  We present coarse-grained simulation results for enhanced ion diffusion in a
charged nanopore grafted with ionomer sidechains. The pore surface is
hydrophobic and its diameter is varied from 2.0 nm to 3.7 nm. The sidechains
have from 2 to 16 monomers (united atom units) and contain sulfonate terminal
groups.
  Our simulation results indicate a strong dependence of the ion diffusion
along the pore axis on the pore parameters. In the case of short sidechains and
large pores the ions mostly occupy the pore wall area, where their distribution
is strongly disturbed by their host sulfonates. In the case of short sidechains
and narrow pores, the mobility of ions is strongly affected by the structuring
and polarization effects of the water molecules. In the case of long
sidechains, and when the sidechain sulfonates reach the pore center, a radial
charge separation occurs in the pore. Such charge separation suppresses the ion
diffusion along the pore axis.
  An enhanced ion diffusion was found in the pores grafted with medium-size
sidechains provided that the ions do not enter the central pore area, and the
water is less structured around the ions and sulfonates. In this case, the 3D
density of the ions has a hollow-cylinder type shape with a smooth and
uninterrupted surface. We found that the maximal ion diffusion has a linear
dependence on the number of sidechain monomers. It is suggested that the
maximal ion diffusion along the pore axis is attained if the effective length
of the sidechain extension into the pore center (measured as twice the gyration
radius of the sidechain with the Flory exponent 1/4) is about 1/3 of the pore
radius.
