General Construction Strategy for Carbon Nanotube Heterojunctions with Two Arbitrary Chiral Vectors that Contain only a Single Pentagon- Heptagon Pair

General Construction Strategy for Carbon Nanotube Heterojunctions with Two Arbitrary Chiral Vectors that Contain only a Single Pentagon- Heptagon Pair | 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 Research Article General Construction Strategy for Carbon Nanotube Heterojunctions with Two Arbitrary Chiral Vectors that Contain only a Single Pentagon- Heptagon Pair Hou-Hsun Ho, Bih-Yaw Jin, Chern Chuang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7765037/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Jan, 2026 Read the published version in Journal of Mathematical Chemistry → Version 1 posted 7 You are reading this latest preprint version Abstract Carbon nanotubes (CNTs) exhibit tunable electronic and structural properties based on their chiral indices, making them versatile for nanoscale applications. The electronic behavior at CNT junctions is particularly significant, prompting a theoretical exploration of their geometric foundations. The Contub algorithm, designed to connect CNTs with arbitrary chiral vectors, identifies the positioning of pentagon and heptagon defects. Despite its theoretical efficiency, the geometrical interpretation between chiral vectors and defects is less than transparent. In this study, we revisit CNT junctions by examining the connections between carbon nanocones (CNCs) and CNTs. This approach allows the mapping of all possible chiral indices onto a CNC, providing a clearer geometric understanding of defect formation and CNT linkage. We also explore cases where CNC-based approaches fail and introduce a “mitered pipe” connection for constructing junctions without intermediate cones. A phase diagram based on the relative diameter difference and the angle between chiral vectors is presented to classify CNT heterojunctions into two types, offering insights into their geometric and electronic properties for potential applications in nanoscale electronic devices. Carbon Nanotube (CNT) Carbon Nanocone (CNC) CNT Heterojunction Chiral Vector Mitered Pipe Connection of CNT Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Jan, 2026 Read the published version in Journal of Mathematical Chemistry → Version 1 posted Editorial decision: Revision requested 03 Dec, 2025 Reviews received at journal 03 Dec, 2025 Reviewers agreed at journal 08 Nov, 2025 Reviewers invited by journal 06 Nov, 2025 Editor assigned by journal 04 Oct, 2025 Submission checks completed at journal 04 Oct, 2025 First submitted to journal 02 Oct, 2025 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-7765037","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":545802681,"identity":"fedfcef5-1fbc-451f-8cff-ca9c925d57fc","order_by":0,"name":"Hou-Hsun Ho","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIie3RsQrCMBCA4UogLoeuV0Sf4UoHHURfpUFwEmcnqTh0Ke5FH8JN3CIBuwiuiovgquBYUNDU0aFxdMgPCQTykcA5js32j6nS5HzPELpR+DmXQiNJmfKSuNUgkJ/bemMGsuf9GvCRTxj8SCoKCAFQrNxbegGnXV/K6haLiKsJYQvFej4UU3D6/lIyXkhIk4D0K+Fp4GmiRE4OJiIDrslxl5PXL4SLUHL06QA5kWbiKqYnE2PDjQdesqCenyjWzIpIZb+JHs9sDNXyju7XUac+SycXKiLf/9TLNEmbzWazmXsDJgtMwCgvUVkAAAAASUVORK5CYII=","orcid":"","institution":"National Taiwan University","correspondingAuthor":true,"prefix":"","firstName":"Hou-Hsun","middleName":"","lastName":"Ho","suffix":""},{"id":545802682,"identity":"31bcedc6-0861-441c-86fa-ced4af22c941","order_by":1,"name":"Bih-Yaw Jin","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Bih-Yaw","middleName":"","lastName":"Jin","suffix":""},{"id":545802683,"identity":"246f7675-4d44-4ad8-aae2-2a96b12f5e15","order_by":2,"name":"Chern Chuang","email":"","orcid":"","institution":"University of Nevada, Las Vegas","correspondingAuthor":false,"prefix":"","firstName":"Chern","middleName":"","lastName":"Chuang","suffix":""}],"badges":[],"createdAt":"2025-10-02 08:53:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7765037/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7765037/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10910-025-01774-1","type":"published","date":"2026-01-10T15:57:03+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":96245668,"identity":"3a4d3b39-55f0-48d3-a041-c2d11171a197","added_by":"auto","created_at":"2025-11-19 07:21:44","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2988910,"visible":true,"origin":"","legend":"","description":"","filename":"CNCmanuscript20251001.docx","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/4c6a322dd12d8c195c6dcbeb.docx"},{"id":96036640,"identity":"44cf7f4d-e98d-43a8-af2a-1605df165a76","added_by":"auto","created_at":"2025-11-17 03:01:18","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5364,"visible":true,"origin":"","legend":"","description":"","filename":"d1089e3c728e4985b3e85f924417c276.json","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/e73a62ad7d9eb22d54b4c523.json"},{"id":96036671,"identity":"5794497c-3463-4fc8-94a6-fcb0ac912da9","added_by":"auto","created_at":"2025-11-17 03:01:21","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":104043,"visible":true,"origin":"","legend":"","description":"","filename":"d1089e3c728e4985b3e85f924417c2761enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/8b2e67c58a8eb78481055b15.xml"},{"id":96036643,"identity":"ba888f46-ee76-43db-ae56-7a6dec6741e4","added_by":"auto","created_at":"2025-11-17 03:01:18","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":216625,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/141c1955649c0e7a5ee5a8cd.png"},{"id":96246243,"identity":"b2216133-28b5-4efb-9db2-dadef957d439","added_by":"auto","created_at":"2025-11-19 