Phase Transitions of Single Semistiff Polymer Chains

Abstract

We study numerically a lattice model of semiflexible homopolymers with nearest neighbor (nn) attraction and energetic preference for straight joints between bonded monomers. For this we use a new Monte Carlo algorithm, the “prunedenriched 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 attractionε and stiffnessx. It shows aθ-collapse line with a transition from open coils (smallε) to molten compact globules (largeε) and a freezing transition toward a state with orientational global order (large stiffnessx). Qualitatively this is similar to a recently studied mean-field theory [S. Doniach, T. Garel, and H. Orland (1996),J. Chem. Phys. 105(4), 1601], but there are important differences in details. In contrast to the mean-field theory and to naive expectations, theθ-temperatureincreases with stiffnessx. The freezing temperature increases even faster, and reaches theθ-line at a finite value ofx. For even stiffer chains, the freezing transition takes place directly, without the formation of an intermediate globular state. Although being in conflict with mean-field theory, the latter had been conjectured already by Doniachet al. on the basis of heuristic arguments and of low-statistics Monte Carlo simulations. Finally, we discuss the relevance of the present model as a very crude model for protein folding.