Molecular understanding of Ni ²⁺ -nitrogen family metal-coordinated hydrogel relaxation times using free energy landscapes

Incorporating dynamic metal-coordination bonds as cross-links into synthetic materials has become attractive not only to improve self-healing and toughness, but also due to the tunability of metal-coordination bonds. However, a priori determination of bond lifetime of metal-coordination complexes, especially important in the rational design of metal-coordinated materials with prescribed properties, is missing. We report an empirical relationship between the energy landscape of metal-coordination bonds, simulated via metadynamics, and the resulting macroscopic relaxation time in ideal metal-coordinated hydrogels. Importantly, we expand the Arrhenius relationship between the macroscopic hydrogel relaxation time and metal-coordinate bond activation energy to include width and landscape ruggedness identified in the simulated energy landscapes. Using biologically relevant Ni2+-nitrogen coordination complexes as a model case, we demonstrate that the quantitative relationship developed from histidine-Ni2+ and imidazole-Ni2+ complexes can predict the average relaxation times of other Ni2+-nitrogen coordinated networks. We anticipate the quantitative relationship presented here to be a starting point for the development of more sophisticated models that can predict relaxation timescales of materials with programmable viscoelastic properties.