banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Pore morphologies and diffusion within hydrated polyelectrolyte membranes: Homogeneous vs heterogeneous and random side chain attachment
Rent this article for


Image of FIG. 1.
FIG. 1.

(a) Chemical structure of a repeat unit of Nafion (EW = 1143) polymer. (b) Bead representation of the polymer architectures studied in this work. A beads are hydrophobic, C beads are hydrophilic.

Image of FIG. 2.
FIG. 2.

Pore morphologies generated at 2 × 104 Δt obtained for (Ax[AC]Ay[AC]) sequences at ϕ w = 0.16. Bead definition: A beads (red), C beads (yellow), and W beads (blue). Iso-surfaces of the W bead densities are drawn at an iso-value of 0.8.

Image of FIG. 3.
FIG. 3.

Pair correlation functions of the W beads for the eight morphologies displayed in Fig. 2 . (a) Polymers (x, y) for which the side chains are highly non-uniformly distributed: (1,5) (filled diamonds), (1,7) (open squares), (1,9) (open triangles), and (1,11) (crosses). (b) Polymers with uniform side chain distribution (y/x = 1): (3,3) (filled diamonds), (4,4) (open squares), (5,5) (open triangles), and (6,6) (crosses).

Image of FIG. 4.
FIG. 4.

Calculated scattering profiles (according to Eq. (15) ) plotted against q-vector for the morphologies shown in Fig. 2 . Architectures for which the distances between nearby branching points along the polymer backbone are the same (y = x) are given by open symbols.

Image of FIG. 5.
FIG. 5.

(a) D Bragg and (b) D Cl–Cl versus asymmetry parameter y/x. Lines in (a) and (b) are linear fits through data for which x + y are the same.

Image of FIG. 6.
FIG. 6.

MSD curves obtained for the morphologies shown in Fig. 2 . (a) Diffusion restricted to the W phase (b) diffusion restricted to the W+C phase. In (a) and (b), the data obtained for the architectures with equidistant branching distances (y = x) are represented by filled diamonds (x = y = 3), filled squares (x = y = 4), filled triangles (x = y = 5), and filled circles (x = y = 6). Non-uniform architectures are represented by open diamonds (x = 1; y = 5), open squares (x = 1; y = 7), open triangles (x = 1;y = 9), and open circles (x = 1; y = 11). The pure water case, for which ϕ w = 1.0 and D MC = 1.0, is also included (crosses). The horizontal lines drawn at MSD = 1.6 × 105 give an indication of the system size.

Image of FIG. 7.
FIG. 7.

D MC plotted against y/x. (a) Diffusion is restricted to the W pore network. (b) Diffusion is restricted to the W + C pore network.

Image of FIG. 8.
FIG. 8.

MC tracer diffusion coefficients D MC for the architectures listed in Table I plotted against D Cl–Cl. The water content ϕ w = 0.16. (a) Diffusion restricted to the W phase. (b) Diffusion restricted to the (W + C) phase.

Image of FIG. 9.
FIG. 9.

(a) Distribution of the maximum displacement obtained for N tracer = 2000 trajectories (a) x + y = 12, (b) x + y = 10, (c) x + y = 8, (d) x + y = 6. The results were obtained for MC runs with a duration of 7.6 × 107 MCS. Dashed lines give an indication of the system size.

Image of FIG. 10.
FIG. 10.

Fraction of trajectories with maximum displacement less than system size (Φisol.(MC)) for all 18 architectures plotted against y/x. Filled (open) symbols were obtained for MC runs of period 7.6 × 107 MCS (2.6 × 107 MCS). (b) Φisol.(DPD) plotted against Φisol.(MC). The error bars in Φisol.(MC) are estimated as (with N tracer = 2000). The drawn line is a linear fit though the data.

Image of FIG. 11.
FIG. 11.

(a) Changes in D Cl–ClD Cl–Cl = D Cl–Cl(y,x)-D Cl–Cl(y = x)) plotted against differences in inter branching distances along the polymer backbones. Curves are quadratic fits obtained for data points for which x + y = constant (b) ΔD Cl–Cl plotted against 2nd moment in the D topol distribution. The drawn line is a linear fit through the data points.

Image of FIG. 12.
FIG. 12.

Snapshot of polymer chain conformation of (1,11) architecture at ϕ w = 0.16. C beads (yellow) are located near the W pores (illustrated by iso-surfaces) in a pair wise fashion. Dashed circles illustrate the pairing of C beads that are topologically close together.

Image of FIG. 13.
FIG. 13.

Comparison between (a) Bragg spacing and (b) diffusion constants for the x + y = 8 membranes (ϕ w = 0.16) with those obtained from Nafion1200 membranes (ϕ w = 0.2). DPD time is 20 000Δt.

Image of FIG. 14.
FIG. 14.

Pore morphologies obtained after 20 000Δt for Nafion1200 membranes at ϕ w = 0.2 (upper figures) and ϕ w = 0.3 (lower figures) for a mixture of polymers with random side chain attachments (left hand side figures) and equidistant side chain attachments (right hand side figures). Polymer A beads (red); B beads (green); C beads (yellow). Water beads are blue. Iso surfaces of the W bead densities are drawn at an iso-value of 0.9.


Generic image for table
Table I.

Distance between water clusters, DCl–Cl (4th column), Bragg spacing D Bragg (5th column), Monte Carlo diffusion constants in W network D MC(W) (6th column), and within W+C network D MC(W+C) (7th column) for 18 chain architectures at hydration level of ϕ w = 0.16. Column 8: Fraction of the W pore space Φisol.(MC) that does not contribute to long range water diffusion, values in parenthesis Φisol.(DPD) give fraction of beads not contained within the largest W cluster for R c rit = 1.025 DPD length units (0.58 nm).

Generic image for table
Table II.

DPD repulsions used here. The approximate Flory-Huggins χij-parameters according to Eq. (14) are given in parentheses. [Reproduced with permission from G. Dorenbos and K. Morohoshi, J. Mater. Chem. 21, 13503 (2011). Copyright 2011 Royal Society of Chemistry.]

Generic image for table
Table III.

Permeability of oxygen (K O2) and hydrogen (K H2) in Barrer calculated at ϕ w = 0.2 and ϕ w = 0.3 within Nafion1200 at T = 40 °C. Values were obtained using the exactly the same procedure described in Ref. 34 . The water diffusion constants at T = 30 °C given in the last column were obtained by assuming a local water mobility of 2.3 × 10−5 cm2/s within the W (W+C) pore networks. K O2 and K H2 values deduced from experiment for Nafion1200 were derived from Ref. 68 . The experimental values were obtained by averaging over available literature values from Refs. 2 and 9 , and 10 for Nafion1100.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pore morphologies and diffusion within hydrated polyelectrolyte membranes: Homogeneous vs heterogeneous and random side chain attachment