A dynamic entanglement model for adaptive networks in amorphous polymers with pH-responsive dual-shape memory effect

The pH-responsive shape memory polymers (pH-SMPs) have recently attracted significant attention due to their unique and spontaneous actuation capabilities. However, there are few constitutive models developed to explore the working principles behind these complex shape memory behaviors. In this study, a dynamic entanglement model was developed for describing the pH-responsive shape memory effect (SME) in SMPs, in which the crosslinking points in polymer networks underwent reversible entanglements and disentanglements. Susceptible-Infected-Susceptible (SIS) model was firstly employed to formulate an entanglement probability function, which was used to identify the working principles for entanglements of polymer networks and shape recovery of the pH-SMPs. An entanglement free-energy function was further formulated to characterize the pH-responsive dual-SMEs based on the Flory-Huggins solution theory. Phase transition theory was then used to characterize glass transition behaviors and recovery strains of the pH-SMPs, by combining Gordon-Taylor and Kohlrausch-Williams-Watts (KWW) equations. Finally, the proposed model was verified using experimental results reported in the literature. This study provides a fundamental approach to explore the working principle and constitutive relationship between reversible entanglement and pH-responsive SME in SMPs.