{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T11:02:15Z","timestamp":1791198135320,"version":"4.1.0"},"reference-count":64,"publisher":"AIP Publishing","issue":"13","funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["C2001-23Y"],"award-info":[{"award-number":["C2001-23Y"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,7]]},"abstract":"<jats:p>Classical nucleation theories relying on quasi-equilibrium thermodynamics fail to capture the far-from-equilibrium structural reordering inherent to early stage condensed-cluster formation. We develop a framework that maps a continuous structural field onto a core\u2013shell model, coupling local non-conservative reordering with mesoscopic phase-boundary propagation. By evaluating the reordering-mediated nucleation time, we analytically distinguish the static potential energy profile from the effective nucleation barrier. Our mean-field solution reveals a kinetic turnover effect: beyond a critical structural-density coupling threshold, rapid reordering dynamics induce a steep interfacial gradient in the structural field, incurring an energetic penalty that suppresses the net driving force for nucleation. This behavior highlights a fundamental non-reciprocity between cluster growth and local structural relaxation. The reordered intermediate states replicate experimentally observed size-dependent structural gradients and offer a resolution to discrepancies between classical predictions and measured nucleation rates, providing testable criteria for multi-step pathways in nanocrystallization and biomolecular condensation.<\/jats:p>","DOI":"10.1063\/5.0352183","type":"journal-article","created":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T10:39:59Z","timestamp":1791196799000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Reordering-mediated nucleation dynamics in early stage phase separation"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0218-4985","authenticated-orcid":false,"given":"Kaicheng","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Chemistry, The Hong Kong University of Science and Technology 1 , Kowloon,","place":["Hong Kong"]},{"name":"IAS Center for AI for Scientific Discoveries, HKUST Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology 2 , Kowloon,","place":["Hong Kong"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9760-6567","authenticated-orcid":false,"given":"Haibin","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Chemistry, The Hong Kong University of Science and Technology 1 , Kowloon,","place":["Hong Kong"]},{"name":"IAS Center for AI for Scientific Discoveries, HKUST Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology 2 , Kowloon,","place":["Hong Kong"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,5]]},"reference":[{"issue":"5932","key":"2026100506395024500_c1","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1126\/science.1172104","article-title":"Observation of single colloidal platinum nanocrystal growth trajectories","volume":"324","year":"2009","journal-title":"Science"},{"issue":"9","key":"2026100506395024500_c2","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1557\/mrs.2020.229","article-title":"Nucleation, growth, and superlattice formation of nanocrystals observed in liquid cell transmission electron microscopy","volume":"45","year":"2020","journal-title":"MRS Bull."},{"key":"2026100506395024500_c3","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1146\/annurev-physchem-032511-143750","article-title":"Nucleation in polymers and soft matter","volume":"65","year":"2014","journal-title":"Annu. Rev. Phys. Chem."},{"issue":"7885","key":"2026100506395024500_c4","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1038\/s41586-021-03905-5","article-title":"Nucleation landscape of biomolecular condensates","volume":"599","year":"2021","journal-title":"Nature"},{"issue":"13","key":"2026100506395024500_c5","doi-asserted-by":"publisher","first-page":"8550","DOI":"10.1021\/acs.chemrev.4c00138","article-title":"Fundamental aspects of phase-separated biomolecular condensates","volume":"124","year":"2024","journal-title":"Chem. Rev."},{"issue":"1","key":"2026100506395024500_c6","doi-asserted-by":"publisher","first-page":"7730","DOI":"10.1038\/s41467-025-62055-8","article-title":"Current practices in the study of biomolecular condensates: A community comment","volume":"16","year":"2025","journal-title":"Nat. Commun."},{"issue":"4","key":"2026100506395024500_c7","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1038\/s41580-025-00897-2","article-title":"The dynamic and heterogeneous composition of biomolecular condensates and its functional relevance","volume":"27","year":"2026","journal-title":"Nat. Rev. Mol. Cell Biol."},{"issue":"303","key":"2026100506395024500_c8","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1080\/14786440009463908","article-title":"On the velocity of solidification and viscosity of super-cooled liquids","volume":"50","year":"1900","journal-title":"London, Edinburgh, Dublin Philos. Mag. J. Sci."