Effect of surface area on equilibrium pressure. Adsorption approach.
Changing droplet radii in a liquid-vapor system is due to the phase transition on the droplet surface. As a variation of the internal energy does not depend on the way the change occurs, we can imagine that a gas condenses on a droplet surface in two stages: in the first stage, autoadsorption occurs on the liquid surface, and in the second stage, adsorbed molecules transfer into the volume by diffusion. Assuming that the energetic effects of the diffusion are independent of the surface curvature, one may conclude that if two liquid bodies differ only with respect to their geometry, the difference of enthalpies of condensation on their surfaces, DeltaH(bd), is equal to the variation of energies of autoadsorption. An estimation of DeltaH(bd) for the simple bodies is presented, and the relationship between the saturation pressure and droplet radii is derived. In the range of micrometer dimensions, the new equation and the Kelvin model lead to close results; for nanocapillaries, the Kelvin equation predicts a divergence of hysteresis loops, whereas the new equation adequately describes the observations. The classical model presumes that a surface area, A, affects the free energy, while the new approach is based on the assumption that A is the repository for the internal energy.
Dobruskin
Vladimir Kh
VKh
dobruskn@netvision.net.il