We numerically evaluate diffusion constants for various polymers with nontrivial topology in solution through Kirkwood's approximation, by generating random configurations through a new method which makes use of the Hopf map of quaternions. Here, the method was recently introduced in the paper: J. Cantarella, T. Deguchi, and C. Shonkwiler, Probability Theory of Random Polygons from the Quaternionic Viewpoint, to appear in Communications on Pure and Applied Mathematics (arXiv:1206.3161). We consider topological polymers such as ring polymers, multiple-ring polymers, and those forming a theta curve or a multiple-theta curve. We assume that the polymers are in solution at the theta temperature of corresponding linear polymers. We then evaluate the mean square radius of gyration for the topological polymers. We also review the diffusion constants of ring polymers with a fixed knot type. We expect that the diffusion constants of topological polymers should be measured in experiments of synthetic polymers.

Hydrodynamic properties of topological polymers through the quaternionic algorithm

245th National Meeting (2013)

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.