Supercooling and nucleation: Difference between revisions
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Volmer and Weber kinetic model <ref>M. Volmer and A. Weber "Keimbildung in übersättigten Gebilden", Zeitschrift für Physikalische Chemie '''119''' pp. 277-301 (1926)</ref> results in the following nucleation rate: | Volmer and Weber kinetic model <ref>M. Volmer and A. Weber "Keimbildung in übersättigten Gebilden", Zeitschrift für Physikalische Chemie '''119''' pp. 277-301 (1926)</ref> results in the following nucleation rate: | ||
:<math>I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right) | :<math>I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right) </math> | ||
==Szilard nucleation model== | ==Szilard nucleation model== | ||
==Homogeneous nucleation temperature== | ==Homogeneous nucleation temperature== | ||
The homogeneous nucleation temperature (<math>T_H</math>) is the [[temperature]] below which it is almost impossible to avoid spontaneous and rapid freezing. | The homogeneous nucleation temperature (<math>T_H</math>) is the [[temperature]] below which it is almost impossible to avoid spontaneous and rapid freezing. | ||
==Zeldovich factor== | ==Zeldovich factor== | ||
The Zeldovich factor <ref>J. B. Zeldovich "On the theory of new phase formation, cavitation", Acta Physicochimica URSS '''18''' pp. 1-22 (1943)</ref> (<math>Z</math>) modifies the Volmer and Weber expression | The Zeldovich factor <ref>J. B. Zeldovich "On the theory of new phase formation, cavitation", Acta Physicochimica URSS '''18''' pp. 1-22 (1943)</ref> (<math>Z</math>) modifies the Volmer and Weber expression, making it applicable to spherical clusters: | ||
:<math>Z= \sqrt{\frac{ \vert \Delta \mu \vert }{6 \pi k_B T n^*}} </math> | :<math>Z= \sqrt{\frac{ \vert \Delta \mu \vert }{6 \pi k_B T n^*}} </math> | ||
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See also Shizgal and Barrett <ref>[http://dx.doi.org/10.1063/1.457366 B. Shizgal and J. C. Barrett "Time dependent nucleation", Journal of Chemical Physics '''91''' pp. 6505-6518 (1989)]</ref>. | See also Shizgal and Barrett <ref>[http://dx.doi.org/10.1063/1.457366 B. Shizgal and J. C. Barrett "Time dependent nucleation", Journal of Chemical Physics '''91''' pp. 6505-6518 (1989)]</ref>. | ||
==Nucleation theorem== | |||
==See also== | ==See also== | ||
*[[Glass transition]] | *[[Glass transition]] | ||
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*[http://dx.doi.org/10.1063/1.3506838 Laura Filion, Michiel Hermes, Ran Ni and Marjolein Dijkstra "Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques", Journal of Chemical Physics '''133''' 244115 (2010)] | *[http://dx.doi.org/10.1063/1.3506838 Laura Filion, Michiel Hermes, Ran Ni and Marjolein Dijkstra "Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques", Journal of Chemical Physics '''133''' 244115 (2010)] | ||
*[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)] | *[http://dx.doi.org/10.1103/PhysRevLett.105.088302 Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters '''105''' 088302 (2010)] | ||
*[http://dx.doi.org/10. | *[http://dx.doi.org/10.1063/1.4747326 M. D. Ediger and Peter Harrowell "Perspective: Supercooled liquids and glasses", Journal of Chemical Physics '''137''' 080901 (2012)] | ||
*[https://doi.org/10.1063/1.5034091 Edgar D. Zanotto and Daniel R. Cassar "The race within supercooled liquids—Relaxation versus crystallization", Journal of Chemical Physics '''149''' 024503 (2018)] | |||
;Books | ;Books | ||
*[http://dx.doi.org/10.1016/S0081-1947(08)60604-9 David T. Wu "Nucleation Theory", Solid State Physics '''50''' pp. 37-187 (1996)] | *[http://dx.doi.org/10.1016/S0081-1947(08)60604-9 David T. Wu "Nucleation Theory", Solid State Physics '''50''' pp. 37-187 (1996)] | ||
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*[http://dx.doi.org/10.1016/j.physrep.2009.03.003 Andrea Cavagna "Supercooled liquids for pedestrians", Physics Reports '''476''' pp. 51-124 (2009)] | *[http://dx.doi.org/10.1016/j.physrep.2009.03.003 Andrea Cavagna "Supercooled liquids for pedestrians", Physics Reports '''476''' pp. 51-124 (2009)] | ||
*[http://www.sciencedirect.com/science/bookseries/14701804/15 Ken F. Kelton and Alan Lindsay Greer "Nucleation in Condensed Matter: Applications in Materials and Biology", Pergamon Materials Series Volume 15 (2010)] ISBN 978-0-08-042147-6 | *[http://www.sciencedirect.com/science/bookseries/14701804/15 Ken F. Kelton and Alan Lindsay Greer "Nucleation in Condensed Matter: Applications in Materials and Biology", Pergamon Materials Series Volume 15 (2010)] ISBN 978-0-08-042147-6 | ||
*[http://arxiv.org/abs/1208.3377 R. Ni "Entropy-Driven Phase Transitions in Colloidal Systems", PhD Thesis, Utrecht University (2012)] ISBN 978-90-393-5798-9 | |||
[[category: Phase transitions]] | [[category: Phase transitions]] | ||
Latest revision as of 11:09, 17 July 2018
Supercooling, undercooling and nucleation.
