Computer simulations of melts of randomly branching polymers

TL;DR

This paper uses computer simulations to analyze the structure and conformations of melts of randomly branching polymers, revealing their compact fractal nature and partial screening of excluded volume effects.

Contribution

It provides detailed simulation data on annealed randomly branching polymers, confirming asymptotic scaling laws and the influence of excluded volume interactions.

Findings

Average tree size scales as R ~ N^{1/d}

Trees behave as compact, territorial fractals

Excluded volume interactions are only partially screened

Abstract

Randomly branching polymers with {\em annealed} connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present computer simulations of melts of annealed randomly branching polymers of $3 \le N \le 1800$ segments in $d=2$ and $d=3$ dimensions. In all cases, we perform a detailed analysis of the observed tree connectivities and spatial conformations. Our results are in excellent agreement with an asymptotic scaling of the average tree size of $R \sim N^{1/d}$, suggesting that the trees behave as compact, {\it territorial} fractals. The observed swelling relative to the size of ideal trees, $R\sim N^{1/4}$, demonstrates that excluded volume interactions are only partially screened in melts of annealed trees. Overall, our results are in good qualitative agreement with the predictions of Flory theory. In particular, we find that the trees swell by the combination of modified branching and path stretching. However, the former effect is subdominant and difficult to detect in $d=3$ dimensions.