“Smart” polyelectrolyte-grafted or “soft” nanochannels with pH-responsiveness have shown great promise for applications like manipulation of ion transport, ion sensing and selection, current rectification, and many more. In this paper, we develop a theory to study the electroosmotic transport in a polyelectrolyte-grafted (or soft) nanochannel with pH-dependent charge density. In one of our recent studies, we have identified that explicit consideration of hydrogen ion concentration is mandatory for appropriately describing the electrostatics of such systems and the resulting monomer concentration must obey a non-unique, cubic distribution. Here, we use this electrostatic calculation to study the corresponding electroosmotic transport. We establish that the effect of pH in the electroosmotic transport in polyelectrolyte-grafted nanochannels introduces two separate issues: first is the consideration of the hydrogen and hydroxyl ion concentrations in describing the electroosmotic body force, and second is the consideration of the appropriate drag force that bears the signature of this cubic monomeric distribution. Our results indicate that the strength of the electroosmotic velocity for the pH-dependent case is always smaller than that for the pH-independent case, with the extent of this difference being a function of the system parameters. Such nature of the electroosmotic transport will be extremely significant in suppressing the electroosmotic flow strength with implications in large number applications such as capillary electrophoresis induced separation, electric field mediated DNA elongation, electrophoretic DNA nanopore sequencing, and many more.
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