Importance of intermolecular uncrossability on single-molecule conformation and intermolecular packing structures in ring polymer melts

Nonconcatenated macromolecular rings are a fascinating class of soft, globule-like objects with promising properties relevant to cutting-edge problems in polymer science and chromosome biophysics. The influence of topological constraints on ring conformations, packing structures, thermodynamics, and dynamics has remained a long-standing and challenging issue for decades. In lattice-based Monte Carlo simulations, by adjusting bond-crossing permissions, we have explored the impact of intra- and inter-molecular topological constraints on ring conformation and packing correlations in high-weight ring polymer melts. We discovered that the uncrossability, or cooperative effect, between chains in different rings is the dominant factor in forming the globule-like single-molecular conformation, thereby governing the strength of the inter-ring correlation hole effect. In contrast, the intra-ring uncrossability provides the stress necessary to prevent the formation of fully compact ring structures, allowing for a moderate level of interpenetration. The combination of this significant correlation hole effect and medium-level interpenetration is the essential reason for a series of unique structural, thermodynamic, and dynamic behaviors/properties of ring polymers in melts. Furthermore, the impact of topological constraints on structures in different degrees of polymerization is analyzed, revealing a competitive mechanism between the intra-ring enclosed loop confinement and inter-ring cooperative effects. This elucidates the intrinsic differences in polymer conformation and packing correlations between rings in high and low degrees of polymerization. Our results offer potential avenues for studying topologically constrained dynamics of rings and set the stage to address structural and thermodynamic challenges in various families of compact polymeric systems.