Bridging experiments and theory: Isolating the effects of metal-ligand interactions on viscoelasticity of reversible polymer networks

Polymer networks cross-linked by reversible metal-ligand interactions possess versatile mechanical properties achieved simply by varying the metal species and quantity. Although prior experiments have revealed the dependence of the network's viscoelastic behavior on the dynamics of metal-ligand interaction, a theoretical framework with quantitative relations that would enable efficient material design, is still lacking. One major challenge is isolating the effect of metal-ligand interaction from other factors in the polymer matrix. To address this challenge, we designed a linear precursor free from solvents, chain entanglements and polymer-metal phase separation to ensure that relaxation of the network is mainly governed by the dissociation and association of the metal-ligand cross-links. The rheological behavior of the networks was thoroughly characterized regarding the changes in cross-link density, binding stoichiometry and coordination stability, allowing quantitative comparison between experimental results and the sticky Rouse model. Through this process, we noticed that the presence of reversible cross-links increases the network modulus at high frequency compared to the linear polymer, and that the effective metal-ligand dissociation time increases dramatically with increasing the cross-link density. Informed by these findings, we modified the expression of the sticky Rouse model. For the polymer in which the metal center and ligands bond in a paired association, the relaxation follows our enhanced sticky Rouse model. For the polymer in which each reversible cross-link consists of multiple metal centers and ligands, the relaxation timescale is significantly extended due to greater restriction on the polymer chains. This systematic study bridges experiments and theory, providing deeper understanding of the mechanical properties of metallopolymers and facilitating material design.