Anomalous Shrinking–Swelling of Nanoconfined End-Charged Polyelectrolyte Brushes: Interplay of Confinement and Electrostatic Effects

In this article, we model the structure and configuration of the end-charged polyelectrolyte (PE) brushes grafted on the inner walls of a nanochannel. When the confinement effect is weak, that is, d0 < h/2 (d0 is the PE brush height without electrostatic effects and h is the nanochannel half-height), d < d0 (d is the brush height with the electrostatic effects), that is, the brushes shrink due to the electrostatic effects. Furthermore, for this case, an increase in salt concentration increases d. On the contrary, for the case in which the confinement effect is strong (i.e., d0 > h/2), d > d0 (i.e., the electrostatic effects swell the brushes), and an increase in salt concentration decreases the brush height. These findings reveal that the behavior of the end-charged brushes shows three unique differences when compared to that of the standard PE brushes with charges along their entire backbone. These differences are (a) the presence of a distinct role of the confinement in dictating how the electrostatic effects mediated by the electric double layer govern the height of end-charged brushes, (b) electrostatic-effect-driven shrinking of end-charged brushes for d0 < h/2 (for backbone-charged brushes, the electrostatic effects always swell the brushes), and (c) swelling of end-charged brushes with an increase in salt concentration for d0 < h/2 (backbone-charged brushes always shrink with an increase in salt concentration). Such unique effects of confinement and electrostatics on PE brushes have not been reported previously, and we anticipate that these findings will shed new light on the structure and properties of PE-brush-functionalized nanochannels with implications in applications such as fabrication of functionalized-nanochannel-based nanofluidic diodes, valves, biosensors, current rectifiers, and so forth.