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Theory of polydisperse reacting polymer systems
Author(s) -
O'Shaughnessy Ben
Publication year - 1995
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.1995.040040307
Subject(s) - thermodynamics , polymer , chemistry , reaction rate constant , relaxation (psychology) , chain (unit) , polymerization , kinetics , diffusion , degree of polymerization , function (biology) , polymer chemistry , physics , organic chemistry , quantum mechanics , psychology , social psychology , evolutionary biology , biology
The kinetics of irreversible reactions between polymer chains of different molecular weights are studied, with emphasis on the case of highly reactive end groups. We calculate the rate constant k ( N , M ) for reaction between chains of lengths N and M respectively, in dilute and semi‐dilute solutions and in the melt. In all cases, k ( N , M ) is dominated by the shortest chain: the limit k ( N ) ≡ k ( N , ∞) is well‐defined and scales as if both chains were of length N . In dilute solutions k ( N , M ) obeys mean field theory, being proportional to the equilibrium reactive group contact probability. For melts and concentrated solutions, k ( N , M ) follows diffusion‐controlled laws: k ( N , M ) ≈ ( R N 3 /τ N )ƒ( M / N ) where R N and τ N are the coil size and relaxation time of the shortest chain N , and ƒ( M / N ) is a cross‐over function describing the approach to the asymptotic form k ( N ) for M / N ≫ 1. We calculate the leading contributions to this cross‐over function, which has universal forms depending on the concentration regime. The implications of these results for high‐conversion free‐radical polymerization are discussed.