Correlation between saturation pressures and dimensions of nanoparticles. Are the fundamental equations really fair?

The relationships between the geometric form and saturation pressure are derived on the basis of thermodynamics and molecular models. A comparison of the relationships with the classical Laplace and Kelvin equations shows that there is a profound conceptual diversity between approaches: the classical equations contain the surface tension, gamma, as a parameter, whereas developed equations include the difference of the potential energies of a nanoparticle and a semi-infinite planar body with respect to the gas phase, which is equal to the difference of energies of autoadsorption on surfaces of bodies. The latter circumstance affords ground for calculating the change of interest proceeding from well-developed methods of adsorption theory. Molecular models are discussed for simple spherical bodies and applied to the processes of nucleation and growth of drops. In the cases of (i) water and mercury drops or capillaries with diameters of approximate to1 mum and (ii) cyclohexane meniscuses on mica cylinders, the classical and new relations predict close results, which are in agreement with experiments; nevertheless, for organic substances, especially at elevated temperatures, noticeable deviations must be expected. The divergence of the approaches makes its appearance in the case of condensation in narrow capillaries with radii approximate to1 - 10 nm when the new equation provides a correct description of experimental facts whereas the Kelvin model predicts unrealistic effects. Considering the growth of surface areas due to the extension or adsorption shows that gamma does not take into account all changes associated with alterations of surface areas, and it is this fact that underlies the probable defect in the classical equations.