The Role of Counterion Size in Defining Star-Shaped Polyelectrolytes Thermodynamics, Conformations, and Ion Dynamics

In this work, we systematically investigate the impact of counterion size on the behavior of star-shaped strong polyelectrolytes in dilute aqueous solutions using Langevin simulations and a primitive model of electrolytes. Varying both the counterion diameter and the number of arms of the polyelectrolyte, we demonstrated that both characteristics significantly impact polyelectrolyte conformations and counterions absorption. Counterions dynamics is also affected, the most interesting aspect being the presence of a fraction of mobile ions slowly diffusing, compared to the average behavior, which increases with polyelectrolyte branching and their size. Informed by the results on systems with single-size counterions, we also investigate possible changes in behavior of these polyelectrolytes when neutralized by a binary mixture of bulky and small counterions at different relative concentration. Our results show that small counterions demonstrate a greater tendency for remaining located within the inner regions of the polyelectrolyte, particularly when their molar fraction is low and the polyelectrolyte is highly branched. This results in the spatial separation of the two species into core-shell-like structures, which dramatically decreases the diffusivity of the smaller counterions. By investigating the partitioning of counterions between the solution and the regions internal to the polyelectrolytes, it is shown that the selectivity toward the smaller species can be significantly enhanced by increasing the number of arms and operating under conditions of counterion scarcity.