{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T11:55:27Z","timestamp":1775044527114,"version":"3.50.1"},"reference-count":52,"publisher":"AIP Publishing","issue":"13","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22573021"],"award-info":[{"award-number":["22573021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22573037"],"award-info":[{"award-number":["22573037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,4,7]]},"abstract":"<jats:p>Topology and topological effects play a key role in the conformational and dynamic properties of polymer chains in varying situations. Among others, threading in ring polymers emerges as a unique topological phenomenon due to a combinational effect of polymer entanglement and the circular topology of the rings. In this work, the threading statistics of interlocked ring polymers (also called [n]catenanes) in melts were investigated by molecular dynamics simulations of the Kremer\u2013Grest model with the aid of a modified algorithm based on primitive path analysis. We mainly studied the threading statistics of [n]catenanes with varying n but fixed chain length of the building blocks (i.e., rings), m = 128, of the chain. We found that the relative capability of the middle rings (along the catenane polymer) to be threaded by other chains is smaller, even though slightly, than that of the edging rings. Furthermore, our simulation results reveal that the probability of threading at the chain level, pthchain(n), in [n]catenane melts can be well understood by a mean-field theory, i.e., pthchain(n)=1\u22121\u2212pthchain(n=1)n. As a key finding of this work, we found that the averaged number of threadings per chain scales with n as Nthchain\u223cn\u03b1, with \u03b1 \u2248 0.7863. This behavior is deeply rooted in the special packing structure of the interlocked ring polymers in a melt, i.e., segregation of territories, which is further attributed to the catenation topology of the chain.<\/jats:p>","DOI":"10.1063\/5.0321313","type":"journal-article","created":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T10:38:29Z","timestamp":1775039909000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Threadings of interlocked ring polymers in melts"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8213-8220","authenticated-orcid":false,"given":"Zhiyuan","family":"Cheng","sequence":"first","affiliation":[{"name":"Key Laboratory of Theoretical Chemistry of Environment Ministry of Education, South China Normal University 1 , 510006 Guangzhou, and , 510006 Guangzhou,","place":["China China"]},{"name":"Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University 1 , 510006 Guangzhou, and , 510006 Guangzhou,","place":["China China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7256-5751","authenticated-orcid":false,"given":"Hong","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Theoretical Chemistry of Environment Ministry of Education, South China Normal University 1 , 510006 Guangzhou, and , 510006 Guangzhou,","place":["China China"]},{"name":"Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University 1 , 510006 Guangzhou, and , 510006 Guangzhou,","place":["China China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7822-7525","authenticated-orcid":false,"given":"Guojie","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Chemistry and Chemical Engineering, Guangzhou University 2 , 510006 Guangzhou,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"2026040106382275500_c1","volume-title":"Principles of Polymer Chemistry","year":"1953"},{"key":"2026040106382275500_c2","volume-title":"Scaling Concepts in Polymer Physics","year":"1979"},{"key":"2026040106382275500_c3","volume-title":"The Theory of Polymer Dynamics","year":"1986"},{"key":"2026040106382275500_c4","volume-title":"Statistical Physics of Macromolecules","year":"1994"},{"key":"2026040106382275500_c5","volume-title":"Polymer Physics","year":"2003"},{"key":"2026040106382275500_c6","volume-title":"Polymer Chemistry","year":"2007"},{"key":"2026040106382275500_c7","doi-asserted-by":"publisher","first-page":"9073","DOI":"10.1021\/acs.macromol.7b01518","article-title":"50th anniversary perspective: Polymer conformation\u2014A pedagogical review","volume":"50","year":"2017","journal-title":"Macromolecules"},{"key":"2026040106382275500_c8","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1038\/s41557-020-0440-5","article-title":"The synthesis, properties and potential applications of cyclic polymers","volume":"12","year":"2020","journal-title":"Nat. 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