Disordered Assemblies of Rubber Bands as a Model of Polymer Rings

A comprehensive understanding of the packing structure of dense assemblies of semiflexible rings is not only fundamental for the dynamical description of polymer rings but also key to understand biopackaging, such as observed in the circular DNA of viruses or genome folding.
In this work, we use X-ray tomography to study disordered packings of rubber bands in a cylindrical container as a simple model of semiflexible polymer rings.
Using advanced computational tools, we study the geometrical and topological features of disordered packings of rubber bands at a single ring-level. The degree of entanglement in the structures is quantified through minimal surfaces and generalized Voronoi tessellations. We found that assemblies of short bands assume a liquid-like disordered structure, with short-range orientational order, revealing a minor influence of the container. In the case of longer bands, the confinement causes folded configurations, and the bands interpenetrate and entangle. Most of the systems are found to display a threading network that percolates the system. Surprisingly, for long bands whose diameter doubles the diameter of the container, we observe that all bands interpenetrate each other in a complex fully-entangled structure.