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

In this paper, we provide a theory to quantify the ionic current (iion) in nanochannels grafted with pH-responsive polyelectrolyte (PE) brushes. We consider the PE brushes to be modeled 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 iion in PE brush-grafted nanochannels accounting for the appropriate coupled configuration-electrostatic description of the PE brushes. iion is obtained as functions of PE brush grafting density, medium pH and salt concentration (c infinity), and the density of polyelectrolyte chargeable sites (PECS). For large c infinity, iion increases linearly with c infinity (as for such c infinity, iion becomes independent of the PE charge and is dominated by the bulk mobility and number density of the electrolyte ions), whereas iion is independent of c infinity at small c infinity (where the electric double layer electrostatics and the total number of ions in the system is dominated by the hydrogen ions). We further witness an enhancement of iion for smaller pH and larger grafting density at low and moderate c infinity, while there is little to no effect of the PECS density on the ionic current except for weakly grafted brushes at low c infinity. We anticipate 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.