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Monte Carlo simulation of random branching in hyperbranched polymers

Richards, E. Louise; Buzza, D. Martin A.; Davies, Geoff R.


E. Louise Richards

Geoff R. Davies


We study the branching statistics of hyperbranched polymers formed from a one-pot melt polymerization of AB2 monomers via Monte Carlo simulation. To simulate the reaction ensemble, we use a 3D percolation-type model where each lattice site of a cubic lattice is assumed to be occupied by a single AB2 monomer and monomers are only allowed to react with their near neighbors (A reacts exclusively with B). We also allow the possibility that the reactivity ratio κ of free B groups on linear AB2 units to those on terminal AB2 units may be different from unity (the so-called “substitution effect”). We study the molecular weight distribution, fractal structure, loop statistics, and degree of branching as a function of both the fraction of reacted A groups pA and the reactivity ratio κ. For pA → 1, we find that the molecular weight distribution of hyperbranched polymers with different pA and κ collapse remarkably well on to a universal curve of the form n(N)Nw2 = A(N/Nw)-τ exp(−BN/Nw), where n(N) is the number density of HBPs with degree of polymerization N and Nw is the weight-average molecular weight (a function of pA and κ) while A, B, and τ are constants independent of pA and κ. Our most accurate determination of τ yields τ = 1.32 ± 0.01, which is significantly different from the mean-field value of τ = 1.5. This demonstrates the importance of fluctuations in our system. The fractal dimension of HBP chains in the reaction melt is found to be in excellent agreement with the hyperscaling prediction of df = 3 [Buzza, D. M. A. Eur. Phys. J. E 2004, 13, 79] but significantly different from the mean-field result of df = 4 and the percolation result of df = 2.53. We find that the loop distribution obeys the scaling form R̂m ∝ m-αpAm, where R̂m is the number density of loops with degree of polymerization m and α ≈ 3 for all κ. Finally, we find excellent agreement between our simulations and the mean-field predictions for the degree of branching.

Journal Article Type Article
Publication Date Mar 20, 2007
Journal Macromolecules
Print ISSN 0024-9297
Electronic ISSN 1520-5835
Publisher American Chemical Society
Peer Reviewed Peer Reviewed
Volume 40
Issue 6
Pages 2210-2218
APA6 Citation Richards, E. L., Buzza, D. M. A., & Davies, G. R. (2007). Monte Carlo simulation of random branching in hyperbranched polymers. Macromolecules, 40(6), 2210-2218. doi:10.1021/ma0700126
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