Thermodynamics, electrostatics, and ionic current in nanochannels grafted with pH-responsive end-charged polyelectrolyte brushes

In this paper, we study the thermodynamics, electrostatics, and an external electric field driven ionic current in a pH-responsive, end-charged polyelectrolyte (PE) brush grafted nanochannel. By employing a mean field theory, we unravel a highly nonintuitive interplay of pH and electrolyte salt concentration in dictating the height of the end-charged PE brush. Larger pH or weak hydrogen ion concentration leads to maximum ionization of the charge-producing group-as a consequence, the resulting the electric double layer (EDL) energy get maximized causing a maximum deviation of the brush height from the value (d₀ ) of the uncharged brush. This deviation may result in enhancement or lowering of the brush height as compared to d₀ depending on whether the PE end locates lower or higher than h/2 (h is the nanochannel half height) and the salt concentration. Subsequently, we use this combined PE-brush-configuration-EDL-electrostatics framework to compute the ionic current in the nanochannel. We witness that the ionic current for smaller pH is much larger despite the corresponding magnitude of the EDL electrostatic potential being much smaller-this stems from the presence of a much larger concentration of H+ ions at small pH and the fact that H+ ions have very large mobilities. In fact, this ionic current shows a steep variation with pH that can be useful in exploring new designs for applications involving quantification and characterization of ionic current in PE-brush-grafted nanochannels.