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The exact treatment of first-order phase transition is an important
topic in thermodynamics. This topic exists as an exact branch of thermodynamics,
only by virtue of the occurrence of sharp discontinuities in properties of
macroscopic systems. In small systems, instead of such discontinities, there are
more or less gradual changes which approach discontinuities more closely as the
system becomes larger. Metastable macroscopic systems below a critical temperature
show nucleation phenomena and depending on the saturation degree the number of
constitutive elements that form the evolving nuclei may vary from a couple of tens
to hundreds of thousands. In Classical Nucleation Theory specific corrections done
on Gibbs' surface tension term take care of small size effects and theoretical
predictions are in fair agreement with early experimental data. However results
obtained by experimental techniques developed in the last decade revealed
systematic deviations from the classical theory. Nuclei that evolve into the new
phase may contain only a few of tens of molecules and continuum thermodynamics
does not apply to such situations. Statistical mechanical methods rely on complex
interaction potentials and the generality of thermodynamic predictions is lost.
However clever modifications introduced in continuum thermodynamics extend its
applicability to small systems even in cases where the thermodynamic limit is not
valid anymore. In all those treatments the grand canonical potential is of central
importance and the driving force for nucleation is the entropy, whatever the
nucleation process maybe.
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