Many-body interactions and correlations in coarse-grained descriptions of polymer solutions
Abstract
We calculate the two-, three-, four-, and five-body (state-independent) effective potentials between the centers of mass (c.m.'s) 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 semiquantitative 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 density dependent two-body potentials that exactly reproduce the pair-correlations between the c.m. of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the density independent three-body potential. Triplet correlations between the c.m. 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 three-body potentials.
- Publication:
-
Physical Review E
- Pub Date:
- August 2001
- DOI:
- 10.1103/PhysRevE.64.021801
- arXiv:
- arXiv:cond-mat/0103206
- Bibcode:
- 2001PhRvE..64b1801B
- Keywords:
-
- 61.25.Hq;
- 61.20.Gy;
- Macromolecular and polymer solutions;
- polymer melts;
- swelling;
- Theory and models of liquid structure;
- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 11 pages, 1 table, 9 figures, RevTeX (revtex.cls)