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  • branching density distribution  (5)
  • nonlinear polymerization  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 32 (1994), S. 901-910 
    ISSN: 0887-6266
    Keywords: nonlinear free radical polymerization ; chain transfer to polymer ; terminal double-bond polymerization ; molecular weight distribution ; branching density distribution ; mathematical model ; Monte Carlo method ; method of moments ; poly (vinyl acetate) ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.
    Additional Material: 10 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 34 (1996), S. 2099-2104 
    ISSN: 0887-6266
    Keywords: molecular weight distribution ; polyradical ; gel ; polymer modification ; nonlinear polymerization ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: No abstract.
    Additional Material: 5 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 36 (1998), S. 2423-2433 
    ISSN: 0887-6266
    Keywords: gelation theory ; nonlinear polymerization ; nonrandom crosslinking ; molecular weight distribution ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: On the basis of the first-order Markovian statistics, we propose a general matrix formula for the weight-average molecular weight of crosslinked polymer systems, explicitly given by M̄w = M̄w,0 + WX0 (I - X)-1 Sf. This equation is valid for both step and chain-growth polymerizations, including those in a nonequilibrium state irrespective of the reactor types used. In the context of the present theory, the onset of gelation is simply stated as a point at which the largest eigenvalue of the matrix X reaches unity (i.e., det(I - X) = 0). The present theory provides a unified point of view for various types of gelling systems. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2423-2433, 1998
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 31 (1993), S. 1363-1371 
    ISSN: 0887-6266
    Keywords: molecular weight distribution ; nonlinear free-radical polymerization ; branching density distribution ; chain transfer to polymer ; long-chain branches ; gelation ; Monte Carlo method ; method of moments ; mathematical model ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A new theory to predict the molecular weight distribution in free radical polymerization that includes chain transfer to polymer is proposed. This theory is based on the branching density distribution of the primary polymer molecules. The branching density distribution provides the information on how each chain is connected to other chains, and therefore, a full molecular weight distribution can be calculated by application of the Monte Carlo simulation. The present theory accounts for the history of the generated branched structure and can be applied to various reaction systems that involve branching and crosslinking regardless of the reactor types used. The present simulation confirmed the validity of the method of moments in a batch polymerization proposed earlier. It was shown clearly why gelation never occurs by chain transfer to polymer without the assistance of other interlinking reaction such as bimolecular termination by combination. © 1993 John Wiley & Sons, Inc.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 32 (1994), S. 911-919 
    ISSN: 0887-6266
    Keywords: nonlinear free radical polymerization ; chain transfer to polymer ; terminal double-bond polymerization ; molecular weight distribution ; branching density distribution ; mathematical model ; Monte Carlo method ; method of moments ; poly(vinyl acetate) ; CSTR ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double bond polymerization that was proposed in Part 1 of this series is extended to a continuous stirred tank reactor. The present model is applied to the free radical polymerization of vinyl acetate in a micromixed continuous stirred tank reactor, and various information on branched structure such as the molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule are calculated. Based on the present simulation model, it was found that the method of moments used successfully to predict various average properties in a batch polymerization cannot be applied to a continuous stirred tank reactor without accounting for the outflow of polymer radicals and the existence of polyradicals. The present model has given an excellent agreement with the experimental results of Chatterjee, Park, and Graessley (1977) for a solution polymerization of vinyl acetate in a continuous stirred tank reactor. © 1994 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 34 (1996), S. 671-681 
    ISSN: 0887-6266
    Keywords: molecular weight distribution ; branching density distribution ; Monte Carlo method ; long-chain branching ; radius of gyration ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The branched structure formation during free radical polymerization of vinyl acetate is investigated in detail by application of the computer simulations on the basis of the Monte Carlo sampling technique. Simulations are made for the whole molecular weight distribution (MWD), the MWDs for polymer molecules containing 0, 1, 2, 3, etc., branch points, the branching density as functions of both size and the number of branch points, the spatial distribution of the branched chains, etc. It was found that the effect of polyradicals on the formed MWD could be neglected for batch polymerizations of the present reaction system. A large number of relatively small branch chains are formed due to both chain transfer to polymer (CTP) and the terminal double-bond polymerization (TDBP). The radius of gyration at a Θ state is found to agree satisfactorily with the Zimm-Stockmayer equation for random branching in spite of the heterogeneous branched structure formed in the polymerization. The present investigation reveals important characteristics of the complex molecular structure formation during free radical polymerization that involves both CTP and TDBP. © 1996 John Wiley & Sons, Inc.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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