Formation of Non-uniform Double Helices for Elastic Rods under Torsion

TL;DR

This paper presents a model for the formation of non-uniform double helices in elastic rods under torsion, highlighting the role of surface friction and demonstrating a method to control helix configurations.

Contribution

The study introduces a comprehensive equilibrium model for elastic rods forming double helices, accounting for surface friction effects and providing a method to design specific helix configurations.

Findings

The model accurately predicts double helix formation under different surface conditions.

Experiments confirm the model's predictions and the influence of twisting and slackening processes.

A method for manufacturing double helices with desired configurations is demonstrated.

Abstract

The spontaneous formation of double helices for filaments under torsion is common and significant. For example, the research on the supercoiling of DNA is helpful for understanding the replication and transcription of DNA. Similar double helices can appear in polymer chains, carbon nanotube yarns, cables, telephone wires and so forth. We noticed that non-uniform double helices can be produced due to the surface friction induced by the self-contact. Therefore an ideal model was presented to investigate the formation of double helices for elastic rods under torque. A general equilibrium condition which is valid for both the smooth surface and the rough surface situations is derived by using the variational method. Based on this, by adding further constraints, the smooth and rough surface situations are investigated in detail respectively. Additionally, the model showed that the specific process of how to twist and slack the rod can determine the surface friction and hence influence the configuration of the double helix formed by rods with rough surfaces. Based on this principle, a method of manufacturing double helices with designed configurations was proposed and demonstrated. Finally, experiments were performed to verify the model and the results agreed well with the theory.