenschaften der erzeugten Polymeren sowie die Kinetik der Polymerisation im homogenen und heterogenen Bereich. Im 2. Teil werden heterogene Katalysatorsysteme auf Titan-Basis behandelt, insbesondere sogenannte trägerfixierte Katalysatoren mit Magnesium-Verbindungen als Trägerkomponente. Hierbei wird insbesondere die Kinetik der Ethylenpolymerisation in den Vordergrund gestellt und die Frage nach dem Grund für die erhöhte Polymerisationsaktivität derartiger Katalysatorsyteme erörtert. Zum Abschluß werden einige Mechanismen im Hinblick auf ihre Übereinstimmung mit experimentellen Befunden diskutiert.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 27 (1982), S. 2249-2267 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: In the present article the kinetics of polymerization of vinyl acetate in suspension up to high conversion was studied. The molecular weight distribution and the side chain branching of polyvinyl acetate produced were examined with respect to micro and macro mixing as well as to reactor type. The following results were achieved: the time-activity curves of the polymerization can be described up to high conversions considering the exponential increase in viscosity of the polymerizing system and combining the viscosity with rate constants of the polymerization. The change of volume of the polymerizing system has no significant influence on kinetics. The narrowest molecular weight distribution of the poly(vinyl acetate) produced was achieved when polymerizing in the homogeneous continuous stirred tank reactor while the broadest molecular weight distribution was observed in the segregated continuous stirred tank reactor. The batch reactor and the flow tube reactor produce polymers with molecular weight distributions lying in between. Considering the side chain branching, another order was found. The batch reactor and the tube reactor show the lowest side chain branching, the homogeneous continuous stirred tank reactor shows a larger one and the segregated continuous stirred tank reactor shows the largest. Possible reasons for the different behavior of the different reactors are discussed. The degree of segregation was determined by experiments.
    Additional Material: 18 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 144 (1971), S. 17-27 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: The copolymerization of ethylene and styrene catalyzed by the soluble ZIEGLER-NATTA-catalyst (π-C5H5)2TiCl2/Al(C2H5)2Cl is investigated.Analytical and kinetical results indicate that two kinds of copolymer species with a different sequence distribution are formed and therefore two different catalyst species with different activity towards ethylene and styrene are assumed to be present in this catalyst system. The composition, of the copolymer formed can be calculated by an equation with a square dependence on the styrene concentration. We therefore assume that not styrene itself, but a dimeric equilibrium product of styrene is the monomer which can be polymerized. This is also supported by gelchromatographic results.
    Notes: Es wird die Copolymerisation von Äthylen und Styrol mit dem löslichen ZIEGLER-NATTA-Katalysator (π-C5H5)2TiCl2/Al(C2H5)2Cl in Benzol als Lösungsmittel untersucht.Analytische und kinetische Befunde weisen darauf hin, daß zwei Arten von Copolymerspezies unterschiedlicher Sequenzverteilung gebildet werden. Demnach sind zwei verschiedene Katalysatorspezies unterschiedlicher Aktivität gegenüber Äthylen und Styrol in diesem löslichen Katalysatorsystem anzunehmen. Die Beschreibung der Copolymerisation gelingt mittels einer Gleichung, in welche das Quadrat der Styrolkonzentration eingeht. Es wird daher angenommen, daß nicht das Styrol selbst, sondern ein dimeres Gleichgewichtsprodukt des Styrols das eigentliche polymerisationsfähige Monomere ist. Hierfür sprechen auch die erzielten gelchromatographischen Befunde.
    Additional Material: 3 Ill.
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  • 7
    Publication Date: 1984-01-01
    Print ISSN: 0014-3057
    Electronic ISSN: 1873-1945
    Topics: Chemistry and Pharmacology , Physics
    Published by Elsevier
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