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

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.

Blessing and Curse: How a Supercapacitor’s Large Capacitance Causes its Slow Charging

“…Still, comparing the fitted time constants τ 1 = 200 s and τ 2 = 9000 s to τ n = 2.9 × 10 2 s and τ ad = 4.8 × 10 2 s as stated in the main text, respectively, we see that our model predicts both timescales within approximately one order of magnitude. Even though we seem to predict τ 1 better than τ 2 , using a smaller diffusion constant D = 2 × 10 −10 m 2 s −1 , to account for slow diffusion in pores [31,39], leads to τ n = 2.3 × 10 3 s and τ ad = 3.6 × 10 3 s and predictions for τ 2 are better than for τ 1 .…”

“…The electrodes were immersed in a 1 M NaCl solution at room temperature, hence, κ −1 = 0.3 nm and bulk diffusivity D = 1.6 × 10 −9 m 2 s −1 . [We ignore that D is smaller in nanopores [31,39] and that different diffusivities may appear in Eqs. ( 4) and ( 5) [42].]…”

Coarse-Grained Modeling of Ion-Containing Polymers

“…Although united atom MD simulations cannot access the length and temporal scales of coarse-grained DPD simulations, they are still capable of modeling larger systems without compromising much of the detailed atomic-level information. Allahyarov et al − applied united-atom MD simulations to investigate the effects of the lengths of the backbone segment and side chain in different confinements on the hydrophilic cluster morphology and proton transport in Nafion-type ionomers. The authors modeled the variations of Nafion under low hydration levels in which the lengths of the backbone segments and side chains are up to 2- and 3-fold higher than in original Nafion, respectively .…”

“…The longer side chains facilitate the formation of larger clusters with higher sulfonate density, which to some extent improves proton transport . Another study investigated the morphological changes induced by a cylindrical pore confinement in Nafion-type ionomers. , They found that the pore diameter and sulfonate density play an important role in ionic cluster shape and transport properties. Specifically, a branched wire-like network was observed along with the pore axis in the larger pores, while sulfonate head groups tend to form smooth clusters in the center part of the pores as the pore diameter is decreased.…”

“…Additionally, ballistic ionic motion was observed in the narrow pores, seemingly due to the collective motion of the ions in such a limited space . Their simulation results indicate that the optimal conditions for enhanced ion transport are pores with medium length side chains under moderate hydration levels, for which the sulfonate ions have sufficient flexibility but do not reach the center of the pore, leading to a distribution of less structured water around both the ions …”