First order phase transitions and the thermodynamic limit
We consider simple mean field continuum models for first order liquid–liquid demixing and solid–liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn–Hillia...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab5caf |
| _version_ | 1797750344018558976 |
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| author | Uwe Thiele Tobias Frohoff-Hülsmann Sebastian Engelnkemper Edgar Knobloch Andrew J Archer |
| author_facet | Uwe Thiele Tobias Frohoff-Hülsmann Sebastian Engelnkemper Edgar Knobloch Andrew J Archer |
| author_sort | Uwe Thiele |
| collection | DOAJ |
| description | We consider simple mean field continuum models for first order liquid–liquid demixing and solid–liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn–Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid–liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit. |
| first_indexed | 2024-03-12T16:32:21Z |
| format | Article |
| id | doaj.art-54b2687dbad74fc9905ca064494d2802 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:32:21Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-54b2687dbad74fc9905ca064494d28022023-08-08T15:26:26ZengIOP PublishingNew Journal of Physics1367-26302019-01-01211212302110.1088/1367-2630/ab5cafFirst order phase transitions and the thermodynamic limitUwe Thiele0https://orcid.org/0000-0001-7989-9271Tobias Frohoff-Hülsmann1Sebastian Engelnkemper2Edgar Knobloch3Andrew J Archer4https://orcid.org/0000-0002-4706-2204Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster , Wilhelm Klemm Str. 9, D-48149 Münster, Germany; Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster , Corrensstr. 2, D-48149 Münster, Germany; Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität , Corrensstr. 40, D-48149 Münster, GermanyInstitut für Theoretische Physik, Westfälische Wilhelms-Universität Münster , Wilhelm Klemm Str. 9, D-48149 Münster, GermanyInstitut für Theoretische Physik, Westfälische Wilhelms-Universität Münster , Wilhelm Klemm Str. 9, D-48149 Münster, GermanyDepartment of Physics, University of California , Berkeley, CA 94720, United States of AmericaDepartment of Mathematical Sciences, Loughborough University , Loughborough, Leicestershire, LE11 3TU, United Kingdom; Interdisciplinary Centre for Mathematical Modelling, Loughborough University , Loughborough, Leicestershire, LE11 3TU, United KingdomWe consider simple mean field continuum models for first order liquid–liquid demixing and solid–liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn–Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid–liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit.https://doi.org/10.1088/1367-2630/ab5cafMaxwell constructionmean-field modelslocalized structuresphase separationcolloidal crystallizationCahn–Hilliard model |
| spellingShingle | Uwe Thiele Tobias Frohoff-Hülsmann Sebastian Engelnkemper Edgar Knobloch Andrew J Archer First order phase transitions and the thermodynamic limit New Journal of Physics Maxwell construction mean-field models localized structures phase separation colloidal crystallization Cahn–Hilliard model |
| title | First order phase transitions and the thermodynamic limit |
| title_full | First order phase transitions and the thermodynamic limit |
| title_fullStr | First order phase transitions and the thermodynamic limit |
| title_full_unstemmed | First order phase transitions and the thermodynamic limit |
| title_short | First order phase transitions and the thermodynamic limit |
| title_sort | first order phase transitions and the thermodynamic limit |
| topic | Maxwell construction mean-field models localized structures phase separation colloidal crystallization Cahn–Hilliard model |
| url | https://doi.org/10.1088/1367-2630/ab5caf |
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