Coalescence Model for Crumpled Globules Formed in Polymer Collapse

TL;DR

This paper introduces a coarse-grained coalescence model for polymer collapse that captures the fractal crumpled globule structure, explaining the slow scaling behavior through hierarchical blob dynamics.

Contribution

The study presents a simplified coalescence model that reproduces key features of crumpled globules, providing insights into their hierarchical structure and slow approach to scaling.

Findings

Model accurately reproduces distance-segment length dependence.

Hierarchical coalescence explains slow scaling behavior.

Wide blob size distribution influences the dynamics.

Abstract

The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not `equilibrate' subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting that the slow approach to scaling is related to the wide distribution of blob sizes.