Relation between energy and the interfacial area

In its thermodynamic definition, the interfacial energy of a solid in the presence of a fluid or another sohd is of unspecified sign. We noted in the microscopic interpretation that its value is always positive with the consequence that the formation of an interface is always imfavorable. 

It comes out from this microscopic interpretation that interfacial energy is in general dependent on 

The question of the dependence of the size has been discussed a lot, and some equations of state have been proposed in the literature such as that of Eotvos in which the product ya depends only on temperature. 

We further note that modeling of nucleation can be discussed analytically only if we assume independence between inlerfacial energy and size. This approximation is more justified if the nuclei have roughly spherical symmetry and if their sizes are large with respect to the lengths of the chemical bond, or if we prefer if the number of building units in the nucleus are sufficiently consequent. 

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