Hierarchical Self-assembly of Simple Hard Polyhedra into Complex Mesophases

Hierarchical Self-assembly of Simple Hard Polyhedra into Complex Mesophases | 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 Hierarchical Self-assembly of Simple Hard Polyhedra into Complex Mesophases Marjolein Dijkstra, Rodolfo Subert This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6664649/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Nature offers many intriguing examples of hierarchically self-assembled mesophases, such as lamellar, gyroid, hexagonal, and cholesteric phases. These structures are typically believed to emerge from complex, competing enthalpic interactions, as observed in block copolymers and amphiphilic surfactants. Here, using extensive Monte Carlo simulations, we demonstrate that even simple achiral hard particles with distorted tetrahedral shapes and purely excluded-volume interactions can spontaneously self-assemble into a diverse range of mesophases and liquid crystal phases, including the unexpected emergence of chiral structures. We attribute the formation of these phases to geometric frustration in the orientational ordering of neighboring particles, induced by their particle shape. The system resolves this frustration by coupling it with an energetically less favorable elastic deformation mode in the orientational ordering, such as twist or splay. We show that simple shape descriptors, such as anisotropy or biaxiality, predict the self-assembly behavior: rod-like particles stabilize cholesteric and twisted lamellar phases, plate-like particles form biaxial and splay nematic phases with randomly distributed splay domains as well as hexagonal cylindrical phases, while moderately anisotropic particles favor gyroid phases. This framework provides valuable insights for designing mesophases in supramolecular chemistry, liquid crystals, colloid science, and nanoparticle assembly. Physical sciences/Materials science/Theory and computation/Coarse-grained models Physical sciences/Materials science/Soft materials/Self-assembly Physical sciences/Materials science/Soft materials/Liquid crystals Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryMovie1.mp4 Supplementary Movie 1 SupplementaryMovie2.mp4 Supplementary Movie 2 SupplementaryMaterials.pdf Cite Share Download PDF Status: Published Journal Publication published 04 Dec, 2025 Read the published version in Nature Communications → 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-6664649","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":475226158,"identity":"415787c3-4e1c-40a8-a733-689d5957968b","order_by":0,"name":"Marjolein Dijkstra","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYHACgwMSB0A0M5iUIVqLBAMDWwKIx0OUFgYGsBYeA+K06DYwbzxgcaauzrz9zDdpHoY7hLWYHWArOCBx47CEzJncbUAtz4jRwgP0y4cDEhIMYC2HidZSJyHB/+YZKVpuMEtISOSwEanlMMgvZw5LzpB4Zmw5x4AYLcebN3+WOFbHL8Gf/PDGm4rDcgS1MDADkQScZ0BYAxgwfiBS4SgYBaNgFIxQAADGojgQ/dkTPwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-9166-6478","institution":"Utrecht University","correspondingAuthor":true,"prefix":"","firstName":"Marjolein","middleName":"","lastName":"Dijkstra","suffix":""},{"id":475226159,"identity":"fef91aab-a441-4a8d-bd5b-9ee1faa21d5e","order_by":1,"name":"Rodolfo Subert","email":"","orcid":"https://orcid.org/0000-0003-1338-5803","institution":"Utrecht University","correspondingAuthor":false,"prefix":"","firstName":"Rodolfo","middleName":"","lastName":"Subert","suffix":""}],"badges":[],"createdAt":"2025-05-14 13:26:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6664649/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6664649/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-65891-w","type":"published","date":"2025-12-04T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97505325,"identity":"fdeb3bb5-0a04-40ce-89a0-459f16151737","added_by":"auto","created_at":"2025-12-05 08:08:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2208525,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6664649/v1_covered_ce7db921-6211-412d-8889-ea0b93e4890d.pdf"},{"id":85983963,"identity":"143d69f0-4341-40ae-890f-90f1d55ac013","added_by":"auto","created_at":"2025-07-04 02:37:49","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":36442637,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Movie 1\u003c/p\u003e","description":"","filename":"SupplementaryMovie1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-6664649/v1/19a7526de9e94ea1e19c1deb.mp4"},{"id":85983965,"identity":"1d56e8bc-b458-4569-bb92-1909fb9650f5","added_by":"auto","created_at":"2025-07-04 02:37:49","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":87675439,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Movie 2\u003c/p\u003e","description":"","filename":"SupplementaryMovie2.mp4","url":"https://assets-eu.researchsquare.com/files/rs-6664649/v1/f6d1001be35283cba7a1a1e0.mp4"},{"id":85983961,"identity":"e53ca418-fe1b-46ca-8fac-49ab24112ee6","added_by":"auto","created_at":"2025-07-04 02:37:48","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":988038,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SupplementaryMaterials.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6664649/v1/8c30b56a7d8f31193a870b96.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Hierarchical Self-assembly of Simple Hard Polyhedra into Complex Mesophases","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6664649/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6664649/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Nature offers many intriguing examples of hierarchically self-assembled mesophases, such as lamellar, gyroid, hexagonal, and cholesteric phases. These structures are typically believed to emerge from complex, competing enthalpic interactions, as observed in block copolymers and amphiphilic surfactants. Here, using extensive Monte Carlo simulations, we demonstrate that even simple achiral hard particles with distorted tetrahedral shapes and purely excluded-volume interactions can spontaneously self-assemble into a diverse range of mesophases and liquid crystal phases, including the unexpected emergence of chiral structures. We attribute the formation of these phases to geometric frustration in the orientational ordering of neighboring particles, induced by their particle shape. The system resolves this frustration by coupling it with an energetically less favorable elastic deformation mode in the orientational ordering, such as twist or splay. We show that simple shape descriptors, such as anisotropy or biaxiality, predict the self-assembly behavior: rod-like particles stabilize cholesteric and twisted lamellar phases, plate-like particles form biaxial and splay nematic phases with randomly distributed splay domains as well as hexagonal cylindrical phases, while moderately anisotropic particles favor gyroid phases. This framework provides valuable insights for designing mesophases in supramolecular chemistry, liquid crystals, colloid science, and nanoparticle assembly.","manuscriptTitle":"Hierarchical Self-assembly of Simple Hard Polyhedra into Complex Mesophases","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-04 02:37:43","doi":"10.21203/rs.3.rs-6664649/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"51895364-b881-4ea9-84f4-cba5ee4693e0","owner":[],"postedDate":"July 4th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":50460929,"name":"Physical sciences/Materials science/Theory and computation/Coarse-grained models"},{"id":50460930,"name":"Physical sciences/Materials science/Soft materials/Self-assembly"},{"id":50460931,"name":"Physical sciences/Materials science/Soft materials/Liquid crystals"}],"tags":[],"updatedAt":"2025-12-05T08:08:08+00:00","versionOfRecord":{"articleIdentity":"rs-6664649","link":"https://doi.org/10.1038/s41467-025-65891-w","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-12-04 05:00:00","publishedOnDateReadable":"December 4th, 2025"},"versionCreatedAt":"2025-07-04 02:37:43","video":"","vorDoi":"10.1038/s41467-025-65891-w","vorDoiUrl":"https://doi.org/10.1038/s41467-025-65891-w","workflowStages":[]},"version":"v1","identity":"rs-6664649","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6664649","identity":"rs-6664649","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}