It is always interesting to learn about a basic science problem which is unsolved.
Biman Bagchi gave a really nice talk yesterday, Nucleation, growth and metastability at large supersaturations.
Pure water remains liquid to -40 degrees celcius. This is supercooling. The key to formation of the solid phase is the presence of nucleation centres. At what rate will they grow?
Formation of the bulk phase is favoured thermodynamically but formations of small regions of solid are unfavourable because of their surface free energy.
Classical nucleation growth theory predicts a rate that is too small by as much as 10 orders of magnitude, compared to experiment!
["This is an embarrassment to natural science"]
Most textbooks overlook this major shortcoming.
Nuclei larger than a critical radius will grow, but there is an energy barrier to formation of these larger nuclei. The classical theory grossly overestimates this barrier. The classical theory is a mean-field theory.
This PRL by Bagchi's group gives a nice discussion of problem and one of his contributions. It includes the figure below. A key thing it shows contradicts the classical model for which the growth of the liquid is assumed to occur through the growth of a single cluster.
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