Stress relaxation and anomalous diffusion in unentangled supramolecular networks

Supramolecular networks are a class of soft materials with applications in matrices for tissue engineering, enhanced oil recovery, sacrificial components in tough double networks, injectable biomaterials for minimally invasive surgery and self-healing soft materials. In most of these applications it is crucial to understand the mechanical properties of the materials and predict the diffusion of the network forming constituents. Recent experiments have revealed that a variety of unentangled associative polymers with different architecture (linear and branched) and different nature of the associating interaction (associative protein domains and metal-ligand bonds) exhibit unexplained apparent superdiffusive behavior. Here, results of a coarse-grained molecular model of star-shaped unentangled associating polymers are presented. The model explains the observed superdiffusive scaling and reveals three basic mechanisms of molecular diffusion: caging dynamics, walking diffusion and molecular hopping, all of which depend strongly on polymer concentration, arm length, and the association/dissociation kinetics. The observed superdiffusive behavior results primarily from molecular hopping, which prevails over walking when the kinetics of attachment are much slower than the relaxation time of dangling strands. Simple scaling relationships are derived to identify the range of rate constants over which this behavior can be expected. The formation of intramolecular associations or loops in the network promotes this superdiffusive scaling by reducing the total number of arms that must detach in order for a hopping event to occur. In addition, the effect of the number of arms on the diffusivity and relaxation modulus is also studied, the model is extended to different architectures, and the impact of the model predictions on practical aspects like the gel erosion of self-healing time are explored.