Polymer collapse and crystallization in bond fluctuation models

TL;DR

This paper investigates the phase transitions of polymers in a bond fluctuation model, revealing how crystallization and collapse behaviors depend on chain length and ground state degeneracy, with implications for controlling transition nature.

Contribution

It explains the convergence of collapse and crystallization temperatures in long polymers and proposes a method to achieve smooth transitions by controlling ground state populations.

Findings

Long polymers show distinct collapse and crystallization transitions at finite length.

As chain length increases, both transition temperatures converge to a single point.

Controlling ground state populations can eliminate sharp phase transitions.

Abstract

While the $\Theta$-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 $\leftrightarrow$ solid) transition. For a version of the bond-fluctuation model (a model where monomers are represented as $2\times 2\times 2$ cubes, and bonds can have lengths between 2 and $\sqrt{10}$) it was recently shown by F. Rampf {\it et al.} that there exist distinct collapse and crystallization transitions for long but {\it 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 the Rampf {\it et al.} model into a non-trivial cubic crystal structure (the `A15' or `Cr$_3$Si' Frank-Kasper structure) which has many degenerate ground states and, as a consequence, Bloch walls. If one controlls 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.