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Monte Carlo Applications in Polymer Science (Paperback)
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Monte Carlo Applications in Polymer Science (Paperback)
Series: Lecture Notes in Chemistry, 27
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The aim of this chapter is to discuss in detail the Monte Carlo
algorithms developed to compute the sequence distributions in
polymers. Because stereoregular polymers constitute a unique form
of copolymer, the stereosequence distributions in vinyl
homopolymers and the sequence distributions in copolymers can be
computed using the same algorithms. Also included is a brief review
of probabilistic models (i. e. , Bernoulli trials and Markov
chains) frequently used to compute the sequence distribtuion. The
determination of sequence distributions is important for the under-
standing of polymer physical properties, to compute the monomer
reactivity para- meters and to discriminate among polymerization
mechanisms. 2. 2. Short review of analytical models, Monte Carlo
algorithms and computer programs. l A Bernoullian model was
developed by Price. Within this model the probability of a given
state of the system is independent of the previous state and does
not condition the next state. The Bernoullian behaviour has been
shown 24 to describe cls-trans distributions among 1, 4 additions
in polybutadienes - , 5 the comonomer distribution in
ethylene-vinyl acetate copolymer , and configura- 6 tional
distributions in polystyrene , poly (vinyl chloride)7, poly (vinyl
alcohol)7 Consider the binary copolymerization:;1,J=1,2 (1) where -
MI* , I = 1,2, is an ionic or radical polymeric chain end, and M, J
= 1,2, J is a monomer. Because the final state (i. e.
General
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