Counter-ion distribution around flexible polyelectrolytes having different molecular architecture.

We explore the monovalent counter-ion distribution around flexible highly-charged polyelectrolytes with different molecular architectures (linear chains, stars, and unknotted and trefoil rings) using molecular dynamics simulations that include an explicit solvent that interacts with the polyelectrolyte. In particular, we find that the molecular topology influences the fraction of counter-ions transiently associating with the polyelectrolyte on a scale of the order of the chain segments, forming a "condensed" counter-ion interfacial layer. As with the hydrogen bonding of water to proteins and other polymers, the persistence time of these interfacial "bound" counter-ions is relatively short, O(1 ps), and we characterize the fluctuations in the number of the counter-ions populating the interfacial layer. We also find that the counter-ions are distributed in a non-uniform fashion on the polyelectrolyte backbone, forming dynamical clusters whose form and average size is sensitive to molecular architecture. In addition, we find that the residual bound counter-ions, not located in either the interfacial layer or the bulk solution, form a diffuse ionic cloud around the polyelectrolyte due to the uncompensated polyelectrolyte charge along the backbone. Generally charge valence strongly influences the extent of the diffuse counter-ion cloud, but in the case of monovalent counter-ions, we find that the size of the diffuse counter-ion cloud nearly coincides with the polyelectrolyte radius of gyration, independent of molecular topology.