Abstract

We employ computer simulations and integral equation theory techniques to perform coarse-graining of self-avoiding ring polymers with different knotedness and to derive effective interaction potentials [1] between the centers of mass (CM) of these macromolecular entities. Different microscopic models for the monomer-monomer interactions and bonding are employed, bringing about an insensitivity of the effective interactions on the microscopic details and a convergence to a universal form for sufficiently long molecules. The pair effective interactions are shown to be accurate up to within the semidilute regime with additional, many-body forces becoming increasingly important as the polymer concentration grows. The dramatic effects of topological constraints in the form of interaction potentials (see figure) are going to be brought forward and critically discussed [2].

We will also show the big impact of topology on the size scaling of a polymer chain in good/poor solvent conditions. This is accomplished calculating the theta temperature for specific topologies and sizes, of a single chain with two complementary methods: scaling law for radius of gyration [3,4] and second virial coefficient calculation [5]. In addition, we investigate the dependence of shape parameters with topology in good/poor solvent conditions.

[1] C. N. Likos, Physics Reports 348(4-5): 267 (2001)

[2] A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter 9(11):2435 (2010)

[3] M. O. Steinhauser, J. Chem. Phys. 122:094901 (2005)

[3] S. S. Jang, Tahir agin and W. A. Goddard, J. Chem. Phys. 119:1843 (2005)

[5] V. Krakoviak, J. P. Hansen and A. A. Louis, Phys. Rev. E 67 :041801 (2003)