[{"day":"10","date_updated":"2026-04-28T07:03:48Z","file_date_updated":"2026-04-28T06:58:40Z","type":"journal_article","year":"2026","publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"language":[{"iso":"eng"}],"date_published":"2026-04-10T00:00:00Z","has_accepted_license":"1","department":[{"_id":"AnSa"},{"_id":"GradSch"}],"article_processing_charge":"Yes (in subscription journal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"hybrid","citation":{"ista":"Wassermair M, Kahl G, Roth R, Archer AJ. 2026. Navigating complex phase diagrams in soft matter systems. Physical Review Letters. 136(14), 148203.","mla":"Wassermair, Michael, et al. “Navigating Complex Phase Diagrams in Soft Matter Systems.” <i>Physical Review Letters</i>, vol. 136, no. 14, 148203, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/nbvt-fgjy\">10.1103/nbvt-fgjy</a>.","short":"M. Wassermair, G. Kahl, R. Roth, A.J. Archer, Physical Review Letters 136 (2026).","ama":"Wassermair M, Kahl G, Roth R, Archer AJ. Navigating complex phase diagrams in soft matter systems. <i>Physical Review Letters</i>. 2026;136(14). doi:<a href=\"https://doi.org/10.1103/nbvt-fgjy\">10.1103/nbvt-fgjy</a>","chicago":"Wassermair, Michael, Gerhard Kahl, Roland Roth, and Andrew J. Archer. “Navigating Complex Phase Diagrams in Soft Matter Systems.” <i>Physical Review Letters</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/nbvt-fgjy\">https://doi.org/10.1103/nbvt-fgjy</a>.","ieee":"M. Wassermair, G. Kahl, R. Roth, and A. J. Archer, “Navigating complex phase diagrams in soft matter systems,” <i>Physical Review Letters</i>, vol. 136, no. 14. American Physical Society, 2026.","apa":"Wassermair, M., Kahl, G., Roth, R., &#38; Archer, A. J. (2026). Navigating complex phase diagrams in soft matter systems. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/nbvt-fgjy\">https://doi.org/10.1103/nbvt-fgjy</a>"},"title":"Navigating complex phase diagrams in soft matter systems","volume":136,"scopus_import":"1","date_created":"2026-04-26T22:01:47Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_place":"publisher","_id":"21764","publisher":"American Physical Society","article_type":"original","abstract":[{"lang":"eng","text":"Colloidal fluids can exhibit complex phase behavior and determining phase diagrams via experiments or computer simulations can be laborious. We demonstrate that the dispersion relation ω(k), obtained from dynamical density functional theory for the uniform density system, is a highly versatile tool for predicting where in the phase diagram complex crystals form. The sign of ω(k) determines whether density modes with wave number k grow or decay over time. We demonstrate the predictive power by investigating the complex phase behavior of particles interacting via core-shoulder pair potentials. With complementary Monte Carlo simulations, we show that regions of the phase diagram where ωðkÞ has one or several unstable (growing) wave numbers are also where crystalline phases occur. Going further, by tuning these\r\nunstable wave numbers via the interaction-potential and state-point parameters, we design systems with quasicrystals in the phase diagram. We identify a system with a certain shoulder range exhibiting at least ten different phases. Our general approach accelerates considerably the mapping of complex phase diagrams, crucial for the design of new materials."}],"acknowledgement":"The authors thank Ms. Katrin Muck for her guidance related to the use of HPC. The MC\r\ncomputer simulation results presented here were enabled via a generous share of CPU time, offered by the Vienna Scientific Cluster (VSC) under Project No. 71263. A. J. A. gratefully acknowledges support from the EPSRC under Grant No. EP/P015689/1. This research was funded in part by the Austrian Science Fund (FWF) [Grant DOI: 10.55776/PIN8759524], gratefully acknowledged by G. K .","oa":1,"status":"public","publication":"Physical Review Letters","month":"04","license":"https://creativecommons.org/licenses/by/4.0/","quality_controlled":"1","ddc":["530"],"file":[{"file_name":"2026_PhysicalReviewLetters_Wassermair.pdf","creator":"dernst","date_updated":"2026-04-28T06:58:40Z","success":1,"date_created":"2026-04-28T06:58:40Z","checksum":"8ffb139122a185fcddbe6a9c901a287c","file_id":"21769","content_type":"application/pdf","file_size":4336488,"relation":"main_file","access_level":"open_access"}],"author":[{"first_name":"Michael","id":"23d132c4-4e98-11ef-b275-9e8d4cd8c917","orcid":"0009-0003-6339-4051","last_name":"Wassermair","full_name":"Wassermair, Michael"},{"first_name":"Gerhard","last_name":"Kahl","full_name":"Kahl, Gerhard"},{"first_name":"Roland","last_name":"Roth","full_name":"Roth, Roland"},{"first_name":"Andrew