Polymer chain stiffness versus excluded volume: A Monte Carlo study of the crossover towards the wormlike chain model

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 $<\cos \theta (s) >$ 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 wormlike chain model, since their persistence length is (roughly) proportional to their cross-sectional radius, for all conditions of practical interest.