Supercooling and nucleation: Difference between revisions

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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 \eqref{eq_IVW}, making it applicable to spherical clusters:
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>

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:

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 I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right) }

Szilard nucleation model[edit]

Homogeneous nucleation temperature[edit]

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[edit]

The Zeldovich factor [2] (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, 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^*}} }

Zeldovich-Frenkel equation[edit]

Zeldovich-Frenkel master equation is given by

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 \frac{\partial N(n, t)}{\partial t} = \frac{\partial }{\partial n} \left( k^+ (n) N^{eq} (n) \frac{\partial }{\partial n} \left( \frac{N(n, t)}{N^{eq}(n)} \right) \right).}

See also Shizgal and Barrett [3].

Nucleation theorem[edit]

See also[edit]

References[edit]

  1. ↑ M. Volmer and A. Weber "Keimbildung in übersättigten Gebilden", Zeitschrift für Physikalische Chemie 119 pp. 277-301 (1926)
  2. ↑ J. B. Zeldovich "On the theory of new phase formation, cavitation", Acta Physicochimica URSS 18 pp. 1-22 (1943)
  3. ↑ B. Shizgal and J. C. Barrett "Time dependent nucleation", Journal of Chemical Physics 91 pp. 6505-6518 (1989)
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