Stability and growth of nuclei during the crystallization of polymers

During the crystallization of linear flexible chain molecules a boundary phase necessarily develops which has a volume of its own. The boundary phase, however, is not autonomous so that Gibbs' phase rule loses its validity. The 2-phase system {crystal; boundary phase} is bivariant, the 3-phase system {crystal, boundary phase; melt} is monovariant. At quasistatic cooling the ability of the crystal nuclei to grow demands the formation of loose loops or tie-molecules. This leads to the final state of the crystallization to be an arrested equilibrium state. The internal equilibrium state cannot be reached under normal circumstances.Dedicated to H.-G. Kilian on the occasion of his 60th birthday.