# Simulation Study of Ion Diffusion in Charged Nanopores with Anchored Terminal Groups

## TL;DR

This study uses coarse-grained simulations to explore how ion diffusion in charged nanopores depends on pore size, sidechain length, and water structuring, revealing conditions for enhanced ion mobility.

## Contribution

It demonstrates that ion diffusion is maximized with medium-length sidechains and specific pore parameters, providing new insights into nanopore design for improved ion transport.

## Key findings

- Ion diffusion depends strongly on pore size and sidechain length.
- Maximum ion diffusion occurs with medium-sized sidechains and specific pore geometries.
- Radial charge separation suppresses ion diffusion in certain configurations.

## Abstract

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.