  Single linear polymer chains in dilute solutions under good solvent
conditions are studied by Monte Carlo simulations with the pruned-enriched
Rosenbluth method up to the chain length $N \sim {\cal O}(10^4)$. Based on the
standard simple cubic lattice model (SCLM) with fixed bond length and the bond
fluctuation model (BFM) with bond lengths in a range between $2$ and
$\sqrt{10}$, we investigate the conformations of polymer chains described by
self-avoiding walks (SAWs) on the simple cubic lattice, and by random walks
(RWs) and non-reversible random walks (NRRWs) in the absence of excluded volume
(EV) interactions. In addition to flexible chains, we also extend our study to
semiflexible chains for different stiffness controlled by a bending potential.
The persistence lengths of chains extracted from the orientational correlations
are estimated for all cases. We show that chains based on the BFM are more
flexible than those based on the SCLM for a fixed bending energy. The
microscopic differences between these two lattice models are discussed and the
theoretical predictions of scaling laws given in the literature are checked and
verified. Our simulations clarify that a different mapping ratio between the
coarse-grained models and the atomistically realistic description of polymers
is required in a coarse-graining approach due to the different crossovers to
the asymptotic behavior.
