Ring polymer physics and rheology: Challenges and opportunities

Understanding the structure and dynamics of ring or cyclic polymers is a long-standing challenge in polymer science, with important implications for emerging biological phenomena such as chromosome territories. This Perspective article provides a comprehensive overview of the current state of ring polymer physics and rheology, highlighting emerging challenges and opportunities for future research. Key scientific questions are considered regarding the properties of synthetic and biological ring polymer systems using theory, simulations, and experiments. This article was inspired by stimulating discussions at a CECAM Flagship workshop on Ring Polymer Dynamics in Prato, Italy, in June 2023. Several of the concepts and results discussed here are also presented in the Journal of Rheology virtual issue on ring polymers (https://pubs.aip.org/jor/collection/1392/Ring-Polymers). Broadly, this article aims to spark conceptual advances in polymer physics and rheology by exploring new phenomena and open scientific questions that are unique to ring polymer systems.