Many-body interactions and correlations in coarse-grained descriptions of polymer solutions - art. no. 021801

We calculate the two-, three-, four-, and five-body (state-independent) eff ective potentials between the centers of mass (c.m.'s) of self-avoiding wal k polymers by Monte Carlo simulations. For full overlap, these coarse-grain ed n-body interactions oscillate in sign as (-1)(n), and decrease in absolu te magnitude with increasing n. We find semiquantitative agreement with a s caling theory, and use this to discuss how the coarse-grained free energy c onverges when expanded to arbitrary order in the many-body potentials. We a lso derive effective density dependent two-body potentials that exactly rep roduce the pair-correlations between the c.m. of the self avoiding walk pol ymers. The density dependence of these pair potentials can be largely under stood from the effects of the density independent three-body potential. Tri plet correlations between the c.m. of the polymers are surprisingly well, b ut not exactly, described by our coarse-grained effective pair potential pi cture. In fact, we demonstrate that a pair potential cannot simultaneously reproduce the two- and three-body correlations in a system with many-body i nteractions. However, the deviations that do occur in our system are very s mall, and can be explained by the direct influence of three-body potentials .