Equilibrated polyethylene single-molecule crystals: Molecular-dynamics simulations and analytic model of the global minimum of the free-energy landscape

The crystalline state of a single polyethylene chain with N = 500 monomers is investigated by extensive MD simulations. The polymer is folded in a well defined lamella with ten stems of approximately equal length, arranged into a regular, hexagonal pattern. The study of the microscopic organization of the lamella, which is in an equilibrium condition, evidences that the two caps are rather flat, i.e. the loops connecting the stems are short. An analytic model of the global minimum of the free energy, based on the assumption that the entropic contribution is mainly due to the combinatorics of the stems and loops and neglecting any conformational contribution, is presented. It provides for the first time a quantitative explanation of the MD results on the equilibrium geometry of single-chain crystals.