Network Percolation in Transient Polymer Networks with Temporal Hierarchy of Energy Dissipation

Transient polymer networks with a temporal hierarchy of energy dissipation have advantages in many applications, ranging from injectable hydrogels to self-healing materials. However, their structure and rheology are often estimated based on their permanent network equivalents. To account for this, we extend the mean-field Miller-Macosko's recursive model to predict the network percolation in metallo-supramolecular polymer networks. Moreover, a simple thermody-namic model is developed to predict the composition of metal complexes with different coordination geometries in a multi-component network. To challenge the theoretical framework with experiments, we form model network hydrogels upon the coordination of phenanthroline-functionalized tetra-arm poly(ethylene glycol) (tetraEPh) with a mixture of Co2+ and Fe2+ metal ions, which are proved to expose different coordination geometry preferences. We demonstrate that even small deviations in the stoichiometric ratio of ligand to metal ions or variation of the coordination geometry preference significantly changes the network structure, which results in remarkably different macroscopic properties compared to those of the equivalent permanent networks. The theoretical model can explain the variation of the lifetime and relative contributions of the fast and slow relaxation modes in the shear modulus at various metal ion compositions. Moreover, the model explains that the significant drop in the modulus in the presence of excessive metal ions is due to the profound formation of threefold connected polymer precursors. The developed theory forms a reliable framework for predicting the time evolution of the junction composition, network percolation, and defect formation in transient polymer networks.