},{"key":"2026100506395024500_c9","first-page":"498","article-title":"Note on a relation between the speed of crystallization and viscosity","volume":"1","year":"1932","journal-title":"Phisik. Zeit. Sowjetunion"},{"issue":"8","key":"2026100506395024500_c10","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1002\/andp.19354160806","article-title":"Kinetische behandlung der keimbildung in \u00fcbers\u00e4ttigten d\u00e4mpfen","volume":"416","year":"1935","journal-title":"Ann. Phys."},{"issue":"1\u20132","key":"2026100506395024500_c11","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0022-3697(61)90054-3","article-title":"The kinetics of precipitation from supersaturated solid solutions","volume":"19","year":"1961","journal-title":"J.\u00a0Phys. Chem. Solids"},{"issue":"7\u20138","key":"2026100506395024500_c12","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1002\/bbpc.19610650704","article-title":"Theorie der alterung von niederschl\u00e4gen durch uml\u00f6sen (Ostwald\u2013Reifung)","volume":"65","year":"1961","journal-title":"Z. Elektrochem., Ber. Bunsengesellschaft Phys. Chem."},{"key":"2026100506395024500_c13","volume-title":"Classical Nucleation Theory in Multicomponent Systems","year":"2006"},{"issue":"15","key":"2026100506395024500_c14","doi-asserted-by":"publisher","first-page":"7610","DOI":"10.1021\/cr400544s","article-title":"Mechanisms of nucleation and growth of nanoparticles in solution","volume":"114","year":"2014","journal-title":"Chem. Rev."},{"issue":"2","key":"2026100506395024500_c15","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1063\/1.1744102","article-title":"Free energy of a nonuniform system. I. Interfacial free energy","volume":"28","year":"1958","journal-title":"J.\u00a0Chem. Phys."},{"issue":"9","key":"2026100506395024500_c16","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1016\/0001-6160(61)90182-1","article-title":"On spinodal decomposition","volume":"9","year":"1961","journal-title":"Acta Metall."},{"issue":"14","key":"2026100506395024500_c17","doi-asserted-by":"publisher","first-page":"145702","DOI":"10.1103\/physrevlett.98.145702","article-title":"Origin of the failure of classical nucleation theory: Incorrect description of the smallest clusters","volume":"98","year":"2007","journal-title":"Phys. Rev. Lett."},{"issue":"20","key":"2026100506395024500_c18","doi-asserted-by":"publisher","first-page":"206102","DOI":"10.1103\/physrevlett.132.206102","article-title":"Crystal nucleation in supercooled atomic liquids","volume":"132","year":"2024","journal-title":"Phys. Rev. Lett."},{"issue":"14","key":"2026100506395024500_c19","doi-asserted-by":"publisher","first-page":"148201","DOI":"10.1103\/physrevlett.134.148201","article-title":"Falsifiability test for classical nucleation theory","volume":"134","year":"2025","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"2026100506395024500_c20","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1038\/nphys2817","article-title":"Visualizing kinetic pathways of homogeneous nucleation in colloidal crystallization","volume":"10","year":"2014","journal-title":"Nat. Phys."},{"issue":"4","key":"2026100506395024500_c21","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1038\/nchem.2675","article-title":"Real-time molecular scale observation of crystal formation","volume":"9","year":"2017","journal-title":"Nat. Chem."},{"issue":"8","key":"2026100506395024500_c22","doi-asserted-by":"publisher","first-page":"16034","DOI":"10.1038\/natrevmats.2016.34","article-title":"Nonclassical nucleation and growth of inorganic nanoparticles","volume":"1","year":"2016","journal-title":"Nat. Rev. Mater."},{"issue":"1","key":"2026100506395024500_c23","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1038\/nchem.2618","article-title":"Multistep nucleation of nanocrystals in aqueous solution","volume":"9","year":"2017","journal-title":"Nat. Chem."},{"issue":"11","key":"2026100506395024500_c24","doi-asserted-by":"publisher","first-page":"6663","DOI":"10.1021\/acs.cgd.6b00794","article-title":"A review of classical and nonclassical nucleation theories","volume":"16","year":"2016","journal-title":"Cryst. Growth Des."},{"issue":"1","key":"2026100506395024500_c25","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1146\/annurev-physchem-082720-100947","article-title":"Classical and nonclassical nucleation and growth mechanisms for nanoparticle formation","volume":"73","year":"2022","journal-title":"Annu. Rev. Phys. Chem."