{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T14:25:59Z","timestamp":1787063159764,"version":"build-2736575974"},"reference-count":91,"publisher":"AIP Publishing","issue":"6","funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001409","name":"Department of Science and Technology, Ministry of Science and Technology, India","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001409","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["LO 418\/29"],"award-info":[{"award-number":["LO 418\/29"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,2,14]]},"abstract":"<jats:p>Using particle-resolved molecular-dynamics simulations, we compute the phase diagram for soft repulsive spherocylinders confined on the surface of a sphere. While crystal (K), smectic (Sm), and isotropic (I) phases exhibit a stability region for any aspect ratio of the spherocylinders, a nematic phase emerges only beyond a critical aspect ratio lying between 8.0 and 9.0. As required by the topology of the confining sphere, the ordered phases exhibit a total orientational defect charge of +2. In detail, the crystal and high-density smectic phases exhibit two +1 defects at the poles, whereas the high-density nematic phase features four +1\/2 defects, which are connected along a great circle. For aspect ratios above the critical value, lowering the packing fraction drives a sequence of transitions: the crystal melts into a smectic phase, which then transforms into a nematic through the splitting of the +1 defects into pairs of +1\/2 defects. Our simulations data can be experimentally verified in Pickering emulsions and are relevant for understanding the morphogenesis in epithelial tissues.<\/jats:p>","DOI":"10.1063\/5.0309849","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T12:27:25Z","timestamp":1770812845000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Phase behavior and defect structure of soft rods on a sphere"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3025-869X","authenticated-orcid":false,"given":"Jaydeep","family":"Mandal","sequence":"first","affiliation":[{"name":"Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science 1 , Bengaluru 560012,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5376-8062","authenticated-orcid":false,"given":"Hartmut","family":"L\u00f6wen","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf 2 , 40225 D\u00fcsseldorf,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9956-1136","authenticated-orcid":false,"given":"Prabal K.","family":"Maiti","sequence":"additional","affiliation":[{"name":"Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science 1 , Bengaluru 560012,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,2,11]]},"reference":[{"key":"2026021107272066300_c1","volume-title":"The Physics of Liquid Crystals","year":"1993"},{"key":"2026021107272066300_c2","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1111\/j.1749-6632.1949.tb27296.x","volume":"51","year":"1949","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"2026021107272066300_c3","doi-asserted-by":"publisher","first-page":"15089","DOI":"10.1021\/acs.chemrev.6b00415","volume":"116","year":"2016","journal-title":"Chem. Rev."},{"key":"2026021107272066300_c4","volume-title":"Functional Organic and Hybrid Nanostructured Materials: Fabrication, Properties, and Applications","year":"2018"},{"key":"2026021107272066300_c5","doi-asserted-by":"publisher","first-page":"1917","DOI":"10.1063\/1.1560871","volume":"82","year":"2003","journal-title":"Appl. Phys. Lett."},{"key":"2026021107272066300_c6","doi-asserted-by":"publisher","first-page":"929","DOI":"10.1038\/nmat2010","volume":"6","year":"2007","journal-title":"Nat. Mater."},{"key":"2026021107272066300_c7","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1016\/j.cap.2012.03.019","volume":"12","year":"2012","journal-title":"Curr. Appl. Phys."},{"key":"2026021107272066300_c8","doi-asserted-by":"publisher","first-page":"2094","DOI":"10.1126\/science.1091749","volume":"302","year":"2003","journal-title":"Science"},{"key":"2026021107272066300_c9","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1103\/revmodphys.72.1017","volume":"72","year":"2000","journal-title":"Rev. Mod. Phys."},{"key":"2026021107272066300_c10","doi-asserted-by":"publisher","first-page":"10236","DOI":"10.1038\/ncomms10236","volume":"7","year":"2016","journal-title":"Nat. Commun."