Simulation study of sulfonate cluster swelling in ionomers

We have performed simulations to study how increasing humidity affects the structure of Nafion-like ionomers under conditions of low sulfonate concentration and low humidity. At the onset of membrane hydration, the clusters split into smaller parts. These subsequently swell, but then maintain constant the number of sulfonates per cluster. We find that the distribution of water in low-sulfonate membranes depends strongly on the sulfonate concentration. For a relatively low sulfonate concentration, nearly all the side-chain terminal groups are within cluster formations, and the average water loading per cluster matches the water content of membrane. However, for a relatively higher sulfonate concentration the water-to-sulfonate ratio becomes nonuniform. The clusters become wetter, while the intercluster bridges become drier. We note the formation of unusual shells of water-rich material that surround the sulfonate clusters.

Figure 1

(Color online) A typical snapshot of hydrated membrane ${\eta }_2$ from Run 3. The spheres represent the end-group oxygens of the side chains. The polymer is shown by red lines. Different bead colors correspond to different bead altitudes, with a blue color (gray in printed version) for low-altitude beads (at the bottom of simulation box) and a red color (black in printed version) for high-altitude beads (at the top of simulation box). The size of all structural elements is schematic rather than space filling. The water molecules and ions are not shown for the sake of clarity. The axis dimension is in nm.

Figure 2

(Color online) Three-dimensional (3D) density $\rho \left(\vec{r}\right)$ of the hydrophobic part of the membrane ${\eta }_2$ for Run 3. The color gradient from blue (gray in printed version) to red (black in printed version), corresponds to the variation of membrane density from low to high values. The axis dimension is in nm.

Figure 3

(Color online) 3D density of water channels for the membrane ${\eta }_2$ and Run 3. The color gradient from blue (gray in printed version) to red (black in printed version) corresponds to the variation of water density from low values to high values. The axis dimension is in nm.

Figure 4

(Color online) Sulfonate-sulfonate pair correlation function $g_{SS}\left(r\right)$ for membrane ${\eta }_2$ as a function of sulfur-sulfur separation distance $r$ for Runs 1–4 from Table . Solid blue line with circles—Run 1, solid green lines with squares-Run 2, dashed black line-Run 3, full red line-Run 4. The bottom figure shows in detail the long-range tail of $g_{SS}\left(r\right)$ used to determine the average multiplet size $R_A^S$ and the separation distance between the sulfonate multiplets $R_B^S$. The calculated values for the parameters $R_A^S$ and $R_B^S$ are given in Table .

Figure 5

(Color online) Sulfonate-sulfonate pair correlation function $g_{SS}\left(r\right)$ as a function of the sulfur-sulfur separation distance $r$. Membrane ${\eta }_1$: blue line with circles-Run 1, full red line-Run 4. Membrane ${\eta }_2$: green line with squares-Run 1, dashed black line-Run 4.

Figure 6

(Color online) Small angle ionomer-peak region of sulfonate-sulfonate structure factor $S\left(q\right)$ for the membranes ${\eta }_1$ and ${\eta }_2$. Line with blue circles-Run 1, line with black squares-Run 3, full red line-Run 4. The step size $\delta q=2\pi /L\approx 0.5{\text{nm}}^{-1}$ defines the resolution along the $x$ axis.

Figure 7

(Color online) Water-water pair correlation function $g_{WW}\left(r\right)$ for the membrane ${\eta }_2$ as a function of the water-water separation distance $r$ for Runs 2–4 from Table . Line with blue circles—Run 2, line with black squares-Run 3, full red line-Run 4. The arrows show the average multiplets size $R_A^W$ and the separation distance $R_B^W$ between the water clusters. The calculated values for the parameters $R_A^W$ and $R_B^W$ are given in Table .

Figure 8

(Color online) The probability distribution $P\left(\alpha \right)$ of the dihedral angle along the side chain of membrane ${\eta }_1$. Line with blue circles-Run 2, full red line-Run 4. The areas of the gauche conformation $(\alpha =82°)$ and the trans conformation $(\alpha =180°)$ are shown separately.

Figure 9

(Color online) Schematics explaining the side-chain stretchinglike relaxation as a result of multiplet swelling from $\lambda =1$ to $\lambda =5$. The small hollow spheres are the water molecules, gray (yellow in online version) small spheres with attached tails are for side chains, big spheres represent the multiplets.

Figure 10

(Color online) The probability distribution $P\left(\alpha \right)$ of the dihedral angle along the backbone of membrane ${\eta }_1$. Line with blue circles-Run 2, full red line-Run 4. The areas of a cis conformation $(\alpha =0°)$ and the gauche conformation $(\alpha =125°)$ are shown separately.

Figure 11

(Color online) The probability distribution $P\left(\alpha \right)$ of the dihedral angle along the side chains. Line with blue circles-membrane ${\eta }_1$, line with red squares-membrane ${\eta }_2$. The areas of the gauche conformation $(\alpha =82°)$ and the trans conformation $(\alpha =180°)$ are shown separately.

Figure 12

(Color online) Schematic pictures explaining the differences between the stretchinglike relaxation of side chains for the membranes ${\eta }_1$ and ${\eta }_2$. The small hollow spheres are the water molecules, gray (yellow in online version) small spheres with attached tails are for side chains, big spheres represent the multiplets.

Figure 13

(Color online) Sulfonate-ion correlation function $g_{SH}\left(r\right)$ as a function of the separation distance $r$. The first and second peak areas are shown separately. Membrane ${\eta }_1$: blue line with circles-Run 3, full red line-Run 4. Membrane ${\eta }_2$: green line with squares-Run 3, dashed black line-Run 4.

Figure 14

(Color online) Mean squared displacement of ions as a function of time for Runs 2–4. Membrane ${\eta }_1$: dashed black line-Run 2, green line with squares-Run 3, full blue line-Run 4. Membrane ${\eta }_2$: red line with circles-Run 4.

Figure 15

Schematic illustration of the multiplet hydration. At a low sulfonate concentration the hydrated multiplets consist of sulfonates and water molecules. At a higher sulfonate concentration each of the multiplets is surrounded by a water shell. The splitting of dry multiplets into smaller hydrated multiplets is also sketched. Vertical/horizontal hatching is used for the water (W) and the sulfonate (S) areas of the multiplet.