[{"intvolume":"       118","title":"Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase","publication":"Proceedings of the National Academy of Sciences","quality_controlled":"1","publication_status":"published","tmp":{"image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"article_processing_charge":"No","date_created":"2026-06-30T06:31:50Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1073/pnas.2107241118"}],"abstract":[{"lang":"eng","text":"Hierarchically self-assembled materials—structures with order at multiple length scales—can be found everywhere. Examples range from collagen structures in human bones to engineered photonic materials. These structures usually assemble from monodisperse microscopic building blocks that interact via complex directional interactions. In this work, we show that hierarchical materials can, in fact, also be assembled from polydisperse building blocks and by entropic interactions alone. Our simple yet powerful assembly mechanism opens up avenues toward rationally exploiting the often undesired polydispersity of colloidal building blocks for programming entropy-driven self-assembly of hierarchical materials."}],"citation":{"ista":"Fernández-Rico C, Dullens RPA. 2021. Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase. Proceedings of the National Academy of Sciences. 118(33), e2107241118.","apa":"Fernández-Rico, C., &#38; Dullens, R. P. A. (2021). Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase. <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2107241118\">https://doi.org/10.1073/pnas.2107241118</a>","ieee":"C. Fernández-Rico and R. P. A. Dullens, “Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase,” <i>Proceedings of the National Academy of Sciences</i>, vol. 118, no. 33. National Academy of Sciences, 2021.","chicago":"Fernández-Rico, Carla, and Roel P. A. Dullens. “Hierarchical Self-Assembly of Polydisperse Colloidal Bananas into a Two-Dimensional Vortex Phase.” <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences, 2021. <a href=\"https://doi.org/10.1073/pnas.2107241118\">https://doi.org/10.1073/pnas.2107241118</a>.","ama":"Fernández-Rico C, Dullens RPA. Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase. <i>Proceedings of the National Academy of Sciences</i>. 2021;118(33). doi:<a href=\"https://doi.org/10.1073/pnas.2107241118\">10.1073/pnas.2107241118</a>","short":"C. Fernández-Rico, R.P.A. Dullens, Proceedings of the National Academy of Sciences 118 (2021).","mla":"Fernández-Rico, Carla, and Roel P. A. Dullens. “Hierarchical Self-Assembly of Polydisperse Colloidal Bananas into a Two-Dimensional Vortex Phase.” <i>Proceedings of the National Academy of Sciences</i>, vol. 118, no. 33, e2107241118, National Academy of Sciences, 2021, doi:<a href=\"https://doi.org/10.1073/pnas.2107241118\">10.1073/pnas.2107241118</a>."},"scopus_import":"1","author":[{"first_name":"Carla","full_name":"Fernández-Rico, Carla","last_name":"Fernández-Rico","id":"492def71-6250-11f0-b278-d41dbd241b62"},{"first_name":"Roel P. A.","full_name":"Dullens, Roel P. A.","last_name":"Dullens"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"National Academy of Sciences","issue":"33","doi":"10.1073/pnas.2107241118","has_accepted_license":"1","year":"2021","volume":118,"month":"08","day":"13","date_published":"2021-08-13T00:00:00Z","extern":"1","OA_place":"publisher","external_id":{"pmid":["34389681"]},"oa_version":"Published Version","type":"journal_article","OA_type":"hybrid","oa":1,"article_type":"original","pmid":1,"status":"public","language":[{"iso":"eng"}],"date_updated":"2026-07-15T07:02:38Z","_id":"22211","ddc":["540"],"publication_identifier":{"issn":["0027-8424"],"eissn":["1091-6490"]},"article_number":"e2107241118"}]