Crystal nucleation is an activated process. In a supersaturated solution, small crystallites may dissolve again. Crystals can only be formed when a (rare) fluctuation leads to the formation of a crystallite with a size that exceeds a threshold. The probability to form such a "critical" crystal nucleus is determined by its excess free energy. For a simple molecular crystal, 1 the free energy change for forming a small crystallite from the liquid is approximately given by where n is the number of particles in the nucleus and ∆µ is the difference between the chemical potentials of the particles in the (metastable) liquid phase and in the (stable) crystal phase. The surface area of the crystallite is denoted by A, and the solid-liquid interfacial free energy is denoted by γ. The free energy of a crystal nucleus contains two competing contributions: a (negative) bulk term favoring the formation of crystallites is counteracted by a (positive) surface term. For small crystallites, the surface term dominates, but for larger crystallites the bulk term becomes more important.In the nucleation of chainlike polymers, we must consider the anisotropy introduced by the shape of the molecules. Assuming that a bundle of chain stems form a cylindrical polymer crystallite with a radius r and a thickness l, the free energy change for forming such a crystallite becomes where n ) πr 2 l is the total number of units in the crystallite; γ e and γ l are the surface free energies corresponding to the stem ends and the lateral surface, respectively. The most favorable size of critical nucleus can be calculated from ∂∆F(n)/∂r ) ∂∆F(n)/∂l ) 0 as l crit ) 4γ e /|∆µ| and r crit ) 2γ l /|∆µ|. Note that as the lateral surface free energy can be smaller by 1 order of magnitude than that of the stem-end surface of polymer crystallites, the critical thickness should be larger by 1 order of magnitude than the critical radius of nucleus. In other words, the most favorable shape of critical nuclei will be fiberlike. 2 This shape requires a large degree of chain alignment, which is a very rare event in thermal fluctuations for an isotropic liquid, especially at high temperatures. As the supercooling is increased, the critical nucleus becomes smaller and less elongated. Therefore, polymer nucleation usually occurs via chain folding and requires a much higher degree of supercooling than is needed to induce crystallization of simple molecular crystals.There are several methods to increase the rate of polymer nucleation. All methods rely in one way or another on reducing the free energy barrier of crystal formation. The simplest method would be to decrease the temperature T and thereby increase the thermodynamic driving force for crystallization. However, from a practical point of view this is often not a viable optionsfor instance, the polymer liquid may vitrify on cooling and results in poor crystallinity. A more practical method is to facilitate the incorporation of polymer chains in a crystallite by prealigning and stretching them in a flow field (ext...