{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T18:08:44Z","timestamp":1761156524534,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,10]],"date-time":"2018-07-10T00:00:00Z","timestamp":1531180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Active matter consists of particles that dissipate energy, from their own sources, in the form of mechanical work on their surroundings. Recent interest in active-passive polymer mixtures has been driven by their relevance in phase separation of (e.g., transcriptionally) active and inactive (transcriptionally silent) DNA strands in nuclei of living cells. In this paper, we study the interfacial properties of the phase separated steady states of the active-passive polymer mixtures and compare them with equilibrium phase separation. We model the active constituents by assigning them stronger-than-thermal fluctuations. We demonstrate that the entropy production is an accurate indicator of the phase transition. We then construct phase diagrams and analyze kinetic properties of the particles as a function of the distance from the interface. Studying the interface fluctuations, we find that they follow the capillary waves spectrum. This allows us to establish a mechanistic definition of the interfacial stiffness and its dependence on the relative level of activity with respect to the passive constituents. We show how the interfacial width depends on the activity ratio and comment on the finite size effects. Our results highlight similarities and differences of the non-equilibrium steady states with an equilibrium phase separated polymer mixture with a lower critical solution temperature. We present several directions in which the non-equilibrium system can be studied further and point out interesting observations that indicate general principles behind the non-equilibrium phase separation.<\/jats:p>","DOI":"10.3390\/e20070520","type":"journal-article","created":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T03:24:19Z","timestamp":1531279459000},"page":"520","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Interfacial Properties of Active-Passive Polymer Mixtures"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1764-9298","authenticated-orcid":false,"given":"Jan","family":"Smrek","sequence":"first","affiliation":[{"name":"Max Planck Institute for Polymer Research, Ackermannweg 10, 55127 Mainz, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1842-9369","authenticated-orcid":false,"given":"Kurt","family":"Kremer","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Polymer Research, Ackermannweg 10, 55127 Mainz, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1103\/RevModPhys.85.1143","article-title":"Hydrodynamics of soft active matter","volume":"85","author":"Marchetti","year":"2013","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"045006","DOI":"10.1103\/RevModPhys.88.045006","article-title":"Active particles in complex and crowded environments","volume":"88","author":"Bechinger","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1103\/PhysRevLett.75.1226","article-title":"Novel Type of Phase Transition in a System of Self-Driven Particles","volume":"75","author":"Vicsek","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjst\/e2012-01529-y","article-title":"Active Brownian particles","volume":"202","author":"Romanczuk","year":"2012","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1140\/epjst\/e2015-02457-0","article-title":"Active brownian particles and run-and-tumble particles: A comparative study","volume":"224","author":"Solon","year":"2015","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1146\/annurev-conmatphys-031214-014710","article-title":"Motility-Induced Phase Separation","volume":"6","author":"Cates","year":"2015","journal-title":"Ann. Rev. Condens. Matter Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"038103","DOI":"10.1103\/PhysRevLett.117.038103","article-title":"How Far from Equilibrium Is Active Matter?","volume":"117","author":"Fodor","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"058301","DOI":"10.1103\/PhysRevLett.116.058301","article-title":"Binary Mixtures of Particles with Different Diffusivities Demix","volume":"116","author":"Weber","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"032118","DOI":"10.1103\/PhysRevE.92.032118","article-title":"Nonequilibrium statistical mechanics of mixtures of particles in contact with different thermostats","volume":"92","author":"Grosberg","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"098002","DOI":"10.1103\/PhysRevLett.118.098002","article-title":"Small Activity Differences Drive Phase Separation in Active-Passive Polymer Mixtures","volume":"118","author":"Smrek","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1093\/nar\/gkt1417","article-title":"Chromosome positioning from activity-based segregation","volume":"42","author":"Ganai","year":"2014","journal-title":"Nucl. Acids Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sewitz, S.A., Fahmi, Z., Aljebali, L., Bancroft, J., Brustolini, O.J.B., Saad, H., Goiffon, I., Varnai, C., Wingett, S., and Wong, H. (2017). Heterogeneous chromatin mobility derived from chromatin states is a determinant of genome organisation in S. cerevisiae. BioRxiv.","DOI":"10.1101\/106344"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1871","DOI":"10.1016\/j.bpj.2014.03.038","article-title":"Chromatin Hydrodynamics","volume":"106","author":"Bruinsma","year":"2014","journal-title":"Biophys. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"098301","DOI":"10.1103\/PhysRevLett.115.098301","article-title":"Negative Interfacial Tension in Phase-Separated Active Brownian Particles","volume":"115","author":"Siebert","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"30006","DOI":"10.1209\/0295-5075\/114\/30006","article-title":"Stochastic thermodynamics for active matter","volume":"114","author":"Speck","year":"2016","journal-title":"EPL"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"084902","DOI":"10.1063\/1.4989764","article-title":"Non-equilibrium surface tension of the vapour-liquid interface of active Lennard\u2013Jones particles","volume":"147","author":"Paliwal","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1063\/1.1747782","article-title":"The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics","volume":"18","author":"Irving","year":"1950","journal-title":"J. Chem. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1038\/nphys3377","article-title":"Pressure is not a state function for generic active fluids","volume":"11","author":"Solon","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4444","DOI":"10.1063\/1.1288390","article-title":"Molecular dynamics results on the pressure tensor of polymer films","volume":"113","author":"Varnik","year":"2000","journal-title":"J. Chem. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1007\/BF01412220","article-title":"Critical phenomena in polymer mixtures: Monte Carlo simulation of a lattice model","volume":"265","author":"Sariban","year":"1987","journal-title":"Colloid Polym. Sci."},{"key":"ref_21","unstructured":"Wilding, N. (1995). Computer Simulation Studies in Condensed-Matter Physics VIII, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1016\/0550-3213(85)90379-7","article-title":"Finite size effects in phase transitions","volume":"257","year":"1985","journal-title":"Nucl. Phys. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5081","DOI":"10.1103\/PhysRevB.44.5081","article-title":"Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study","volume":"44","author":"Ferrenberg","year":"1991","journal-title":"Phys. Rev. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"8175","DOI":"10.1063\/1.475118","article-title":"Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin-film geometry: A Monte Carlo simulation","volume":"107","author":"Werner","year":"1997","journal-title":"J. Chem. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1103\/PhysRevE.59.728","article-title":"\u201cIntrinsic\u201d profiles and capillary waves at homopolymer interfaces: A Monte Carlo study","volume":"59","author":"Werner","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"134905","DOI":"10.1063\/1.1866072","article-title":"Capillary waves in a colloid-polymer interface","volume":"122","author":"Vink","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"D\u00fcnweg, B., Landau, D.P., and Milchev, A.I. (2003). Polymers at Surfaces and Interfaces. Computer Simulations of Surfaces and Interfaces, Springer.","DOI":"10.1007\/978-94-010-0173-1"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5002","DOI":"10.1063\/1.477113","article-title":"Extended capillary wave theory and the ellipsometric coefficient","volume":"109","author":"Stecki","year":"1998","journal-title":"J. Chem. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/7\/520\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:11:28Z","timestamp":1760195488000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/7\/520"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,10]]},"references-count":28,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["e20070520"],"URL":"https:\/\/doi.org\/10.3390\/e20070520","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,7,10]]}}}