Molecular understanding of Ni2+-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.

Expanding the stoichiometric window for metal cross-linked gel assembly using competition.

Polymer networks with dynamic cross-links have generated widespread interest as tunable and responsive viscoelastic materials. However, narrow stoichiometric limits in cross-link compositions are typically imposed in the assembly of these materials to prevent excess free cross-linker from dissolving the resulting polymer networks. Here we demonstrate how the presence of molecular competition allows for vast expansion of the previously limited range of cross-linker concentrations that result in robust network assembly. Specifically, we use metal-coordinate cross-linked gels to verify that stoichiometric excessive metal ion cross-linker concentrations can still result in robust gelation when in the presence of free ion competing ligands, and we offer a theoretical framework to describe the coupled dynamic equilibria that result in this effect. We believe the insights presented here can be generally applied to advance engineering of the broadening class of polymer materials with dynamic cross-links.