Solid-liquid equilibrium and nucleation from the melt

4 Solid-liquid equilibrium and nucleation from the melt 

If melting is difficult to characterize in molecular terms, nucleation and growth of crystalline particles from the melt is an even more elusive phenomenon. Given the extreme difficulty of obtaining molecular level information, phenomenological, macroscopic nucleation theories have been formulated [13] before and aside from numerical molecular simulation. These theories constitute an almost completely parallel approach to the matter and their description does not belong in this book, although points of contact with molecular level simulations have been explored [14]. 

The following treatment of nucleation in classical nucleation theory (CNT) provides a glimpse of the methods and reasoning of classical theories. A supersaturated solution is assumed to contain spherical nuclei of radius R and with ric particles, and the Gibbs free energy change on formation of these nuclei includes a term in the difference between the free energies of the solid and the liquid, Ap, and a term that represents 

X is a typical diffusion distance, is the self-diffusion coefficient, and puq is the density of the liquid. Expressions of this kind have a rather unpleasant look and require funny numerical coefficients with lots of ns. More seriously, they are problematic because their overall reliability is the product of the reliability factors of all the embedded assumptions and approximations, a product that is nearly zero at the third assumption with 0.5 probability of being realistic. Models can be improved, phenomenological equations can be elaborated upon, densities can be taken as variable instead of constant, but one never gets past the basic stumbling points of a model, which is in all likelihood inadequate for the description of nucleation of crystals of complex organic molecules, for which the crucial quantities R, X, and y are unknown or possibly even undefined. 

At the other extreme, the formulation of molecular level theories is difficult if not impossible due to the intrinsic complexity of the molecular shape and potential in organic compounds. Molecular simulation studies of solid-liquid transformations concern mainly theLennard-Jones fluid (the spherical horse ), a hypothetical system 

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SOLID-LIQUID EQUILIBRIUM AND NUCLEATION FROM THE MELT 339... 

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