Ionic current in nanochannels grafted with pH-responsive polyelectrolyte brushes modeled using augmented strong stretching theory

Abstract

Here, we provide a theory to quantify the ionic current (i ion ) in nanochannels grafted with pH-responsive polyelectrolyte (PE) brushes. We consider the PE brushes to be modelled by our recently proposed augmented strong stretching theory (SST) model that improves the existing SST models by incorporating the effects of excluded volume interactions and an extended mass action law. Use of such augmented SST for this problem implies that this is the first study on computing i ion in PE-brush-grafted nanochannels accounting for the appropriate coupled con guration-electrostatic description of the PE brushes. i ion is obtained as functions of PE brush grafting density, medium pH and salt concentration (c ∞ ), and the density of polyelectrolyte chargeable sites (PECS). For large c ∞ , i ion increases linearly with c ∞ (as for such c ∞ , i ion becomes independent of the PE charge and is dominated by the bulk mobility and number density of the electrolyte ions), while iion is independent of c ∞ at small c ∞ (where the EDL electrostatics and the total number of ions in the system is dominated by the hydrogen ions). We further witness an enhancement of i ion for smaller pH and larger grafting density at low and moderate c ∞ , while there is little to no effect of the PECS density on the ionic current except for weakly grafted brushes at low c ∞ . We believe that this study will serve as a theoretical foundation for a large number of applications that are based on the brush-induced modification of the ionic current in a nanochannel.