},{"issue":"17","key":"2026100506395024500_c26","doi-asserted-by":"publisher","first-page":"174905","DOI":"10.1063\/1.1887168","article-title":"Nucleation of ordered solid phases of proteins via a disordered high-density state: Phenomenological approach","volume":"122","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"issue":"11","key":"2026100506395024500_c27","doi-asserted-by":"publisher","first-page":"2346","DOI":"10.1039\/c0nr00628a","article-title":"The two-step mechanism of nucleation of crystals in solution","volume":"2","year":"2010","journal-title":"Nanoscale"},{"issue":"1","key":"2026100506395024500_c28","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1038\/nmat4083","article-title":"Two-step nucleation mechanism in solid\u2013solid phase transitions","volume":"14","year":"2015","journal-title":"Nat. Mater."},{"issue":"7762","key":"2026100506395024500_c29","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1038\/s41586-019-1317-x","article-title":"Observing crystal nucleation in four dimensions using atomic electron tomography","volume":"570","year":"2019","journal-title":"Nature"},{"issue":"1","key":"2026100506395024500_c30","doi-asserted-by":"publisher","first-page":"5007","DOI":"10.1038\/s41467-021-24857-4","article-title":"Probing atom dynamics of excited Co\u2013Mo\u2013S nanocrystals in 3D","volume":"12","year":"2021","journal-title":"Nat. Commun."},{"issue":"10","key":"2026100506395024500_c31","doi-asserted-by":"publisher","first-page":"e2008880118","DOI":"10.1073\/pnas.2008880118","article-title":"Three-step nucleation of metal\u2013organic framework nanocrystals","volume":"118","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"issue":"1","key":"2026100506395024500_c32","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1038\/s41563-024-02025-5","article-title":"Formation, chemical evolution and solidification of the dense liquid phase of calcium (bi)carbonate","volume":"24","year":"2025","journal-title":"Nat. Mater."},{"issue":"23","key":"2026100506395024500_c33","doi-asserted-by":"publisher","first-page":"e2424950122","DOI":"10.1073\/pnas.2424950122","article-title":"Multiphasic size-dependent growth dynamics of nanoparticle ensembles","volume":"122","year":"2025","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100506395024500_c34","doi-asserted-by":"publisher","DOI":"10.1038\/s41563-026-02727-y","article-title":"Crystal nucleation and growth in high-entropy alloys revealed by atomic electron tomography","year":"2026","journal-title":"Nat. Mater."},{"issue":"1","key":"2026100506395024500_c35","doi-asserted-by":"publisher","first-page":"3260","DOI":"10.1038\/s41467-020-16892-4","article-title":"Uncovering the effects of interface-induced ordering of liquid on crystal growth using machine learning","volume":"11","year":"2020","journal-title":"Nat. Commun."},{"issue":"6","key":"2026100506395024500_c36","doi-asserted-by":"publisher","first-page":"064205","DOI":"10.1103\/physrevb.108.064205","article-title":"Crystal nucleation and growth in liquids: Cooperative atom attachment and detachment","volume":"108","year":"2023","journal-title":"Phys. Rev. B"},{"issue":"4","key":"2026100506395024500_c37","doi-asserted-by":"publisher","first-page":"eaav7399","DOI":"10.1126\/sciadv.aav7399","article-title":"How crystals form: A theory of nucleation pathways","volume":"5","year":"2019","journal-title":"Sci. Adv."},{"issue":"24","key":"2026100506395024500_c38","doi-asserted-by":"publisher","first-page":"246101","DOI":"10.1103\/physrevlett.129.246101","article-title":"Crystal polymorphism induced by surface tension","volume":"129","year":"2022","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"2026100506395024500_c39","doi-asserted-by":"publisher","first-page":"064110","DOI":"10.1103\/physreve.106.064110","article-title":"Using classical density functional theory to determine crystal-fluid surface tensions","volume":"106","year":"2022","journal-title":"Phys. Rev. E"},{"issue":"10","key":"2026100506395024500_c40","doi-asserted-by":"publisher","first-page":"104502","DOI":"10.1063\/5.0225658","article-title":"A microscopic approach to crystallization: Challenging the classical\/non-classical dichotomy","volume":"161","year":"2024","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100506395024500_c41","first-page":"1","article-title":"First-passage fundamentals","volume-title":"A Guide to First-Passage Processes","author":"Redner","year":"2001"},{"key":"2026100506395024500_c42","doi-asserted-by":"publisher","first-page":"128545","DOI":"10.1016\/j.physa.2023.128545","article-title":"A first look at first-passage processes","volume":"631","year":"2023","journal-title":"Physica A"},{"key":"2026100506395024500_c43","volume-title":"Random Walks in Biology","year":"1993"},{"key":"2026100506395024500_c44","volume-title":"Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems","year":"2006"},{"issue":"3","key":"2026100506395024500_c45","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1103\/revmodphys.65.599","article-title":"Electron transfer reactions in chemistry: Theory and experiment","volume":"65","year":"1993","journal-title":"Rev. Mod. Phys."