{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:02:47Z","timestamp":1753873367015,"version":"3.41.2"},"reference-count":29,"publisher":"AIP Publishing","issue":"4","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2014,1,28]]},"abstract":"<jats:p>We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self-assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension of Wertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r \u2261 \u03b5AB\/\u03b5AA of the interaction between patches A and B, \u03b5AB, and between A patches, \u03b5AA (\u03b5BB is set to 0) as well as the relative position of the A patches, i.e., the angle \u03b8 between the (lattice) directions of the A patches. We found that both r and \u03b8 (60\u00b0, 90\u00b0, or 120\u00b0) have a profound effect on the phase diagram. In the empty fluid regime (r &amp;lt; 1\/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for \u03b8 = 120\u00b0 but deteriorates as \u03b8 decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.<\/jats:p>","DOI":"10.1063\/1.4863135","type":"journal-article","created":{"date-parts":[[2014,1,31]],"date-time":"2014-01-31T18:09:33Z","timestamp":1391191773000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":24,"title":["Three-dimensional patchy lattice model: Ring formation and phase separation"],"prefix":"10.1063","volume":"140","author":[{"given":"J. M.","family":"Tavares","sequence":"first","affiliation":[{"name":"Universidade de Lisboa 1 Centro de F\u00edsica Te\u00f3rica e Computacional, , Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal and , Rua Conselheiro Em\u00eddio Navarro 1, P-1950-062 Lisbon, Portugal"},{"name":"Instituto Superior de Engenharia de Lisboa 1 Centro de F\u00edsica Te\u00f3rica e Computacional, , Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal and , Rua Conselheiro Em\u00eddio Navarro 1, P-1950-062 Lisbon, Portugal"}]},{"given":"N. G.","family":"Almarza","sequence":"additional","affiliation":[{"name":"CSIC 2 Instituto de Qu\u00edmica F\u00edsica Rocasolano, , Serrano 119, E-28006 Madrid, Spain"}]},{"given":"M. M.","family":"Telo da Gama","sequence":"additional","affiliation":[{"name":"Universidade de Lisboa 3 Centro de F\u00edsica Te\u00f3rica e Computacional, , Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal and Departamento de F\u00edsica, Faculdade de Ci\u00eancias, , Campo Grande, P-1749-016 Lisbon, Portugal"},{"name":"Universidade de Lisboa 3 Centro de F\u00edsica Te\u00f3rica e Computacional, , Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal and Departamento de F\u00edsica, Faculdade de Ci\u00eancias, , Campo Grande, P-1749-016 Lisbon, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2014,1,30]]},"reference":[{"key":"2023062004035520900_c1","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1038\/nmat1949","volume":"6","year":"2007","journal-title":"Nat. Mater."},{"key":"2023062004035520900_c2","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1002\/marc.201090000","volume":"31","year":"2010","journal-title":"Macromol. 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