Smaller is Stronger: Topological Load-bearing of Crumpled 2D Macromolecule

Smaller is Stronger: Topological Load-bearing of Crumpled 2D Macromolecule | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Smaller is Stronger: Topological Load-bearing of Crumpled 2D Macromolecule Yilun Liu, Runze Liang, Kai Kang, Huichao Liu, Yingbo Yan, Yan Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7200954/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Two-dimensional (2D) macromolecules represent atomically thin materials that can form vast crumpled configurations with complex topological microstructures in confined space, establishing a new frontier in macromolecular mechanics. Here, we unveil a universal negative size effect, where smaller sheets yield substantially stronger load-bearing capabilities than larger ones. Through coarse-grained molecular dynamics simulations, we find a negative scaling relationship between compression pressure or modulus and Föppl–von Kármán number, with the power index governed by crumpled density, independent of material parameters. Energy landscape analysis reveals that smaller sheets preferentially develop concentrated ridge networks with minimal self-folding, creating more efficient pathways for load transfer and strain energy absorption. During densification, we observe a universal topological evolution pattern where the ridge-to-vertex increment ratio maintains a constant 1.5, securing advantageous ridge density of smaller sheets throughout compression. Experimental validations across paper, aluminum foil, polydimethylsiloxane, and silicone rubber substantiate this size-dependent behavior transcending molecular to macroscopic scales. This study deepens our understanding of 2D macromolecule mechanics, establishing fundamental principles for engineering next-generation structural metamaterials with precisely tailored load-bearing characteristics. Physical sciences/Engineering/Mechanical engineering Physical sciences/Materials science/Nanoscale materials/Two-dimensional materials Physical sciences/Materials science/Structural materials/Mechanical properties 2D macromolecules Topological load-bearing Size effect Confined mechanics Structure-property relation Full Text Additional Declarations There is NO Competing Interest. Supplementary Files VideoS1.mp4 Video S1 VideoS2.mp4 Video S2 VideoS3.mp4 Video S3 VideoS4.mp4 Video S4 SISmallerisStrongerTopologicalLoadbearingofCrumpled2DMacromoleculenew.docx Supplemental information for manuscript Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7200954","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":492578411,"identity":"dd1515fc-5406-41b6-96eb-9c309655ad13","order_by":0,"name":"Yilun Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYDACZuYGBoYCCQZ+IPvAAyAfLMqDVwsjUIuBBIMkkDqQAOTzENTCANYCRAeA7ASYanxaDI4ztkkXGFgkbr52+CHQlsPs9hIJjA/etjHIm+PSchioZYaBROK222kGQC1pzDwSCcyGc9sYDHc24NHCA9aSANJiA9LCJs3bxpAAdio+LZtnp38AapEAaWH/TZSWDdI5CFuY8WmRPMzYbA3UYjzjdk7BgQQDoF/OPGyWnHNOwnADDi185w8fvM1TUSfbPzt984cPFYeT2duTD354U2Yjj8sWBVRxA4ZkSEwxSGBXDwTyDWgCdjiVjoJRMApGwYgFALyiU/fmiG8rAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-3070-096X","institution":"Xi'an Jiaotong University","correspondingAuthor":true,"prefix":"","firstName":"Yilun","middleName":"","lastName":"Liu","suffix":""},{"id":492578412,"identity":"2737615a-79d1-4da6-b02e-b79f5fb4ca4c","order_by":1,"name":"Runze Liang","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Runze","middleName":"","lastName":"Liang","suffix":""},{"id":492578413,"identity":"79391f4e-e1e1-49ed-8c40-05d46b6ad671","order_by":2,"name":"Kai Kang","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Kang","suffix":""},{"id":492578414,"identity":"9b1f1991-49cf-4fa3-8fc7-4c95a8dabe19","order_by":3,"name":"Huichao Liu","email":"","orcid":"https://orcid.org/0009-0004-0782-1001","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Huichao","middleName":"","lastName":"Liu","suffix":""},{"id":492578415,"identity":"e975cbbe-9cda-4785-981c-cfc3b702bb7f","order_by":4,"name":"Yingbo Yan","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yingbo","middleName":"","lastName":"Yan","suffix":""},{"id":492578416,"identity":"a3be0a02-2110-442b-b8c2-c41a47f53530","order_by":5,"name":"Yan Chen","email":"","orcid":"https://orcid.org/0000-0003-1723-0112","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2025-07-24 03:25:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7200954/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7200954/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90501037,"identity":"3c4836a6-0907-497e-9fa3-3eb7e204884f","added_by":"auto","created_at":"2025-09-03 11:44:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1478073,"visible":true,"origin":"","legend":"","description":"","filename":"SmallerisStrongerTopologicalLoadbearingofCrumpled2DMacromoleculenew.