},{"issue":"19","key":"2026100506395024500_c46","doi-asserted-by":"publisher","first-page":"194113","DOI":"10.1063\/5.0298872","article-title":"Illuminating non-equilibrium multi-step reaction dynamics with stochastic Marcus state model","volume":"163","year":"2025","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100506395024500_c47","volume-title":"The Fokker\u2013Planck Equation: Methods of Solution and Applications","year":"1996","edition":"2"},{"key":"2026100506395024500_c48","first-page":"39","article-title":"Path integral associated with the Fokker\u2013Planck equation BT\u2014Path integrals: And their applications in quantum","volume-title":"Statistical and Solid State Physics","author":"Papadopoulos","year":"1978"},{"key":"2026100506395024500_c49","volume-title":"Statistical Physics of Fields","year":"2007"},{"key":"2026100506395024500_c50","volume-title":"Quantum Field Theory in a Nutshell","year":"2010"},{"key":"2026100506395024500_c51","volume-title":"Quantum Field Theory: A Diagrammatic Approach","year":"2021"},{"issue":"6","key":"2026100506395024500_c52","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1143\/jpsj.12.570","article-title":"Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems","volume":"12","year":"1957","journal-title":"J.\u00a0Phys. Soc. Jpn."},{"issue":"1","key":"2026100506395024500_c53","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1088\/0034-4885\/29\/1\/306","article-title":"The fluctuation\u2013dissipation theorem","volume":"29","year":"1966","journal-title":"Rep. Prog. Phys."},{"issue":"4761","key":"2026100506395024500_c54","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1126\/science.233.4761.330","article-title":"Brownian motion and nonequilibrium statistical mechanics","volume":"233","year":"1986","journal-title":"Science"},{"issue":"3\u20134","key":"2026100506395024500_c55","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1515\/jnum-2012-0013","article-title":"New development in freefem++","volume":"20","year":"2012","journal-title":"J.\u00a0Numer. Math."},{"issue":"1","key":"2026100506395024500_c56","doi-asserted-by":"publisher","first-page":"011035","DOI":"10.1103\/physrevx.5.011035","article-title":"Statistical mechanics where Newton\u2019s third law is broken","volume":"5","year":"2015","journal-title":"Phys. Rev. X"},{"issue":"4","key":"2026100506395024500_c57","doi-asserted-by":"publisher","first-page":"041009","DOI":"10.1103\/physrevx.10.041009","article-title":"Scalar active mixtures: The nonreciprocal Cahn\u2013Hilliard model","volume":"10","year":"2020","journal-title":"Phys. Rev. X"},{"issue":"1","key":"2026100506395024500_c58","doi-asserted-by":"publisher","first-page":"7035","DOI":"10.1038\/s41467-023-42713-5","article-title":"Non-reciprocity across scales in active mixtures","volume":"14","year":"2023","journal-title":"Nat. Commun."},{"issue":"11","key":"2026100506395024500_c59","doi-asserted-by":"publisher","first-page":"117103","DOI":"10.1103\/physrevlett.134.117103","article-title":"Nonreciprocal Ising model","volume":"134","year":"2025","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"2026100506395024500_c60","doi-asserted-by":"publisher","first-page":"034401","DOI":"10.1088\/1367-2630\/ae4f19","article-title":"Nonreciprocal constitutive laws for oriented active solids","volume":"28","year":"2026","journal-title":"New J. Phys."},{"key":"2026100506395024500_c61","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1146\/annurev.physchem.53.082301.113146","article-title":"TRANSITION PATH SAMPLING: Throwing ropes over rough Mountain passes, in the dark","volume":"53","year":"2002","journal-title":"Annu. Rev. Phys. Chem."},{"issue":"4","key":"2026100506395024500_c62","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1038\/s43588-023-00428-z","article-title":"Machine-guided path sampling to discover mechanisms of molecular self-organization","volume":"3","year":"2023","journal-title":"Nat. Comput. Sci."},{"key":"2026100506395024500_c63","unstructured":"K.\n            Zhu\n           and H.Su, \u201cKinetic turnover in the early-stage nucleation of multi-shell condensed clusters,\u201d arXiv:2608.24792 (2026)."},{"key":"2026100506395024500_c64","doi-asserted-by":"publisher","first-page":"1891","DOI":"10.1038\/s41557-025-01928-3","article-title":"A label-free method for measuring the composition of multicomponent biomolecular condensates","volume":"17","year":"2025","journal-title":"Nat. Chem."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0352183\/21160787\/134116_1_5.0352183.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0352183\/21160787\/134116_1_5.0352183.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T10:40:02Z","timestamp":1791196802000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/13\/134116\/3405892\/Reordering-mediated-nucleation-dynamics-in-early"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,5]]},"references-count":64,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2026,10,7]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0352183","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10,7]]},"published":{"date-parts":[[2026,10,5]]},"article-number":"134116"}}