Volmer and Weber kinetic model[edit]
Volmer and Weber kinetic model [1] results in the following nucleation rate:
Szilard nucleation model[edit]
Homogeneous nucleation temperature[edit]
The homogeneous nucleation temperature () is the temperature below which it is almost impossible to avoid spontaneous and rapid freezing.
Zeldovich factor[edit]
The Zeldovich factor [2] () modifies the Volmer and Weber expression, making it applicable to spherical clusters:
Zeldovich-Frenkel equation[edit]
Zeldovich-Frenkel master equation is given by
See also Shizgal and Barrett [3].
Nucleation theorem[edit]
See also[edit]
References[edit]
- ↑ M. Volmer and A. Weber "Keimbildung in übersättigten Gebilden", Zeitschrift für Physikalische Chemie 119 pp. 277-301 (1926)
- ↑ J. B. Zeldovich "On the theory of new phase formation, cavitation", Acta Physicochimica URSS 18 pp. 1-22 (1943)
- ↑ B. Shizgal and J. C. Barrett "Time dependent nucleation", Journal of Chemical Physics 91 pp. 6505-6518 (1989)
- Related reading
- J. Frenkel "Statistical Theory of Condensation Phenomena", Journal of Chemical Physics 7 pp. 200-201 (1939)
- Lawrence S. Bartell and David T. Wu "Do supercooled liquids freeze by spinodal decomposition?", Journal of Chemical Physics 127 174507 (2007)
- Pieter Rein ten Wolde, Maria J. Ruiz-Montero and Daan Frenkel "Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling", Journal of Chemical Physics 104 pp. 9932-9947 (1996)
- Richard C. Flagan "A thermodynamically consistent kinetic framework for binary nucleation", Journal of Chemical Physics 127 214503 (2007)
- Laura Filion, Michiel Hermes, Ran Ni and Marjolein Dijkstra "Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques", Journal of Chemical Physics 133 244115 (2010)
- Ran Ni, Simone Belli, René van Roij, and Marjolein Dijkstra "Glassy Dynamics, Spinodal Fluctuations, and the Kinetic Limit of Nucleation in Suspensions of Colloidal Hard Rods", Physical Review Letters 105 088302 (2010)
- M. D. Ediger and Peter Harrowell "Perspective: Supercooled liquids and glasses", Journal of Chemical Physics 137 080901 (2012)
- Edgar D. Zanotto and Daniel R. Cassar "The race within supercooled liquids—Relaxation versus crystallization", Journal of Chemical Physics 149 024503 (2018)
- Books
- David T. Wu "Nucleation Theory", Solid State Physics 50 pp. 37-187 (1996)
- Chantal Valeriani "Numerical studies of nucleation pathways of ordered and disordered phases", PhD Thesis (2007)
- Dimo Kashchiev "Nucleation", Butterworth-Heinemann (2000) ISBN 978-0-7506-4682-6
- Andrea Cavagna "Supercooled liquids for pedestrians", Physics Reports 476 pp. 51-124 (2009)
- Ken F. Kelton and Alan Lindsay Greer "Nucleation in Condensed Matter: Applications in Materials and Biology", Pergamon Materials Series Volume 15 (2010) ISBN 978-0-08-042147-6
- R. Ni "Entropy-Driven Phase Transitions in Colloidal Systems", PhD Thesis, Utrecht University (2012) ISBN 978-90-393-5798-9