Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

Details Many-body interactions and correlations in coarse-grained descriptions of polymer solutions Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

2001-03-09

arxiv.org/abs/cond-mat/0103206v1

Phys. Rev. E. 64, 021801 (2001)

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 1 table, 9 figures, RevTeX (revtex.cls)

Scientific paper

10.1103/PhysRevE.64.021801

We calculate the two, three, four, and five-body (state independent) effective potentials between the centers of mass (CM) of self avoiding walk polymers by Monte-Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (-1)^n, and decrease in absolute magnitude with increasing n. We find semi-quantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective {\em density dependent} 2-body potentials which exactly reproduce the pair-correlations between the CM of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the {\em density independent} 3-body potential. Triplet correlations between the CM of the polymers are surprisingly well, but not exactly, described by our coarse-grained effective pair potential picture. In fact, we demonstrate that a pair-potential cannot simultaneously reproduce the two and three body correlations in a system with many-body interactions. However, the deviations that do occur in our system are very small, and can be explained by the direct influence of 3-body potentials.

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