Aggregation and structural phase transitions of semiflexible polymer bundles: a braided circuit topology approach

TL;DR

This paper introduces a braided circuit topology framework to analyze the topology and phase transitions in aggregates of semiflexible polymers, revealing new insights into their structural reordering and entanglement.

Contribution

It extends circuit topology to multichain systems, providing topological measures as order parameters for structural phase transitions in polymer aggregates.

Findings

Circuit topological motifs effectively characterize phase transitions.

The framework detects structural re-ordering beyond traditional measures.

Topological measures correlate with polymer aggregation and entanglement.

Abstract

We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single isolated folded linear chains, the number and arrangement of contacts within the circuitry of a folded chain give rise to increasingly complex fold topologies. Another avenue for achieving complexity is through the interaction and entanglement of two or more folded linear chains. The braided circuit topology approach describes the topology of such multiple-chain systems and offers topological measures such as writhe, complexity, braid length, and isotopy class. This extension of circuit topology to multichains reveals the interplay between collapse, aggregation, and entanglement. In this work, we show that circuit topological motif fractions are ideally suited order parameters to characterise structural phase transitions in entangled systems that can detect structural re-ordering other measures cannot.