Nucleation Theory and Small System Thermodynamics

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.