Computer simulations of randomly branching polymers: Annealed vs. quenched branching structures

Abstract

We present computer simulations of three systems of randomly branching polymers in d=3 dimensions: ideal trees and self-avoiding trees with annealed and quenched connectivities. In all cases, we performed a detailed analysis of trees connectivities, spatial conformations and statistical properties of linear paths on trees, and compare the results to the corresponding predictions of Flory theory. We confirm that, overall, the theory predicts correctly that trees with quenched ideal connectivity exhibit {\it less} overall swelling in good solvent than corresponding trees with annealed connectivity even though they are more strongly stretched on the path level. At the same time, we emphasize the inadequacy of the Flory theory in predicting the behaviour of other, and equally relevant, observables like contact probabilities between tree nodes. We show, then, that contact probabilities can be aptly characterized by introducing a novel critical exponent, ${\theta }_{path}$, which accounts for how they decay as a function of the node-to-node path distance on the tree.

25 pages, 12 figures, including supplementary data

Cited by in corpus (10)

• Computer simulations of melts of randomly branching polymers
• Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure
• Beyond Flory theory: Distribution functions for interacting lattice trees
• Marginally compact hyperbranched polymer trees
• Amoeba Monte Carlo algorithms for random trees with controlled branching activity: efficient trial move generation and universal dynamics
• Entropy of self-avoiding branching polymers: mean field theory and Monte Carlo simulations
• The configurational entropy of random trees
• Configurational entropy of randomly double-folding ring polymers
• Ring polymers in two-dimensional melts double-fold around randomly branching "primitive shapes"
• Coherent modeling of double-folded ring polymers and their underlying random tree structure