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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?

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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.

However this rate behaviour is for transfer of molecules across existing phase interfaces and so has nothing to do with nucleation which concerns the formation of new interfaces. Nucleation requires the formation of sizable clusters of molecules in one phase or the other. This formation is a random process. Exactly how big a cluster has to be to be regarded as a true region of the phase depends a lot on the specific system and state. However at any temperature there is a certain critical size above which the cluster is stable. Although transient cluster formation still occurs at all temperatures, at equilibrium the rate of growth of any phase is effectively zero and so the formation of new phase regions above the critical size is highly unlikely.

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  • $\begingroup$ Under what conditions do we have independent transfer of molecules or nucleation? In boiling, we see nucleation but if I leave a cup of water on a table we don't. Similarly in winter liquid nucleate on car winters/in our breathing. Is nucleation only an effect seen when the current state is not stable (during heating/cooling) or metastable (supercool/heated liquid) and not during phase equilibrium? $\endgroup$ – Yandle Oct 26 '14 at 18:24

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