  Recently, it has been demonstrated [Magee et al., 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.