07:25:10","extension":"jpeg","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":576031,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/b3cab679c377cf477044225b.jpeg"},{"id":96036641,"identity":"5b5bc12a-62e1-4974-88a3-13022bf77912","added_by":"auto","created_at":"2025-11-17 03:01:18","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":289592,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/247a1bfa84edacf1a22dd077.png"},{"id":96246772,"identity":"8567b5ed-be1e-4009-ae37-f5532de0d895","added_by":"auto","created_at":"2025-11-19 07:26:40","extension":"jpeg","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":243254,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/c5860a292a4f857f52fdf24e.jpeg"},{"id":96036653,"identity":"c343b5ce-1812-47d0-815b-6b9b65a2494c","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":216830,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/833ed4716fe019d31d550365.png"},{"id":96036645,"identity":"d800b0fe-ea2e-4d24-acbe-84759686cf1a","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"jpeg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":380658,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/ee50778e6426af1658c7532f.jpeg"},{"id":96246435,"identity":"7f5cade2-6d44-4163-9157-c937bfe39ecf","added_by":"auto","created_at":"2025-11-19 07:26:00","extension":"jpeg","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":335140,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/981a334d664dadb2df920b6a.jpeg"},{"id":96036649,"identity":"7ba9d729-3d6f-4478-acaf-19c25aaf486c","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"jpeg","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":298550,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/7f15654be1d79bd24dc9e511.jpeg"},{"id":96036647,"identity":"9a0951a2-1a21-4a78-91ac-308ff45c1f9d","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"jpeg","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":391048,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/5c1641d035f6dbc8dbe1f80f.jpeg"},{"id":96036646,"identity":"163ef1da-d650-4dfd-ad2b-358414d5885a","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"jpeg","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":335759,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/7363849e41d993d40240ac48.jpeg"},{"id":96036655,"identity":"a0fc7b29-67d7-4db2-aeaf-46174d3a5c05","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"jpeg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":325393,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/a6689e6048570bc08b83c015.jpeg"},{"id":96036651,"identity":"027102df-aa17-4341-a5cf-ca39a733d9d7","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":322800,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/5133de90a377a7a514aef60d.png"},{"id":96246956,"identity":"46592a98-8c2c-4b73-a9b9-6a43f5d3eb82","added_by":"auto","created_at":"2025-11-19 07:26:57","extension":"jpeg","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":223372,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/5bc35a41603febb5b58ea59a.jpeg"},{"id":96036650,"identity":"ff08f0ae-1a45-432c-96ca-b5b2e879bf54","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":39103,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/42b6a069296c4911fac737ce.png"},{"id":96246307,"identity":"ce9b9cdf-3f3a-4f85-ad49-caf07988b620","added_by":"auto","created_at":"2025-11-19 07:25:22","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":105642,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/f2879811723a5f44dfd5e30b.png"},{"id":96246832,"identity":"2ba19edf-de2c-4554-9f61-2f9a15f3ca00","added_by":"auto","created_at":"2025-11-19 07:26:44","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":36423,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/2a4cd82ffb0bfe19eda7b8de.png"},{"id":96036667,"identity":"f25282fd-2caf-4d35-b85d-16637a264928","added_by":"auto","created_at":"2025-11-17 03:01:20","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":47586,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/f94de21ffadfacf8136668e5.png"},{"id":96036658,"identity":"5ad8f90c-acd0-4974-80ca-7d7b2850de92","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":34091,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/6910a0cdd4b39fb1aa18bdd9.png"},{"id":96036657,"identity":"197fcfec-cc11-4a08-8bd7-fa89c88d3bc1","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":87309,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/98ead822c5d3b9b0d8694bf3.png"},{"id":96036656,"identity":"15fd67a7-4208-464a-b882-883a4eff66f2","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":72430,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/ab34aee529003d5a8ef1d4c8.png"},{"id":96036660,"identity":"6812e7b0-f6ba-48c9-b793-0a8e7b1750cf","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":65781,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/c75f178ece19bd92a54823a7.png"},{"id":96036665,"identity":"8e49665a-aab5-4105-a0e3-9a88fd222fc6","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":83294,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/47df6d63131bfd6b8d6a3dfa.png"},{"id":96036663,"identity":"7f584ab9-4b96-4439-adb6-1fb06e8b7b5f","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77004,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/24bba8c5edc4e9b2aed0c012.png"},{"id":96036664,"identity":"cb9b6ea5-636e-4179-9ef3-464ab7038239","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":57506,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/50c6d04350aae20ccee565ff.png"},{"id":96036666,"identity":"9d0fba92-6700-492f-b5ef-3d3cfdf75653","added_by":"auto","created_at":"2025-11-17 