A Strongly Coarse-Grained, Charge-Fluctuating Model for Polyelectrolytes

Coarse-graining techniques are a powerful approach for the modeling of uncharged polymeric materials over many length scales. However, for charged polymers (polyelectrolytes), the ability to coarse-grain over large length scales has been limited by the ability of the coarse-grained model to faithfully describe the underlying charge distribution and fluctuations of the fine-grained model. Here, we develop a theoretical and computational formalism for coarse-graining polyelectrolytes over non-trivial length scales. Our method begins on a discretized grid to properly account for the vital entropic contributions associated with a polyelectrolyte's counterions, and uses carefully chosen approximations to develop an off-lattice version. Effective particle interactions and charge fluctuations in our model are parameterized by simulations of the underlying fine-grained model. We demonstrate the successes and failures of our approach and outline important strategies going forward in refining such a model, as well as potential applications in polyelectrolyte rheology.