Impact of chain ends on the amorphous chain topology in semi-crystalline polymers

The thermomechanical properties of semicrystalline polymers are strongly dependent on the topological features of the chain segments found in the amorphous domains. In this contribution, we aim to clarify the main factors controlling the amorphous chain topology in lamellar, melt-crystallized polymers of finite molecular weight. We derive a self-consistent mean-field model for the statistical distribution of amorphous chains under the constraints of uniform amorphous density, number of chain ends and crystallinity. We find that chain ends are preferentially segregated at the crystal-amorphous interphase to relieve the excess of injected chains, in line with recent experimental observations. We also show that long tails -- when present -- displace loops and bridges from the core of the amorphous domains. This effect provides a mechanism of entropic suppression of the population (and mean length) of inter-crystalline stress transmitters (“tie molecules") in finite molecular weight polymers. While in the current work the number fraction of tie-molecules is uniquely determined to maximize conformational entropy, we discuss how our approach can be modified by using ideas borrowed from the Huang-Brown model. We thus demonstrate how disparate approaches to modelling amorphous chain topology can coexist in the same theoretical framework. Finally, we discuss how our model can be extended to include trapped entanglements and mass transport between crystalline and amorphous domains (i.e., the alpha relaxation).