Determination of the Critical Size of Secondary Nuclei on the Lateral Growth Front of Lamellar Polymer Crystals

Nucleation is the rate-limiting first step of crystallization. The energy barrier related to form the critical nucleus predominantly affects the nucleation rate. Determination of the size of the critical nucleus is a key for understanding the mechanism of nucleation and allows testing theories. However, it has been a great challenge for both experimentalists and theorists to quantify this size. In this work, we propose a method for computing the size of critical secondary nuclei formed on the lateral growth front of lamellar crystals of folded polymer chains. For secondary nucleation of random copolymers, the exponent in a power-law relation between the spherulitic radial growth rate and the content of crystallizable units is related to the number of repeating units within the critical secondary nuclei. For miscible blends of crystallizable and amorphous polymers, the spherulitic radial growth rate as a function of the volume fraction crystallizable polymer chains also follows a power-law relation with the exponent related to the number of polymer chains in each critical secondary nucleus. Based essentially on the stochastic nature of the nucleation process of random copolymers and polymer blends during crystallization, this approach does not require the prior knowledge on the detailed nucleation pathway and folding conformation. Presenting results for poly(butylene succinate), its random copolymers and blends, we show that a critical secondary nucleus consists of 15-27 butylene succinate units, corresponding to five to eight stems when the polymers were isothermally crystallized from a quiescent melt at temperatures ranging from 70 to 95 degrees C. These stems in a critical secondary nucleus are derived from one or two polymer chains. Our results contest the classical Lauritzen-Hoffman theory, which expects that the critical secondary nucleus is formed by a single stem. The approach presented here can be generally applied to the lamellar crystals of other crystallizable flexible polymers. In addition, our approach is not limited to secondary nucleation and can be adopted for primary nucleation as well.