text: Nucleation is the formation and growth of a new phase with or without the presence of external surface. The presence of this surface results in heterogeneous nucleation whereas in its absence homogeneous nucleation occurs. Heterogeneous nucleation occurs in cases where there are pre-existing nuclei present, such as tiny dust particles suspended in a liquid or gas or reacting with a glass surface containing . For the process of Hoffman nucleation and its progression to Lauritzen–Hoffman growth theory, homogeneous nucleation is the main focus. Homogeneous nucleation occurs where no such contaminants are present and is less commonly seen. Homogeneous nucleation begins with small clusters of molecules forming from one phase to the next. As the clusters grow, they aggregate through the condensation of other molecules. The size continues to increase and ultimately form macroscopic droplets (or bubbles depending on the system).
  Nucleation is often described mathematically through the change in Gibbs free energy of n moles of vapor at vapor pressure P that condenses into a drop.  Also the nucleation barrier, in polymer crystallization, consists of both enthalpic and entropic components that must be over come. This barrier consists of selection processes taking place in different length and time scales which relates to the multiple regimes later on. This barrier is the free energy required to overcome in order to form nuclei. It is the formation of the nuclei from the bulk to a surface that is the interfacial free energy. The interfacial free energy is always a positive term and acts to destabilize the nucleus allowing the continuation of the growing polymer chain.  The nucleation continues as a favorable reaction.