  We report a theoretical study of 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 ion size as well as pH-dependence
of charged polyelectrolyte layer grafted on a rigid surface in an electrolyte.
The influence of ion size on properties in a soft nanochannel is evaluated by
numerically calculating ion number densities and 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 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 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 electrostatic potential and electroosmotic velocity and a
decrease in ion number densities. More importantly, we demonstrate that in
polyelectrolyte layer, pH-dependence of 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 on electrostatic and electroosmotic
properties.
