Ion size effect on electrostatic and electroosmotic properties in soft nanochannels with pH-dependent charge density

We report a theoretical study of the ion size effect on various properties in a soft nanochannel with pH-dependent charge density. We develop a free energy based mean-field theory taking into account the ion size as well as pH-dependence of a charged polyelectrolyte layer grafted on a rigid surface in an electrolyte. The influence of the ion size on properties in a soft nanochannel is evaluated by numerically calculating ion number densities and the electrostatic potential. We demonstrate that unlike in point-like ions, for finite sizes of ions, a uniform distribution of chargeable sites within the polyelectrolyte layer causes unphysical discontinuities in ion number densities not only for the hydrogen ion but also for other kinds of ions. It is shown that the same cubic spatial distribution of chargeable sites as for point-like ions is necessary to ensure continuity of the ion number density and zero ion transport at the polyelectrolyte layer-rigid solid interface. We find that considering finite ion size causes an increase in the electrostatic potential and electroosmotic velocity and a decrease in ion number densities. More importantly, we demonstrate that in the polyelectrolyte layer, the pH-dependence of the polyelectrolyte charge density makes accumulation of hydrogen ions stronger than for the other positive ion species in the electrolyte and such a tendency is further enhanced by considering finite ion size. In addition, we discuss how consideration of finite ion size affects the role of various parameters in electrostatic and electroosmotic properties.