Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density

Nanochannels, functionalized by grafting with a layer of charged polyelectrolyte (PE), have been employed for a large number of applications such as flow control, ion sensing, ion manipulation, current rectification and nanoionic diode fabrication. Recently, we established that such PE-grafted nanochannels, often denoted as "soft" nanochannels, can be employed for highly efficient, streaming-current-induced electrochemomechanical energy conversion in the presence of a background pressure-driven transport. In this paper, we extend our calculation for the practically realizable situation when the PE layer demonstrates a pH-dependent charge density. Consideration of such pH dependence necessitates consideration of hydrogen and hydroxyl ions in the electric double layer charge distribution, cubic distribution of the monomer profile, and a PE layer-induced drag force that accounts for this given distribution of the monomer profile. Our results express a hitherto unknown dependence of the streaming electric field (or the streaming potential) and the efficiency of the resultant energy conversion on parameters such as the pH of the surrounding electrolyte and the pK(a) of the ionizable group that ionizes to produce the PE charge-we demonstrate that increase in the pH and the PE layer thickness and decrease in the pKa and the ion concentration substantially enhance the energy conversion efficiency.