Thermodynamic formalism for a liquid microcluster in vapor

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Abstract
A thermodynamic formalism is developed for a liquid microcluster which is so small that the homogeneous properties of the bulk liquid are not attained even at the center. The system is carefully defined by a mathematical boundary, and then the thermodynamic variables are introduced in such a manner that the interaction of molecules inside and outside the boundary is taken into consideration. It is shown that the variables may be classified into the extensive and the intensive ones and the Gibbs-Duhem relation may also be derived. It is clarified that both the surface tension in Nishioka’s formalism with the equimolecular dividing surface and that in Gibbs’s formalism with the surface of tension represent the reversible works of a very similar nature. Finally, complication due to translation and rotation of a microcluster in vapor is discussed, and the use of the internal free energy of a microcluster to get the cluster-size dependence of the surface tension in Nishioka’s formalism is shown to be reasonable.