Polymer chain stiffness vs. excluded volume: A Monte Carlo study of the crossover towards the worm-like chain model

¹ Institut für Physik, Johannes Gutenberg Universität Mainz - Staudinger Weg 7, 55099 Mainz, Germany
² Theoretische Physik, Martin-Luther-Universität Halle Wittenberg - von Senckendorffplatz 1, 06120 Halle, Germany

^a hsu@uni-mainz.de

Received: 31 July 2010
Accepted: 30 September 2010

Abstract

When the local intrinsic stiffness of a polymer chain varies over a wide range, one can observe both a crossover from rigid-rod–like behavior to (almost) Gaussian random coils and a further crossover towards self-avoiding walks in good solvents. Using the pruned-enriched Rosenbluth method (PERM) to study self-avoiding walks of up to N_b=50000 steps and variable flexibility, the applicability of the Kratky-Porod model is tested. Evidence for non-exponential decay of the bond-orientational correlations ⟨cos θ(s)⟩ for large distances s along the chain contour is presented, irrespective of chain stiffness. For bottle-brush polymers on the other hand, where experimentally stiffness is varied via the length of side-chains, it is shown that these cylindrical brushes (with flexible backbones) are not described by the Kratky-Porod worm-like chain model, since their persistence length is (roughly) proportional to their cross-sectional radius, for all conditions of practical interest.