Semicrystalline polyethylene as a network in the gelation regime

We propose an equivalence between the mass average tie molecule probability in semicrystalline polymers and the gel fraction from the theory of networks in the gelation regime. Not only does this equivalence provide a formal framework for analysis of semicrystalline polymer structure (e.g., chain and network topology) and properties (e.g., deformation resistance)—and thus set the foundation for a quantitative structure-performance relationship for semicrystalline polyethylene—but also it establishes how to calculate tie molecule probabilities for semicrystalline polymer systems with molar mass dispersity. We use the framework to predict that a polyethylene blend consisting of specific low molar mass and high molar mass components will exhibit deformation response equivalent to a neat polymer with an intermediate molar mass, and we measure stress strain response over a range of temperatures to confirm our prediction.