{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T14:05:36Z","timestamp":1780409136322,"version":"3.54.1"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T00:00:00Z","timestamp":1780358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>The analytical investigations of 3-miktoarm star (3-arm \u03bc-star) copolymers of type A2B and AB2 are performed in the framework of mean-field approximation and Flory\u2013Huggins theory. The total entropy of mixing and the Helmholtz free energy of interaction are calculated for the number NA monomers of type A and number NB monomers of type B, respectively. The results confirm that the Helmholtz free energy of miktoarm star copolymers differs from that of polymer blends. The temperature dependence of the Helmholtz free energy allowed us to construct a phase diagram of the solution of miktoarm star copolymers, showing regions of stability, instability, and metastability. The analytical results confirm that a miktoarm star copolymer is not merely a mixture of different homo-arm star polymers and are consistent with a previous investigation performed by liquid chromatography under the critical conditions. Moreover, we performed molecular dynamics simulations of a dilute solution of 3-miktoarm star copolymer of type A2B with a certain number of beads (300 + 300 + 200 + 1) and star copolymer of type AB2 with number of beads (300 + 200 + 200 + 1), accordingly. The calculations of the radius of gyration and monomer density profiles of the 3-miktoarm star copolymers of type A2B and AB2 in confined geometry of two repulsive surfaces (Dirichlet\u2013Dirichlet boundary conditions) and one repulsive and other one attractive surface (Dirichlet\u2013Neumann boundary conditions) by molecular dynamics simulations are performed. The obtained analytical and numerical results indicate that a dilute solution of miktoarm star copolymers can be used in biotechnology and medicine for drug and gene transmission as well as for the production of new functional materials.<\/jats:p>","DOI":"10.3390\/ijms27115029","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T12:45:08Z","timestamp":1780404308000},"page":"5029","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytical Investigations and Molecular Dynamics Simulations of 3-Miktoarm Star (3-Arm \u03bc-Star) Copolymers A2B and AB2"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9776-5357","authenticated-orcid":false,"given":"Pawel","family":"Karbowniczek","sequence":"first","affiliation":[{"name":"Faculty of Materials Engineering and Physics, Cracow University of Technology, 30-719 Cracow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0147-5422","authenticated-orcid":false,"given":"Zoriana","family":"Danel","sequence":"additional","affiliation":[{"name":"Faculty of Materials Engineering and Physics, Cracow University of Technology, 30-719 Cracow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6743","DOI":"10.1021\/acs.chemrev.6b00008","article-title":"Star Polymers","volume":"116","author":"Ren","year":"2016","journal-title":"Chem. 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