Comparison of Different Model Equations for Size- and Shape-Dependent Integral and Partial Molar Gibbs Energies of Nanophases to Screen Out the Incorrect Ones

Equations for the integral molar Gibbs energy of nanophases and the partial molar Gibbs energy of components dissolved in nanophases have been derived here by extending the classical thermodynamics of Gibbs to nanosizes in three different ways, found in the literature: according to Kelvin, the nanoeffect is proportional to the curvature of the phase; according to Searcy, the nanoeffect is proportional to d<i>A</i>/d<i>V</i> (where <i>A</i> and <i>V</i> are the surface area and the volume of the nanophase, respectively); and according to the previous papers of the present author, the nanoeffect is proportional to the specific surface area of the nanophase defined as <i>A</i>/<i>V</i>. It has been shown in many experiments that for all possible shapes of all nanophases, their molar Gibbs energies are inversely proportional to their characteristic sizes, such as to the radius of a nanosphere, to the side length of a nanocube, or to the thickness of a thin film. It is shown that the approaches due to Kelvin (curvature) and Searcy (d<i>A</i>/d<i>V</i>) lead to some controversial results versus experimental evidence, so they are excluded here. Moreover, they both contradict the nucleation theory of Gibbs, providing the same equations for the equilibrium size of a spherical nanophase and for the critical size of the spherical nucleus, being the second reason to exclude these equations. Moreover, the model by Searcy contradicts the nucleation theory of Gibbs, providing the same equation for the equilibrium size of a cubic nanophase and for the critical size of the cubic nucleus, being the third reason to exclude this equation. It is also shown that the previous approach by the author (<i>A</i>/<i>V</i>) is free of such contradictions; therefore, it is suggested for further use here.