Borromean linking in dense Olympic gels and its viscoelastic impact

Determine the prevalence of Borromean linking among ring polymers in dense Olympic gel networks and characterize the influence of such Borromean links on the viscoelastic properties of the gel.

Background

Topological constraints in polymer systems are often analyzed using the Gauss linking number (GLN), which captures pairwise linking but cannot detect higher-order Brunnian structures such as Borromean rings. Analyses of kinetoplast DNA and ring-polymer systems typically rely on GLN-based tools and therefore miss Borromean linking.

Although algorithms based on knot invariants like the Jones polynomial can, in principle, detect Borromean rings, their computational cost is prohibitive for large systems, especially because the number of possible triplets grows cubically with the number of molecules. Consequently, the likelihood of Borromean linking in dense Olympic gel networks and its rheological implications remain unresolved.