},{"key":"2026021107272066300_c11","doi-asserted-by":"publisher","first-page":"4157","DOI":"10.1039\/c0sm00065e","volume":"6","year":"2010","journal-title":"Soft Matter"},{"key":"2026021107272066300_c12","doi-asserted-by":"publisher","first-page":"134903","DOI":"10.1063\/5.0245950","volume":"162","year":"2025","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c13","doi-asserted-by":"publisher","first-page":"6458","DOI":"10.1039\/d5sm00482a","volume":"21","year":"2025","journal-title":"Soft Matter"},{"key":"2026021107272066300_c14","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1039\/d2sm00799a","volume":"19","year":"2023","journal-title":"Soft Matter"},{"key":"2026021107272066300_c15","doi-asserted-by":"publisher","first-page":"164903","DOI":"10.1063\/1.4947256","volume":"144","year":"2016","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c16","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1080\/00018730903043166","volume":"58","year":"2009","journal-title":"Adv. Phys."},{"key":"2026021107272066300_c17","doi-asserted-by":"publisher","first-page":"5081","DOI":"10.1103\/PhysRevE.62.5081","volume":"62","year":"2000","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c18","first-page":"167","volume":"1","year":"1885","journal-title":"J.\u00a0Math. Pures Appl."},{"key":"2026021107272066300_c19","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1051\/jp2:1992133","volume":"2","year":"1992","journal-title":"J.\u00a0Phys. II"},{"key":"2026021107272066300_c20","doi-asserted-by":"publisher","first-page":"021711","DOI":"10.1103\/physreve.74.021711","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c21","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1103\/physreve.57.610","volume":"57","year":"1998","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c22","doi-asserted-by":"publisher","first-page":"037802","DOI":"10.1103\/physrevlett.101.037802","volume":"101","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c23","doi-asserted-by":"publisher","first-page":"104707","DOI":"10.1063\/1.2890724","volume":"128","year":"2008","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c24","doi-asserted-by":"publisher","first-page":"L022701","DOI":"10.1103\/physreve.104.l022701","volume":"104","year":"2021","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c25","doi-asserted-by":"publisher","first-page":"8120","DOI":"10.1039\/C7SM01704A","volume":"13","year":"2017","journal-title":"Soft Matter"},{"key":"2026021107272066300_c26","doi-asserted-by":"publisher","first-page":"011709","DOI":"10.1103\/physreve.86.011709","volume":"86","year":"2012","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c27","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1038\/nphys1920","volume":"7","year":"2011","journal-title":"Nat. Phys."},{"key":"2026021107272066300_c28","doi-asserted-by":"publisher","first-page":"247802","DOI":"10.1103\/physrevlett.106.247802","volume":"106","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c29","doi-asserted-by":"publisher","first-page":"247801","DOI":"10.1103\/physrevlett.106.247801","volume":"106","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c30","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.ijnonlinmec.2015.04.003","volume":"75","year":"2015","journal-title":"Int. J. Non-Linear Mech."},{"key":"2026021107272066300_c31","doi-asserted-by":"publisher","first-page":"033135","DOI":"10.1103\/physrevresearch.5.033135","volume":"5","year":"2023","journal-title":"Phys. Rev. Res."},{"key":"2026021107272066300_c32","doi-asserted-by":"publisher","first-page":"9586","DOI":"10.1039\/d4sm01263a","volume":"20","year":"2024","journal-title":"Soft Matter"},{"key":"2026021107272066300_c33","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1093\/pnasnexus\/pgae470","volume":"3","year":"2024","journal-title":"PNAS Nexus"},{"key":"2026021107272066300_c34","doi-asserted-by":"publisher","first-page":"144505","DOI":"10.1063\/1.4932373","volume":"143","year":"2015","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c35","doi-asserted-by":"publisher","first-page":"011703","DOI":"10.1103\/physreve.67.011703","volume":"67","year":"2003","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c36","doi-asserted-by":"publisher","first-page":"065504","DOI":"10.1103\/physrevlett.88.065504","volume":"88","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c37","doi-asserted-by":"publisher","first-page":"025501","DOI":"10.1103\/physrevlett.92.025501","volume":"92","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c38","first-page":"229","volume":"89","year":"2009","journal-title":"J.\u00a0Indian Inst. Sci."