Editing Supercooling and nucleation
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'''Supercooling''', undercooling and nucleation. | '''Supercooling''', undercooling and nucleation. | ||
==Volmer and Weber kinetic model== | ==Volmer and Weber kinetic model== | ||
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> | 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>: | ||
:<math>I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right) </math> | :<math>\label{eq_IVW}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 | The Zeldovich factor, <math>Z</math>, modifies the Volmer and Weber expression \eqref{eq_IVW}, 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> | ||
==See also== | ==See also== | ||
*[[Glass transition]] | *[[Glass transition]] | ||
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<references/> | <references/> | ||
;Related reading | ;Related reading | ||
*[http://dx.doi.org/10.1063/1.2779036 Lawrence S. Bartell and David T. Wu "Do supercooled liquids freeze by spinodal decomposition?", Journal of Chemical Physics '''127''' 174507 (2007)] | *[http://dx.doi.org/10.1063/1.2779036 Lawrence S. Bartell and David T. Wu "Do supercooled liquids freeze by spinodal decomposition?", Journal of Chemical Physics '''127''' 174507 (2007)] | ||
*[http://dx.doi.org/10.1063/1.471721 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)] | *[http://dx.doi.org/10.1063/1.471721 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)] | ||
*[http://www.amolf.nl/publications/theses/valeriani/valeriani.html Chantal Valeriani "Numerical studies of nucleation pathways of ordered and disordered phases", PhD Thesis (2007)] | |||
*[http://dx.doi.org/10.1063/1.2800001 Richard C. Flagan "A thermodynamically consistent kinetic framework for binary nucleation", Journal of Chemical Physics '''127''' 214503 (2007)] | *[http://dx.doi.org/10.1063/1.2800001 Richard C. Flagan "A thermodynamically consistent kinetic framework for binary nucleation", Journal of Chemical Physics '''127''' 214503 (2007)] | ||
*[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/10.1016/j.physrep.2009.03.003 Andrea Cavagna "Supercooled liquids for pedestrians", Physics Reports '''476''' pp. 51-124 (2009)] | ||
;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)] | ||
* Dimo Kashchiev "Nucleation", Butterworth-Heinemann (2000) ISBN 978-0-7506-4682-6 | * Dimo Kashchiev "Nucleation", Butterworth-Heinemann (2000) ISBN 978-0-7506-4682-6 | ||
*[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://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 | ||
[[category: Phase transitions]] | [[category: Phase transitions]] |