  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.
