{"doi":"10.1073/pnas.2213160120","title":"Molecular understanding of Ni <sup>2+</sup> -nitrogen family metal-coordinated hydrogel relaxation times using free energy landscapes","abstract":"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 Ni 2+ -nitrogen coordination complexes as a model case, we demonstrate that the quantitative relationship developed from histidine-Ni 2+ and imidazole-Ni 2+ complexes can predict the average relaxation times of other Ni 2+ -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.","journal":"Proceedings of the National Academy of Sciences","year":2023,"id":329365,"datarank":0.4493598410330987,"base_score":2.995732273553991,"endowment":2.995732273553991,"self_citation_contribution":0.4493598410330987,"citation_network_contribution":0.0,"self_endowment_contribution":0.4493598410330987,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":19,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9546,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2023-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1052523,"name":"Seth Cazzell","orcid":null,"position":1,"is_corresponding":false},{"id":1052057,"name":"Jake Song","orcid":"0000-0003-1254-6206","position":2,"is_corresponding":false},{"id":1052058,"name":"Niels Holten‐Andersen","orcid":"0000-0002-5318-9674","position":3,"is_corresponding":false},{"id":109876,"name":"Markus J. Buehler","orcid":"0000-0002-4173-9659","position":4,"is_corresponding":false},{"id":692089,"name":"Eesha Khare","orcid":"0000-0001-8696-9821","position":0,"is_corresponding":true}],"reference_count":42,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-07-19T01:09:01.509601Z","pmid":"36649435","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}