Supercooling and nucleation

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Supercooling, undercooling and nucleation.

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[edit] Volmer and Weber kinetic model

Volmer and Weber kinetic model [1] results in the following nucleation rate:

\[I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right) \tag{1} \]

[edit] Szilard nucleation model

[edit] Homogeneous nucleation temperature

The homogeneous nucleation temperature (\(T_H\)) is the temperature below which it is almost impossible to avoid spontaneous and rapid freezing.

[edit] Zeldovich factor

The Zeldovich factor [2] (\(Z\)) modifies the Volmer and Weber expression (1), making it applicable to spherical clusters:

\[Z= \sqrt{\frac{ \vert \Delta \mu \vert }{6 \pi k_B T n^*}} \]

[edit] Zeldovich-Frenkel equation

Zeldovich-Frenkel master equation is given by

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

See also Shizgal and Barrett [3].

[edit] Nucleation theorem

[edit] See also

[edit] References

  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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