},{"key":"2026021107272066300_c39","doi-asserted-by":"publisher","first-page":"6755","DOI":"10.1063\/1.471343","volume":"104","year":"1996","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c40","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1063\/1.473404","volume":"106","year":"1997","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c41","doi-asserted-by":"publisher","first-page":"1932","DOI":"10.1103\/PhysRevE.59.1932","volume":"59","year":"1999","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c42","first-page":"177","volume-title":"Optical Methods and Physics of Colloidal Dispersions","year":"2007"},{"key":"2026021107272066300_c43","doi-asserted-by":"publisher","first-page":"22423","DOI":"10.1039\/c5cp01478f","volume":"17","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021107272066300_c44","doi-asserted-by":"publisher","first-page":"5447","DOI":"10.1063\/1.481112","volume":"112","year":"2000","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c45","doi-asserted-by":"publisher","first-page":"10034","DOI":"10.1063\/1.481637","volume":"112","year":"2000","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c46","doi-asserted-by":"publisher","first-page":"094501","DOI":"10.1063\/1.3552951","volume":"134","year":"2011","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c47","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1146\/annurev-chembioeng-061114-123209","volume":"6","year":"2015","journal-title":"Annu. Rev. Chem. Biomol. Eng."},{"key":"2026021107272066300_c48","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1126\/science.1133162","volume":"315","year":"2007","journal-title":"Science"},{"key":"2026021107272066300_c49","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1038\/nature21718","volume":"544","year":"2017","journal-title":"Nature"},{"key":"2026021107272066300_c50","doi-asserted-by":"publisher","first-page":"048102","DOI":"10.1103\/physrevlett.117.048102","volume":"117","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c51","doi-asserted-by":"publisher","first-page":"3246","DOI":"10.1038\/s41467-018-05666-8","volume":"9","year":"2018","journal-title":"Nat. Commun."},{"key":"2026021107272066300_c52","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1038\/s41567-020-01083-1","volume":"17","year":"2021","journal-title":"Nat. Phys."},{"key":"2026021107272066300_c53","doi-asserted-by":"publisher","first-page":"054610","DOI":"10.1103\/physreve.104.054610","volume":"104","year":"2021","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c54","doi-asserted-by":"publisher","first-page":"024701","DOI":"10.1103\/physreve.107.024701","volume":"107","year":"2023","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c55","doi-asserted-by":"publisher","first-page":"054503","DOI":"10.1063\/5.0163349","volume":"159","year":"2023","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c56","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1080\/00268970110069551","volume":"99","year":"2001","journal-title":"Mol. Phys."},{"key":"2026021107272066300_c57","doi-asserted-by":"publisher","first-page":"13729","DOI":"10.1021\/jp051834c","volume":"109","year":"2005","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026021107272066300_c58","doi-asserted-by":"publisher","first-page":"5237","DOI":"10.1063\/1.1674820","volume":"54","year":"1971","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c59","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/0097-8485(94)80023-5","volume":"18","year":"1994","journal-title":"Comput. Chem."},{"key":"2026021107272066300_c60","doi-asserted-by":"publisher","first-page":"3684","DOI":"10.1063\/1.448118","volume":"81","year":"1984","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c61","doi-asserted-by":"publisher","first-page":"1769","DOI":"10.1256\/qj.05.227","volume":"132","year":"2006","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"2026021107272066300_c62","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/0021-9991(83)90014-1","volume":"52","year":"1983","journal-title":"J.\u00a0Comput. Phys."},{"key":"2026021107272066300_c63","volume-title":"The Art of Molecular Dynamics Simulation","year":"2004"},{"key":"2026021107272066300_c64","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0263-7855(96)00018-5","volume":"14","year":"1996","journal-title":"J.\u00a0Mol. Graphics"},{"key":"2026021107272066300_c65","doi-asserted-by":"publisher","first-page":"234111","DOI":"10.1063\/5.0126437","volume":"157","year":"2022","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c66","doi-asserted-by":"publisher","first-page":"155704","DOI":"10.1103\/physrevlett.107.155704","volume":"107","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c67","doi-asserted-by":"publisher","first-page":"035702","DOI":"10.1103\/physrevlett.114.035702","volume":"114","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c68","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1016\/0378-4371(92)90005-B","volume":"187","year":"1992","journal-title":"Physica