Structure and stability of helices in square-well homopolymers

Recently, it has been demonstrated [Magee, Phys. Rev. Lett. 96, 207802 (2006)] that isolated square-well homopolymers can spontaneously break chiral symmetry and "freeze" into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics combined with an optimized parallel tempering scheme to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to lambda) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a "window" of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature; however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.