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7200954/v1_covered_311cbed0-8305-4b3f-b5b9-10121aca4335.pdf"},{"id":87903746,"identity":"e104c9f5-8de6-45c5-86c5-e784bb961c40","added_by":"auto","created_at":"2025-07-30 08:38:16","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3027844,"visible":true,"origin":"","legend":"Video S1","description":"","filename":"VideoS1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7200954/v1/8eccb0c3fd4bfe4e4980e8f9.mp4"},{"id":87903253,"identity":"d81b5ca0-35b9-4945-b2d7-133526273e3a","added_by":"auto","created_at":"2025-07-30 08:30:16","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1219085,"visible":true,"origin":"","legend":"Video S2","description":"","filename":"VideoS2.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7200954/v1/77b6417f4fbe22a66702b75c.mp4"},{"id":87903747,"identity":"b706b539-9d66-437b-b7ff-2215ebf741a4","added_by":"auto","created_at":"2025-07-30 08:38:16","extension":"mp4","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":5667301,"visible":true,"origin":"","legend":"Video S3","description":"","filename":"VideoS3.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7200954/v1/c903ac53afa0883ac7d84e93.mp4"},{"id":87903251,"identity":"33fdc4fc-54e5-455d-b1d0-b540bedefe75","added_by":"auto","created_at":"2025-07-30 08:30:16","extension":"mp4","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":429997,"visible":true,"origin":"","legend":"Video S4","description":"","filename":"VideoS4.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7200954/v1/ae0851ecfb03ee49c95ccd25.mp4"},{"id":87903757,"identity":"0a561c70-51de-4572-9e4e-40b108786502","added_by":"auto","created_at":"2025-07-30 08:38:17","extension":"docx","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":3575390,"visible":true,"origin":"","legend":"Supplemental information for manuscript","description":"","filename":"SISmallerisStrongerTopologicalLoadbearingofCrumpled2DMacromoleculenew.docx","url":"https://assets-eu.researchsquare.com/files/rs-7200954/v1/df731b5057443a911c620a7b.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Smaller is Stronger: Topological Load-bearing of Crumpled 2D Macromolecule","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"2D macromolecules, Topological load-bearing, Size effect, Confined mechanics, Structure-property relation","lastPublishedDoi":"10.21203/rs.3.rs-7200954/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7200954/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTwo-dimensional (2D) macromolecules represent atomically thin materials that can form vast crumpled configurations with complex topological microstructures in confined space, establishing a new frontier in macromolecular mechanics. Here, we unveil a universal negative size effect, where smaller sheets yield substantially stronger load-bearing capabilities than larger ones. Through coarse-grained molecular dynamics simulations, we find a negative scaling relationship between compression pressure or modulus and F\u0026ouml;ppl\u0026ndash;von K\u0026aacute;rm\u0026aacute;n number, with the power index governed by crumpled density, independent of material parameters. Energy landscape analysis reveals that smaller sheets preferentially develop concentrated ridge networks with minimal self-folding, creating more efficient pathways for load transfer and strain energy absorption. During densification, we observe a universal topological evolution pattern where the ridge-to-vertex increment ratio maintains a constant 1.5, securing advantageous ridge density of smaller sheets throughout compression. Experimental validations across paper, aluminum foil, polydimethylsiloxane, and silicone rubber substantiate this size-dependent behavior transcending molecular to macroscopic scales. This study deepens our understanding of 2D macromolecule mechanics, establishing fundamental principles for engineering next-generation structural metamaterials with precisely tailored load-bearing characteristics.\u003c/p\u003e","manuscriptTitle":"Smaller is Stronger: Topological Load-bearing of Crumpled 2D Macromolecule","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-30 08:30:11","doi":"10.21203/rs.3.rs-7200954/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e48b5a5e-bbfd-42c7-9336-f91f8c0dd7e9","owner":[],"postedDate":"July 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":52302693,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":52302694,"name":"Physical sciences/Materials science/Nanoscale materials/Two-dimensional materials"},{"id":52302695,"name":"Physical sciences/Materials science/Structural materials/Mechanical properties"}],"tags":[],"updatedAt":"2025-09-03T11:35:49+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-30 08:30:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7200954","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7200954","identity":"rs-7200954","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}