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  • 1
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 357-371 
    ISSN: 0887-6266
    Keywords: gelation theory ; nonlinear polymerization ; molecular weight distribution ; branched polymers ; polymer modification ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A Markovian model is proposed for nonrandom branching reactions, by using free-radical polymerization that involves chain transfer to polymer as an example. Free-radical polymerizations are kinetically controlled; therefore, each primary polymer molecule experiences different history of branched structure formation. By assuming that the primary chains with the identical birth time conform to the same chain connection probabilities, the nonlinear structural development can be viewed as a system in which the primary chains formed at different birth times are combined into nonlinear polymers in accordance with the first-order Markov chain statistics. An explicit formula for the weight-average chain length is derived in a matrix form. The onset of gelation is simply stated as a point at which the largest eigenvalue of the transition matrix X reaches unity, i.e., det(X - I) = 0. This criterion for the onset of gelation can be considered as an extension of the Flory/Stockmayer theory to a nonequilibrium reaction system. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 357-371, 1998
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 33 (1995), S. 841-853 
    ISSN: 0887-6266
    Keywords: molecular weight distribution ; branching density distribution ; radius of gyration ; Monte Carlo method ; branched polymers ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The Monte Carlo sampling technique is used to investigate the branched structure formation during free-radical polymerization that involves chain transfer to polymer. This method accounts for the history of the generated branched structure and can provide virtually any structural information, because one can observe each polymer molecule directly. In this paper, we investigate the whole molecular weight distribution (MWD) for both pre- and postgelation periods, the MWDs for polymer molecules containing 0, 1, 2, 3, … branch points, the branching density of polymer molecules as functions of both size and the number of branch points, the spatial distribution of the branched chains at the theta state, etc. Contrary to the term ‘long-chain’ branching, many branch chains are relatively small, and the branched structures formed are significantly different from those usually depicted to introduce ‘branched polymers’ in many introductory textbooks. The radii of gyration at the theta state can be approximated by the Zimm-Stockmayer equation for random branching, in spite of various violations against the assumptions used in deriving the equation © 1995 John Wiley & Sons, Inc.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1515-1532 
    ISSN: 0887-6266
    Keywords: emulsion polymerization ; molecular weight distribution ; chain transfer to polymer ; branched polymers ; Monte Carlo method ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A modelistic study of the molecular weight distribution (MWD) formed in emulsion polymerization that involves chain transfer to polymer is conducted, by focusing our attention to the effect of very small reaction volume on the formed MWD. In emulsion polymerization, a polymer radical that causes polymer transfer reaction must choose the partner only within the same particle, which makes the expected size of the polymer molecule to be chosen smaller compared with the corresponding polymerization system that involves an infinitely large number of polymeric species. The usual assumption for homogeneous polymerization that the rate of chain transfer to a particular polymer molecule is proportional to its chain length cannot be used, except when branching frequency is low and particle size is large enough. This fact invalidates the direct use of models developed for homogeneous nonlinear polymerizations to emulsion polymerizations. Model equations that could be used to assess the significance of the limited space effects on the MWD under a given polymerization condition are also proposed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1515-1532, 1997
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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