# Does Nucleation Occur during Phase Equilibrium?

I understand that during phase transition nucleation must occur. I'm wondering, once phase equilibrium is established, does nucleation still occur? For instance, in liquid-vapour equilibrium, does independent water molecules just simply enter and leave the liquid-vapour interface, or does some kind of nucleation (say liquid to vapour) have to happen during equilibrium phase transition?

There are actually two questions here. At phase equilibrium, yes independent water molecules do enter and leave the liquid vapour interface. The rate of crossing of individual molecules from one phase to another is characterized by an Arrhenius type rate equation of the form: $$\alpha \exp \left[ - \frac{\Delta E}{kT} \right]$$ where $\Delta E$ is the activation energy and $\alpha$ is the so called rate constant. There is a separate rate equation for liquid-vapour and for vapour to liquid. The difference between the liquid-to-vapour and vapour-to-liquid activation energies is the latent heat per molecule. The rate constant is dependent on a large number of factors and usually has to be experimentally determined. The two exponentials cross at the equilibrium temperature so that at this point the rates of transfer in each direction are equal. Below this temperature the vapour-to-liquid rate is higher, above the liquid-to-vapour rate is higher.