A"},{"key":"2026021107272066300_c69","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s101890170134","volume":"4","year":"2001","journal-title":"Eur. Phys. J. E"},{"key":"2026021107272066300_c70","doi-asserted-by":"publisher","first-page":"031802","DOI":"10.1103\/physreve.75.031802","volume":"75","year":"2007","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c71","doi-asserted-by":"publisher","first-page":"174701","DOI":"10.1063\/1.4919307","volume":"142","year":"2015","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c72","doi-asserted-by":"publisher","first-page":"2126","DOI":"10.1103\/physreva.42.2126","volume":"42","year":"1990","journal-title":"Phys. Rev. A"},{"key":"2026021107272066300_c73","doi-asserted-by":"publisher","first-page":"064903","DOI":"10.1063\/1.1849159","volume":"122","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c74","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1103\/revmodphys.84.497","volume":"84","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"2026021107272066300_c75","doi-asserted-by":"publisher","first-page":"4216","DOI":"10.1103\/physreve.59.4216","volume":"59","year":"1999","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c76","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1038\/nature11710","volume":"493","year":"2013","journal-title":"Nature"},{"key":"2026021107272066300_c77","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1038\/s41467-020-20842-5","volume":"12","year":"2021","journal-title":"Nat. Commun."},{"key":"2026021107272066300_c78","doi-asserted-by":"publisher","first-page":"198001","DOI":"10.1103\/physrevlett.127.198001","volume":"127","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"2026021107272066300_c79","doi-asserted-by":"publisher","first-page":"15691","DOI":"10.1039\/d2cp00060a","volume":"24","year":"2022","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026021107272066300_c80","doi-asserted-by":"publisher","first-page":"164505","DOI":"10.1063\/5.0143417","volume":"158","year":"2023","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026021107272066300_c81","doi-asserted-by":"publisher","first-page":"2464","DOI":"10.1039\/d3sm01567j","volume":"20","year":"2024","journal-title":"Soft Matter"},{"key":"2026021107272066300_c82","doi-asserted-by":"publisher","first-page":"1110","DOI":"10.1038\/nmat4387","volume":"14","year":"2015","journal-title":"Nat. Mater."},{"key":"2026021107272066300_c83","doi-asserted-by":"publisher","first-page":"012013","DOI":"10.1103\/physrevresearch.2.012013","volume":"2","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"2026021107272066300_c84","doi-asserted-by":"publisher","first-page":"5667","DOI":"10.1038\/s41598-017-05569-6","volume":"7","year":"2017","journal-title":"Sci. Rep."},{"key":"2026021107272066300_c85","doi-asserted-by":"publisher","first-page":"045006","DOI":"10.1103\/RevModPhys.88.045006","volume":"88","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"2026021107272066300_c86","doi-asserted-by":"publisher","first-page":"010501","DOI":"10.1103\/physrevx.12.010501","volume":"12","year":"2022","journal-title":"Phys. Rev. X"},{"key":"2026021107272066300_c87","doi-asserted-by":"publisher","first-page":"8561","DOI":"10.1039\/d3sm00796k","volume":"19","year":"2023","journal-title":"Soft Matter"},{"key":"2026021107272066300_c88","doi-asserted-by":"publisher","first-page":"015409","DOI":"10.1103\/1c8b-hmxv","volume":"112","year":"2025","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c89","doi-asserted-by":"publisher","first-page":"022306","DOI":"10.1103\/physreve.91.022306","volume":"91","year":"2015","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c90","doi-asserted-by":"publisher","first-page":"052615","DOI":"10.1103\/physreve.97.052615","volume":"97","year":"2018","journal-title":"Phys. Rev. E"},{"key":"2026021107272066300_c91","doi-asserted-by":"publisher","first-page":"185001","DOI":"10.1088\/1361-648x\/ad21a7","volume":"36","year":"2024","journal-title":"J.\u00a0Phys.: Condens. Matter"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0309849\/20899266\/064906_1_5.0309849.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0309849\/20899266\/064906_1_5.0309849.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T12:27:28Z","timestamp":1770812848000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/164\/6\/064906\/3379265\/Phase-behavior-and-defect-structure-of-soft-rods"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,11]]},"references-count":91,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,2,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0309849","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,2,14]]},"published":{"date-parts":[[2026,2,11]]},"article-number":"064906"}}