Supercooling and nucleation

From SklogWiki
Jump to: navigation, search

Supercooling, undercooling and nucleation.

Volmer and Weber kinetic model[edit]

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)

Szilard nucleation model[edit]

Homogeneous nucleation temperature[edit]

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

Zeldovich factor[edit]

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

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

Zeldovich-Frenkel equation[edit]

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].

Nucleation theorem[edit]

See also[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)
Related reading