Impact of Chain Ends on the Amorphous Phase Topology in Melt-Crystallized Polymers

The thermophysical properties of semicrystalline polymers are strongly dependent on the topology of the chain segments in the amorphous domains. Here, we investigate the main factors controlling the amorphous topology in lamellar, melt-crystallized polymer samples of finite molecular weight using a pseudoequilibrium approach, which maximizes the entropy of the chains in the kinetically selected lamellar stack morphology. We derive a self-consistent mean-field approximation for the distribution of amorphous chain segments under the constraints of uniform amorphous density, fixed number-average molecular weight, and crystallinity. In the grand-canonical ensemble, we find simple expressions for the chain entropy and probability distribution, extending the previous work. A few key results are summarized here. (1) The surface density of bridges between lamellae is given universally by (3pla)−1, where p is the packing length, for long chains and large interlamellar distance la. (2) Chain ends are preferentially segregated to the crystal–amorphous interphase to relieve the excess injected chains, consistent with recent experimental observations. However, a small fraction of long tails displaces loops and bridges from the core of the amorphous domains. This effect provides a mechanism of thermodynamic suppression of the population (and mean length) of intercrystalline stress transmitters (“tie molecules”) in polymers of finite molecular weight. (3) Chains in the semicrystalline structure are found to be slightly elongated perpendicular to the lamellae to maximize entropy, at odds with Fischer’s solidification model. Because of this, our approach predicts a higher fraction of chains forming bridges in comparison to the classic Huang–Brown model.