Understanding the roles of molecular topology and entanglement in polymer crystallization using ring polymers

We investigate the effects of entanglement and molecular topologies on polymer crystallization using atomistic molecular dynamics (MD) simulations of cyclic and linear polyethylene (PE). For unlinked ring polymers, the non-concatenation and non-knotting constraints induce more collapsed conformations and higher melt free energy than their linear counterparts. Using a scaling theory, we predict the enhanced melt free energy can lead to a weak melting temperature enhancement ΔT_m for rings of moderate sizes. The predicted melting temperatures for ring PE agree with our atomistic MD simulation results. However, we expect ΔT_m to decrease with increasing molecular weight and become negligible when the chains are much longer than the entanglement strand. Despite the similar melting temperatures, we show that the isothermal crystal nucleation of rings is much faster than that of linear PE. The lack of conventional molecular entanglements in unlinked molten rings promotes nucleation kinetics. To further demonstrate the effect of molecular entanglement on crystal nucleation, we vary the entanglement density in molten linear PE by collapsing the radii of gyration using external potentials. Although the melting temperatures of the collapsed linear chains remain the same, distinct nucleation kinetics are observed. By analyzing the entanglement topologies using the primitive path analysis (PPA), we quantify the effects of entanglement density on polymer crystal nucleation rates.