Linear molecular weight dependence of lamellar aspect ratio in polyethylene

Krishnaswamy proposed that the lamellar growth rate of polyethylene was associated with the molecular weight due to chain entanglements. [1] In the Krishnaswamy model the chain diffusion rate to the growing crystal might be proportional to the number of chain entanglements which in turn is proportional to the molecular weight. This kinetic effect should lead to variability in the asymmetry of lamellar crystals in melt crystallized polymers, which could impact the hierarchical growth of fibers and superstructures. However, there is no method to verify this predicted dependence of the aspect ratio for melt crystallized polymers so the proposition has remained conjecture. In this talk, a new hierarchical scattering function, the Unified Born-Green model (UBG), is presented that can quantify the lamellar aspect ratio allowing experimental verification of the Krishnaswamy model. [2] This model also quantifies the local degree of crystallinity within a lamellar stack and two types of disorder in addition to the lamellar thickness. The local degree of crystallinity, when compared to the bulk crystallinity allows for a quantification of lamellar stack clustering. The UBG function can also describe higher order structures such as fibers and mesoscopic crystalline domains for block copolymers.