Polymer collapse and crystallization in bond fluctuation models

While the Θ-collapse of single long polymers in bad solvents is usually a continuous (tri-critical) phase transition, there are exceptions where it is preempted by a discontinuous crystallization (liquid solid) transition. For a version of the bond fluctuation model (a model where monomers are represented as 2 × 2 × 2 cubes, and bonds can have lengths between 2 and SQRT 10) it was recently shown by Rampf et al. that there exist distinct collapse and crystallization transitions for long but finite chains. But as the chain length goes to infinity, both transition temperatures converge to the same T*, i.e. infinitely long polymers collapse immediately into a solid state. We explain this by the observation that polymers crystallize in Rampf et al.'s model into a non-trivial cubic crystal structure (the "A15" or "Cr3Si" Frank-Kasper structure) which has many degenerate ground states and, as a consequence, Bloch walls. If one controls the polymer growth such that only one ground state is populated and Bloch walls are completely avoided, the liquid-solid transition is a smooth cross-over without any sharp transition at all