On the equilibrium pressure of phases with very small dimensions

Abstract

Following Mayer's and Frenkel's statistical treatment of condensation, two difference equations are proposed, that could be considered as most general forms of the Thomson-Gibbs formula relating the equilibrium vapor pressure of small phases with their dimension. The first equation (18) assumes the knowledge of the complete ``cluster integral'' for particles of each size. The second one (19) takes into account the internal partition function of the most stable configuration only. Both equations, being discontinuous, give supersaturation ranges in which particles could be considered as critical nuclei in the condensation process. The computer calculation of the cluster integrals for (2- to 14-atomic) particles of a monatomic substance with central forces, using the Lennard-Jones 6–12 potential, shows a negligible difference between the numerical values of the supersaturations obtained by Eqs. (18) and (19). On the other hand, from the comparison of these data with the Thomson-Gibbs formula for the same model, it follows that the latter is a fairly good approximation even for particles of only a few atoms. A discussion of the most stable structure of small particles and of the smoothing effect of their entropy terms on the vapor pressure curve, enables us to affirm that such particles have a pronounced liquid character even at low temperatures.