Supercooling and nucleation

Supercooling, undercooling and nucleation.

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_{B}T}}\right)

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

Z={\sqrt {\frac {\vert \Delta \mu \vert }{6\pi k_{B}Tn^{*}}}}

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).

↑ 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)