Specific Counterion Effects on the Swelling Behavior of Strong Polyelectrolyte Brushes

It is well known that specific types of counterions affect the hydration of polyelectrolytes both in the bulk and at interfaces, but the mechanisms of this effect have not yet been fully understood. In this work, we have designed a model system, consisting of imidazolium-based cationic polyelectrolyte brushes with controlled grafting densities, to systematically investigate how specific counterion properties affect well-established swelling mechanisms in brushes. With this approach, we show that two swelling mechanisms, namely, counterion influence on the ion osmotic pressure and counterion influence on brush-solvent nonelectrostatic interactions, are simultaneously at play. Here, we demonstrate that the former effect can be related to the polarizability of the counterions, while the latter effect can be correlated to the hydration enthalpy of the counterions. We further demonstrate that the interplay of these two mechanisms depends on the brush grafting density and ionic strength of the medium such that under certain conditions, one effect can dominate over the other. Specifically, at low ionic strength and low grafting density, swelling of the brush is significantly influenced by the polarizability of counterions, while at high grafting density and high ionic strength, the hydration enthalpy of ions is the dominating factor. Moreover, by employing a theoretical model, we rationalize the experimental findings and further quantify the contribution of specific counterion effects as a function of grafting density and ionic strength. We believe such an approach improves the general understanding of the influence of ions on the polyelectrolyte brush swelling and even beyond.