Consistent Coarse-graining strategy for polymer solutions in the thermal crossover from good to theta solvent

We extend our previously developed coarse-graining strategy for linear polymers with a tunable num- ber n of effective atoms (blobs) per chain [G. D’Adamo et al., J. Chem. Phys. 137, 024901 (2012)] to polymer systems in thermal crossover between the good-solvent and the θ regimes. We consider the thermal crossover in the region in which tricritical effects can be neglected, i.e., not too close to the θ point, for a wide range of chain volume fractions = c/c* (c* is the overlap concentration), up to ≈ 30. Scaling crossover functions for global properties of the solution are obtained by Monte Carlo simulations of the Domb-Joyce model with suitably rescaled on-site repulsion. They provide the in- put data to develop a minimal coarse-grained model with four blobs per chain (tetramer model). As in the good-solvent case, the coarse-grained model potentials are derived at zero density, thus avoiding the inconsistencies related to the use of state-dependent potentials. We find that the coarse- grained model reproduces the properties of the underlying, full-monomer system up to some reduced density which increases when lowering the temperature towards the θ state. Close to the lower- temperature crossover boundary, the tetramer model is accurate at least up to ≃ 10, while near the good-solvent regime reasonably accurate results are obtained up to ≃ 2. The density region in which the coarse-grained model is predictive can be enlarged by developing coarse-grained models with more blobs per chain. We extend the strategy used in the good-solvent case to the crossover regime. This requires a proper treatment of the length rescalings as before, but also a proper temper- ature redefinition as the number of blobs is increased. The case n = 10 is investigated in detail. We obtain the potentials for such finer-grained model starting from the tetramer ones. Comparison with full-monomer results shows that the density region in which accurate predictions can be obtained is significantly wider than that corresponding to the tetramer case.