A spontaneous equilibrium free energy model for rubber elasticity of slide-ring materials to understand pulley effect and dangling effect

• Published in: Polymer (Guilford) Vol. 328; p. 128451
• Main Author: Xing, Ziyu
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 23.05.2025
• Subjects: Constitutive model; Dangling effect; Free energy model; Pulley effect; Slide-ring material; Constitutive model; Dangling effect; Pulley effect; Slide-ring material; Free energy model
• ISSN: 0032-3861
• DOI: 10.1016/j.polymer.2025.128451

The investigation of long-term sustained load-bearing and high mechanical properties of materials has been a subject of significant research interest. Scientists have recently developed slide-ring (SR) materials as a non-sacrificial reinforcement system, capable of reversible load-bearing through the pulley effect. However, the existing rubber elasticity theories have been inadequate in analyzing the sliding and dangling of chains within the ring structure, and the response mechanism of SR networks under large deformations remains poorly understood. This study proposes a new constitutive theory that incorporates the spontaneous equilibrium free energy model to better comprehend the pulley effect and dangling effect in slide-ring materials. To achieve this, the total free energy (strain energy density) of SR materials is decomposed into two components: one corresponds to the pulley effect based on rubber elasticity, and the other to the dangling effect based on the tube-like model. Each crucial free energy component is corrected considering nonlinear force-extension relationship of polymer chains, while maintaining a spontaneous equilibrium relationship. The proposed model facilitates the estimation of key parameters of SR materials, such as the number of sliding segments, and exhibits strain hardening-softening-hardening behavior. Meanwhile, based on the Rouse-Bueche-Zimm bead-spring model, the viscoelastic and thermomechanical properties of SR materials can be analyzed by proposed model. To validate the effectiveness of the proposed model, experimental results reported in the literature are utilized for comparison. The proposed model is compared with existing approaches, including the Mooney-Rivlin equation, scaling theory, topological knot theory, freely jointed chain model, worm-like chain model and Anssari-Benam model. This comparison showcases the distinctive characteristics and accuracy of the proposed model in capturing the mechanical behavior of SR materials. In this paper, a constitutive model for slide-ring polymers is proposed to develop rubber elasticity and understand pulley effect and dangling effect. Meanwhile, based on configuration of slide-ring network, the proposed model provides a strategy to model the strain hardening-softening-hardening behavior of slide-ring materials. [Display omitted] •A constitutive model for slide-ring materials to develop rubber elasticity and understand pulley effect and dangling effect.•A spontaneous equilibrium model to analysis pulley effect and the sliding of chains.•A free energy model is developed to understand the strain hardening-softening-hardening behavior.