# Phase diagram of thick ribbons in a bad solvent

## TL;DR

This study explores the phase behavior of thick, hydrophobic ribbons in bad solvents, revealing various stable configurations and the conditions that favor twisted, globular, or rolled structures through simulations and analytical models.

## Contribution

It introduces a comprehensive phase diagram for thick ribbons in bad solvents, highlighting the stabilization of twisted structures without energetic bias.

## Key findings

- Multiple stable configurations identified: rolled, curled, twisted, globule.
- Twisted ribbons can be the ground state even without energetic preference for twisting.
- Increasing solvent size favors symmetry-breaking and globular conformations.

## Abstract

Ribbons are topological objects of biological and technological importance. Here, we study the folding of thick ribbons with hydrophobic surfaces in a bad solvent in regimes in which either the ribbon's thickness or the solvent molecule size is not vanishingly small compared to the ribbon's width. Extensive Monte Carlo simulations show that ribbons of various lengths and with a small stiffness adopt several distinct configurations as the ground state that include rolled (Archimedean spiral), curled, twisted and globule conformations. Analytic and numerical calculations based on the consideration of putative ground states lead to phase diagrams that qualitatively agree with the simulation results. A symmetry breaking of the planar rolled configuration in favor of the elongated twisted and the globular ribbons is observed on increasing the solvent size. Interestingly, the twisted ribbon is found as the ground state in the absence of any energetic preference for twisting. We show that the twist of the DNA double helix structure can be stabilized when modeled as a hydrophobic thick ribbon even in the limit of vanishing solvent size.