  We review a coarse-graining strategy (multiblob approach) for polymer
solutions in which groups of monomers are mapped onto a single atom (a blob)
and effective blob-blob interactions are obtained by requiring the
coarse-grained model to reproduce some coarse-grained features of the
zero-density isolated-chain structure. By tuning the level of coarse graining,
i.e. the number of monomers to be mapped onto a single blob, the model should
be adequate to explore the semidilute regime above the collapse transition,
since in this case the monomer density is very small if chains are long enough.
The implementation of these ideas has been previously based on a
transferability hypothesis, which was not completely tested against
full-monomer results (Pierleoni et al., J. Chem. Phys, 127, 171102 (2007)). We
study different models proposed in the past and we compare their predictions to
full-monomer results for the chain structure and the thermodynamics in the
range of polymer volume fractions \Phi between 0 and 8. We find that the
transferability assumption has a limited predictive power if a
thermodynamically consistent model is required. We introduce a new tetramer
model parametrized in such a way to reproduce not only zero-density
intramolecular and intermolecular two-body probabilities, but also some
intramolecular three-body and four-body distributions. We find that such a
model correctly predicts three-chain effects, the structure and the
thermodynamics up to \Phi ~ 2, a range considerably larger than that obtained
with previous simpler models using zero-density potentials. Our results show
the correctness of the ideas behind the multiblob approach but also that more
work is needed to understand how to develop models with more effective monomers
which would allow us to explore the semidilute regime at larger chain volume
fractions.
