Supercooling and nucleation
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Supercooling, undercooling and nucleation.
Volmer and Weber kinetic model
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \label{eq_IVW} I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right)}
Szilard nucleation model
Homogeneous nucleation temperature
The homogeneous nucleation temperature (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_H} ) is the temperature below which it is almost impossible to avoid spontaneous and rapid freezing.
Zeldovich factor
The Zeldovich factor, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} , modifies the Volmer and Weber expression \eqref{eq_IVW}, making it applicable to spherical clusters:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z= \sqrt{\frac{ \vert \Delta \mu \vert }{6 \pi k_B T n^*}} }
See also
References
- ↑ M. Volmer and A. Weber "Keimbildung in übersättigten Gebilden", Zeitschrift für Physikalische Chemie 119 pp. 277-301 (1926)
- Related reading
- 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)
- Chantal Valeriani "Numerical studies of nucleation pathways of ordered and disordered phases", PhD Thesis (2007)
- 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)
- Andrea Cavagna "Supercooled liquids for pedestrians", Physics Reports 476 pp. 51-124 (2009)
- Books
- 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
- 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