A rheological model of slide-ring materials to understand the pulley effect between rings and chains

The rheology and viscoelasticity of slide-ring (SR) materials, polymer networks featuring polymer chains threading through mobile cross-linking rings, remain incompletely understood despite their superior damage resistance and fatigue performance attributed to the pulley effect. This study develops a rheological model integrating ideal springs, ideal pots, and a nonlinear pot to capture the distinctive viscoelastic response arising from chain sliding dynamics across broad frequency and temperature ranges. The proposed framework reveals the complex intermolecular and intramolecular interactions inherent in SR networks, with particular emphasis on the pulley effect as the dominant mechanism governing nonlinear behavior. Results of an analysis using the proposed model are validated against experimental data on SR materials from the literature, demonstrating superior descriptive capability compared with classical linear rheological models. The time-temperature equivalence of SR materials is analyzed based on free-volume theory and the tube model. The results provide preliminary insights into design strategies for tuning SR material viscoelasticity and establish a foundation for understanding the dependence associated with the pulley effect.