Local ion environment in polyamide membranes revealed by molecular dynamics

TL;DR

This work builds a molecular dynamics model of a polyamide RO membrane and interrogates the local ion environment of inserted cations. By analyzing radial distribution functions, coordination-number distributions, and nearest-neighbor patterns, the study shows that ion-oxygen coordination distances in the membrane are largely similar to those in solution, but the polymer reduces the coordination number by reallocating density to polymer groups and solvent shells. Ions remain mostly hydrated in the membrane, with polymer oxygens (carboxylate and amide) providing partial coordination that hinders mobility, especially for amide oxygens in monovalent ions. The results highlight the limitations of traditional solvation metrics and emphasize the role of polymer-ion interactions and fixed charges in shaping ion transport, with implications for designing next-generation RO membranes.

Abstract

In reverse osmosis (RO) and nanofiltration (NF) membranes, the polymer structure and interactions with solvent and solutes dictate the permeability and selectivity. However, these interactions have not been fully characterized within hydrated polymer membranes. In this study, we elucidate the local atomic neighborhood around ions within a RO membrane using molecular dynamics (MD). We built a MD model of a RO membrane closely following experimental synthesis and performed long time scale simulations of ions moving within the polymer. We find that the ion-oxygen nearest neighbor distance within the membrane is essentially the same as in solution, indicating that ions coordinate similarly in the confined membrane as in water. However, we do find that the average coordination number decreases in the polymer, which we attribute primarily to shifting the outer portion of the solvation shell beyond the cutoff, rather than being entirely stripped away. We find that cations bind tightly to both the carboxylate and amide oxygen atoms within the membrane. Even in ionized membranes, binding to amide oxygen atoms appears to play a substantial role in hindering ion mobility. Finally, we find that commonly used measures of ionic solvation structure such as coordination numbers do not fully capture the solvation structure, and we explore other measures such as the chemical composition of the nearest neighbors and the radial distribution function.

Figures (32)

• Figure 1: Visualization of the membrane monomers and fully equilibrated membrane after polymerization. The interface (initially created by the harmonic walls, but which remains after polymerization) is clearly shown. The atom colors are as follows: carbon is gray, hydrogen is white, nitrogen is blue, oxygen is red, and chlorine is green.
• Figure 2: Fully hydrated membrane model. (A) Visualization of the membrane after hydration. The water molecules have been replaced by a light blue surface mesh. The wt% water is 23%, and the density of the inner 50% of the membrane is 1.34 g/cm$^3$. (B) A 2D representation of the membrane with the water density distribution plotted in the marginal axis. The membrane polymer density is plotted as a kernel density estimate (KDE) in the x-z plane in greyscale. The KDE is weighted by the polymer mass, such that the darker regions are the densest parts of the membrane. The water is plotted as contour lines from a KDE on top of the polymer, with darker contour lines representing greater water density. The water mass density profile is shown in the marginal axis. Each bin has a z-width of 2 Å.
• Figure 3: Ion-oxygen distances demonstrate how cations bind with different oxygen species in solution and in membrane. We extracted ion-oxygen distances from the radial distribution functions with bin width 0.01 Å. We include first peak location (A), first peak width (B), first minimum location (C), and average distance up to the first minimum (D). The hashed bars are for these ions in solution, and thus are always for ion-water oxygen. The gray "All" bar corresponds to all oxygen atoms in the system regardless of species or functional group. Peaks must be separated by at least 0.05 Å and must be at least 0.1 Å in width. The first peak width is the width at half max. The average to cutoff is calculated with all ion-oxygen distances less than the first minimum in the RDF.
• Figure 4: The tightly bound nearest neighbors are distributed across water, amide, and carboxylate oxygens, but more distant neighbors can include other polymer groups. We present distributions of the average number of nearest neighbors for Na$^+$, Rb$^+$, and Sr$^{2+}$. The color indicates the distribution up to the $n$th nearest neighbor, such that the sum across one color will yield $n$. For example, on average for the two nearest neighbors of Na$^+$, there is one water molecule and a 50:50 split of either an amide oxygen or a carboxylate oxygen. For all ions, the first four neighbors are all oxygen atoms, but they are distributed differently among water molecules, amide oxygens, and carboxylate oxygens.
• Figure 5: Ions bind tightly to carboxylate groups and amide oxygens in the membrane, and they maintain partial hydration shells. We show representative snapshots of Na$^+$ (A), Rb$^+$ (B) and Sr$^{2+}$ (C) in the 50% ionized membrane and distributions of the average coordination shells (D) and the 8 nearest neighbors (E) in the membrane for all ions. Coloring in the visualization follows Figure \ref{['fig:membrane3D_equilibration']}. We include the carboxylic acid group, other cations, anions, and the amine group to emphasize that we see little to no interactions between these species and the cations. The total coordination number for each ion is given in the legend of (D). These total coordination numbers are distributed according to the plot.