The paper presents numerical results from extensive molecular-dynamics simulations of the crystallization process of a single polyethylene chain with N=500 monomers. The development of the ordered structure is seen to proceed along different routes involving either the global reorganization of the chain or, alternatively, well-separated connected nuclei. No dependence on the thermal history was observed at the late stages of the crystallization. The folding process involves several intermediate ordered metastable states, in strong analogy with the experiments, and ends up in a well-defined long-lived lamella with ten stems of approximately equal length, arranged into a regular, hexagonal pattern. This behavior may be seen as a microscopic manifestation of the Ostwald step rule. Both the metastable states and the long-lived one are evidenced as the local minima and the global one of the free-energy landscape, respectively. The study of the microscopic organization of the lamella evidenced that the two caps are rather flat, i.e., the loops connecting the stems are short. Interestingly, annealing the chain through the different metastable states leaves the average number of monomers per loop nearly unchanged. It is also seen that the chain ends, the so-called cilia, are localized on the surface of the lamella, in agreement with the experiments, and that structural fluctuations take place on the lamella surface, as noted by recent Monte Carlo simulations. The study of the melting process evidences that the degree of hysteresis is small.

Larini, L., & Leporini, D. (2005). A manifestation of the Ostwald step rule: Molecular-dynamics simulations and free-energy landscape of the primary nucleation and melting of single-molecule polyethylene in dilute solution. The Journal of Chemical Physics, 123(14).