J.","full_name":"Archer, Andrew J.","last_name":"Archer"}],"doi":"10.1103/nbvt-fgjy","oa_version":"Published Version","external_id":{"arxiv":["2603.18918"]},"arxiv":1,"PlanS_conform":"1","article_number":"148203","publication_status":"published","issue":"14","intvolume":"       136"},{"abstract":[{"text":"We investigate the phase ordering (pattern formation) of systems of two-dimensional core–shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.","lang":"eng"}],"article_type":"original","acknowledgement":"The computational results presented here were enabled via a generous share of CPU time, offered by the Vienna Scientific Cluster (VSC) under Project No. 71263. The authors thank Ms. Katrin Muck for her guidance related to the use of HPC. A.J.A. gratefully acknowledges support from the EPSRC under Grant No. EP/P015689/1.","publisher":"AIP Publishing","_id":"18174","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"scopus_import":"1","date_created":"2024-10-06T22:01:12Z","quality_controlled":"1","ddc":["530"],"corr_author":"1","isi":1,"publication":"The Journal of chemical physics","month":"09","oa":1,"status":"public","department":[{"_id":"GradSch"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"date_published":"2024-09-28T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["1089-7690"]},"year":"2024","file_date_updated":"2024-10-07T11:25:00Z","day":"28","date_updated":"2025-09-08T09:55:52Z","volume":161,"title":"Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system","citation":{"mla":"Wassermair, Michael, et al. “Fingerprints of Ordered Self-Assembled Structures in the Liquid Phase of a Hard-Core, Square-Shoulder System.” <i>The Journal of Chemical Physics</i>, vol. 161, no. 12, 124503, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0226954\">10.1063/5.0226954</a>.","ista":"Wassermair M, Kahl G, Roth R, Archer AJ. 2024. Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system. The Journal of chemical physics. 161(12), 124503.","short":"M. Wassermair, G. Kahl, R. Roth, A.J. Archer, The Journal of Chemical Physics 161 (2024).","ieee":"M. Wassermair, G. Kahl, R. Roth, and A. J. Archer, “Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system,” <i>The Journal of chemical physics</i>, vol. 161, no. 12. AIP Publishing, 2024.","chicago":"Wassermair, Michael, Gerhard Kahl, Roland Roth, and Andrew J. Archer. “Fingerprints of Ordered Self-Assembled Structures in the Liquid Phase of a Hard-Core, Square-Shoulder System.” <i>The Journal of Chemical Physics</i>. AIP Publishing, 2024. <a href=\"https://doi.org/10.1063/5.0226954\">https://doi.org/10.1063/5.0226954</a>.","ama":"Wassermair M, Kahl G, Roth R, Archer AJ. Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system. <i>The Journal of chemical physics</i>. 2024;161(12). doi:<a href=\"https://doi.org/10.1063/5.0226954\">10.1063/5.0226954</a>","apa":"Wassermair, M., Kahl, G., Roth, R., &#38; Archer, A. J. (2024). Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system. <i>The Journal of Chemical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0226954\">https://doi.org/10.1063/5.0226954</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"Yes (in subscription journal)","arxiv":1,"intvolume":"       161","issue":"12","article_number":"124503 ","publication_status":"published","oa_version":"Published Version","doi":"10.1063/5.0226954","file":[{"checksum":"f3874e64ef94e94b2376f00a1fee24c3","file_size":15009000,"file_id":"18185","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_name":"2024_JourChemicalPhysics_Wassermair.pdf","creator":"dernst","success":1,"date_updated":"2024-10-07T11:25:00Z","date_created":"2024-10-07T11:25:00Z"}],"author":[{"full_name":"Wassermair, Michael","last_name":"Wassermair","id":"23d132c4-4e98-11ef-b275-9e8d4cd8c917","first_name":"Michael"},{"full_name":"Kahl, Gerhard","last_name":"Kahl","first_name":"Gerhard"},{"full_name":"Roth, Roland","last_name":"Roth","first_name":"Roland"},{"full_name":"Archer, Andrew J.","last_name":"Archer","first_name":"Andrew J."}],"pmid":1,"external_id":{"isi":["001325268300004"],"pmid":["39344889"],"arxiv":["2409.06447"]}}]