Resolving Paradoxes of Classical Nucleation Theory

We present a new model of homogeneous aggregation that contains the essential physical ideas of the classical predecessors, the Becker-Doring and Lifshitz-Slyovoz models. These classical models, which give different predictions, are asymptotic limits of the new model at small (BD) and large (LS) cluster sizes. Since the new theory is valid for large and small clusters, it allows for a complete description of the nucleation process; one that can predict the creation of super-critical clusters at the Zeldovich nucleation rate, and the diffusion limited growth of large clusters during coarsening. By retaining the physically valid ingredients from both models, we explain the seeming incompatibilities and arbitrary choices of the classical models.