A molecular based derivation of the nucleation theorem

Abstract

We show that, for condensation in an almost ideal vapor, the nucleation theorem is essentially a consequence of the law of mass action. The usual form of the theorem, with the effects of the translational degrees of freedom of the cluster included, is then derived using statistical mechanics and molecular theory, but only under the assumptions that the cluster excludes a volume to the surrounding vapor and that the vapor is ideal. The form of the result obtained via molecular theory is such that it appears unlikely (but not impossible) that the theorem remains valid for cases when the vapor is nonideal. This suggests that further work is necessary before the theorem can be regarded as established. We also consider the effects of the presence of a carrier gas.