Supercooling and nucleation: Difference between revisions

Latest revision as of 10:09, 17 July 2018

Supercooling, undercooling and nucleation.

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

I^{V W} = N^{e q} (n^{*}) k^{+} (n^{*}) = k^{+} (n^{*}) N_{A} \exp (- \frac{W (n^{*})}{k_{B} T})

The homogeneous nucleation temperature ( $T_{H}$ ) is the temperature below which it is almost impossible to avoid spontaneous and rapid freezing.

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

Z = \sqrt{\frac{| Δ μ |}{6 π k_{B} T n^{*}}}

Zeldovich-Frenkel master equation is given by

\frac{\partial N (n, t)}{\partial t} = \frac{\partial}{\partial n} (k^{+} (n) N^{e q} (n) \frac{\partial}{\partial n} (\frac{N (n, t)}{N^{e q} (n)})) .

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

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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.
 ==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>