Phase Transitions of Single Semi-stiff Polymer Chains

TL;DR

This paper investigates the phase behavior of semi-stiff polymers using a new simulation algorithm, revealing complex transitions including coil-globule and freezing, with implications for understanding protein folding.

Contribution

It introduces an efficient algorithm (PERM) for simulating semi-stiff polymers and maps their detailed phase diagram, highlighting differences from mean field predictions.

Findings

Theta-temperature increases with chain stiffness.

Freezing transition occurs at higher temperatures for stiffer chains.

Direct freezing transition without globule formation for very stiff chains.

Abstract

We study numerically a lattice model of semiflexible homopolymers with nearest neighbor attraction and energetic preference for straight joints between bonded monomers. For this we use a new algorithm, the "Pruned-Enriched Rosenbluth Method" (PERM). It is very efficient both for relatively open configurations at high temperatures and for compact and frozen-in low-T states. This allows us to study in detail the phase diagram as a function of nn-attraction epsilon and stiffness x. It shows a theta-collapse line with a transition from open coils to molten compact globules (large epsilon) and a freezing transition toward a state with orientational global order (large stiffness x). Qualitatively this is similar to a recently studied mean field theory (Doniach et al. (1996), J. Chem. Phys. 105, 1601), but there are important differences. In contrast to the mean field theory, the theta-temperature increases with stiffness x. The freezing temperature increases even faster, and reaches the theta-line at a finite value of x. For even stiffer chains, the freezing transition takes place directly without the formation of an intermediate globule state. Although being in contrast with mean filed theory, the latter has been conjectured already by Doniach et al. on the basis of low statistics Monte Carlo simulations. Finally, we discuss the relevance of the present model as a very crude model for protein folding.