A coarse-graining procedure for flexible polymer chains with bonded and nonbonded interactions

Starting from the united atom model, we construct a coarse-grained model for a flexible polymer chain, in which some successive $CH2$ atoms are combined into an effective segment. To connect the coarse-grained model with the atomistic model, we propose a scheme to obtain the effective potentials acting between bonded and nonbonded segments from atomistic molecular dynamics simulation for a single isolated chain. We assume that the total effective potential is a sum of potential components for independent coarse-grained variables. The effective bond potentials are determined by simply taking the logarithm of the corresponding distribution functions calculated from the atomistic simulations. On the other hand, to consider the characteristic entropy effects of the polymer chain system, the effective nonbonded potentials are evaluated using the canonical ensemble average for fixed distance between the segments. We confirmed that the coarse-grained model using these effective potentials can reproduce the radii of gyration and various distribution functions of the coarse-grained variables over a wide temperature range. We also confirmed that the effective potentials obtained for the isolated chain system are applicable to the melt system. A detailed analysis of the distribution functions showed that the effective bond length and the effective torsion angle correlate strongly with the effective bond angle. In order to improve the quality of our coarse-grained potentials, these correlations should be taken into account.