Efficient electrochemomechanical energy conversion in nanochannels grafted with end-charged polyelectrolyte brushes at medium and high salt concentration†
We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.