Polymer collapse and crystallization in bond fluctuation models

Abstract

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 √ 10) it was recently shown by F. 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 the Rampf et al. 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 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.In spite of having been studied for several decades, the phase transitions of a single long polymer in a bad solvent are still a subject of active research with occasional big surprises. When temperature is lowered, most polymers undergo a Θ-collapse, which is typically a continuous (tri-critical) phase transition. At the transition point, repulsive entropic effects and attractive energetic forces would cancel exactly for an infinitely long chain. For finite chain length N theory [1, 2] predicts logarithmic corrections which are also seen in simulations [2][3][4] and in experiments [5], and which also affect the unmixing transition of long polymers [6]. Qualitatively, the Θ-transition resembles a gas-liquid transition, with the open coil resembling the gas and the dense globule being analogous to a liquid. At even worse solvent conditions, in many models (e.g. in off-lattice polymers with Lennard-Jones interactions between monomers [7]) there occurs a second 'liquid-solid' transition that is similar to crystallization. Since it is a discontinuous transition, its properties are usually not universal and are not described by perturbative renormalization group methods.But there are well known cases where this Θ-collapse is preempted by a discontinuous 'freezing' or crystallization transition. One example is semi-stiff polymers [8], another is provided by (off-lattice) monomers with hard core repulsion and attractive interactions which extend only very little beyond the core [9,10]. Still another is the cooperative one-step collapse of some proteins [11] A very surprising behavior which falls between these two possibilities -Θ-collapse with subsequent liquid-solid transition, and immediate gas-solid freezing -was observed by . In their model, the specific heats of finite chains show rounded peaks at distinct temperatures T crys (N ) < T Θ (N ), but as the chain length N diverges,Thus, while finite...

Phase transitions in a linear self-interacting polymer on FCC lattice using flat energy interacting growth walk algorithm

“…From the computed DoS of short ISAWs, by analysing the specific heat and zeros of the partition function, we observed separate freezing and coil-globule transitions. While freezing transition is observed in o-lattice models [25][26][27][28][29], and in bond fluctuation models of Rampf et al on a simple cubic lattice [30], it is conjectured to be absent in ISAW on SC and FCC lattices [31]. The question of freezing transition is controversial, since it is not clear if the indications attributed to freezing transition in the present work as well as in other works [17,18] is a real phase transition or due to surface rearrangements.…”

“…On the other hand Grassberger argued based on modified bond fluctuation model, that there is no such freezing transition. But it is a continuous cross over from disordered liquid to a densely packed configurations [31]. Thus whether the low temperature peak in specific heat of ISAW and inner locus in PFZ on a complex temperature plane indicates a first order freezing transition or a continuous cross over due to surface rearrangement is an interesting open problem and requires detailed investigation.…”