03:01:20","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37855,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/ad730b7d58988920dc703c5e.png"},{"id":96036662,"identity":"545c35b7-b040-4e04-9d9e-221b5cc72f34","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":40730,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/f7f6726810df9d5c1c3fd8b8.png"},{"id":96036669,"identity":"5617e01f-2b59-4a82-934e-37abbd0c0972","added_by":"auto","created_at":"2025-11-17 03:01:20","extension":"xml","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":102724,"visible":true,"origin":"","legend":"","description":"","filename":"d1089e3c728e4985b3e85f924417c2761structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/e362b510581acb87c1a98854.xml"},{"id":96036661,"identity":"d784c3d8-494b-4ca4-b164-8bd2baeade9a","added_by":"auto","created_at":"2025-11-17 03:01:19","extension":"html","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":123837,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1/f0e27155a170cd17bb28dc36.html"},{"id":100069151,"identity":"6a6f1892-94e0-4ddd-bd5a-799e897b30f7","added_by":"auto","created_at":"2026-01-12 16:10:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2674447,"visible":true,"origin":"","legend":"","description":"","filename":"CNCmanuscript20251001.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7765037/v1_covered_4f677a6f-7cea-4ce5-a690-99ce876d7494.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"General Construction Strategy for Carbon Nanotube Heterojunctions with Two Arbitrary Chiral Vectors that Contain only a Single Pentagon- Heptagon Pair","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"journal-of-mathematical-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jomc","sideBox":"Learn more about [Journal of Mathematical Chemistry](http://link.springer.com/journal/10910)","snPcode":"10910","submissionUrl":"https://submission.nature.com/new-submission/10910/3","title":"Journal of Mathematical Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Carbon Nanotube (CNT), Carbon Nanocone (CNC), CNT Heterojunction, Chiral Vector, Mitered Pipe Connection of CNT","lastPublishedDoi":"10.21203/rs.3.rs-7765037/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7765037/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCarbon nanotubes (CNTs) exhibit tunable electronic and structural properties based on their chiral indices, making them versatile for nanoscale applications. The electronic behavior at CNT junctions is particularly significant, prompting a theoretical exploration of their geometric foundations. The Contub algorithm, designed to connect CNTs with arbitrary chiral vectors, identifies the positioning of pentagon and heptagon defects. Despite its theoretical efficiency, the geometrical interpretation between chiral vectors and defects is less than transparent. In this study, we revisit CNT junctions by examining the connections between carbon nanocones (CNCs) and CNTs. This approach allows the mapping of all possible chiral indices onto a CNC, providing a clearer geometric understanding of defect formation and CNT linkage. We also explore cases where CNC-based approaches fail and introduce a \u0026ldquo;mitered pipe\u0026rdquo; connection for constructing junctions without intermediate cones. A phase diagram based on the relative diameter difference and the angle between chiral vectors is presented to classify CNT heterojunctions into two types, offering insights into their geometric and electronic properties for potential applications in nanoscale electronic devices.\u003c/p\u003e","manuscriptTitle":"General Construction Strategy for Carbon Nanotube Heterojunctions with Two Arbitrary Chiral Vectors that Contain only a Single Pentagon- Heptagon Pair","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-17 03:01:14","doi":"10.21203/rs.3.rs-7765037/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-03T21:11:24+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-03T12:40:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"105381472014637737741315117965550647646","date":"2025-11-08T14:33:09+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-06T14:30:28+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-04T15:20:05+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-04T15:18:23+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Mathematical Chemistry","date":"2025-10-02T08:46:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-mathematical-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jomc","sideBox":"Learn more about [Journal of Mathematical Chemistry](http://link.springer.com/journal/10910)","snPcode":"10910","submissionUrl":"https://submission.nature.com/new-submission/10910/3","title":"Journal of Mathematical Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f872334b-a868-40db-b7d9-349290489325","owner":[],"postedDate":"November 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-01-12T16:01:41+00:00","versionOfRecord":{"articleIdentity":"rs-7765037","link":"https://doi.org/10.1007/s10910-025-01774-1","journal":{"identity":"journal-of-mathematical-chemistry","isVorOnly":false,"title":"Journal of Mathematical Chemistry"},"publishedOn":"2026-01-10 15:57:03","publishedOnDateReadable":"January 10th, 2026"},"versionCreatedAt":"2025-11-17 03:01:14","video":"","vorDoi":"10.1007/s10910-025-01774-1","vorDoiUrl":"https://doi.org/10.1007/s10910-025-01774-1","workflowStages":[]},"version":"v1","identity":"rs-7765037","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7765037","identity":"rs-7765037","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}