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

TL;DR

This paper uses computer simulations to compare annealed and quenched randomly branching polymers in three dimensions, analyzing their conformations, connectivity, and contact probabilities, and assessing Flory theory's predictive accuracy.

Contribution

It introduces a novel critical exponent, $ heta_{path}$, to better characterize contact probabilities and evaluates Flory theory's limitations for these polymer systems.

Findings

Quenched trees swell less than annealed trees in good solvent.

Flory theory accurately predicts overall swelling but fails for contact probabilities.

Introduction of $ heta_{path}$ improves understanding of node contact decay.

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.