  Semiflexible macromolecules in dilute solution under very good solvent
conditions are modeled by self-avoiding walks on the simple cubic lattice
($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain
stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence
of excluded volume interactions, the persistence length $\ell_p$ of the
polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b=
\exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing,
and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the
pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$
are varied over a wide range $(0.005 \leq q_b \leq 1, \; N \leq 50000$), and
also a stretching force $f$ is applied to one chain end (fixing the other end
at the origin). In the absence of this force, in $d=2$ a single crossover from
rod-like behavior (for contour lengths less than $\ell_p$) to swollen coils
occurs, invalidating the Kratky-Porod model, while in $d=3$ a double crossover
occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and
then to coils that are swollen due to the excluded volume interaction. If the
stretching force is applied, excluded volume interactions matter for the force
versus extension relation irrespective of chain stiffness in $d=2$, while
theories based on the Kratky-Porod model are found to work in $d=3$ for stiff
chains in an intermediate regime of chain extensions. While for $q_b \ll 1$ in
this model a persistence length can be estimated from the initial decay of
bond-orientational correlations, it is argued that this is not possible for
more complex wormlike chains (e.g. bottle-brush polymers). Consequences for the
proper interpretation of experiments are briefly discussed.
