(a) Chemical formula of Nafion®. (b) Bead representation of the considered membrane polymers.
Pore morphologies obtained for various EW membranes at water contents ϕ = 0.2 and ϕ = 0.4. A and B beads are colored red, acidic C beads are colored yellow, water (W) beads are colored blue. All structures were acquired at a DPD time of 1000 and system size L = 40, which correspond to a box edge length of 28.4 nm.
(a) Calculated scattering intensities plotted vs q-vector for ϕ = 0.1, 0.2, 0.3, and 0.4. (b) D Bragg vs ϕ. Solid lines give the values according to Eqs. (11) and (12).
(a) Diffusion coefficients of H2, O2, and N2 in water and in dry Naf1200 (H+-form) (filled symbols). (b) Solubility of H2, O2, and N2 in pure water and dry Nafion (filled symbols) vs temperature. All gas pressures are 1 atm.
Jumping probabilities, , for entering the water phase as function of temperature.
(a) Number of O2 particles located on T and W nodes vs MC time. Total number of particles N = 4,000. (b) Same data as in (a) converted to particle concentrations (in mmol/l). Dashed lines are drawn at the equilibrium O2 solubility = 1.01 and = 6.11 mmol/l (T = 40 °C).
MSD sampled over N = 4000 particle trajectories vs MC time obtained for EW1200 at water contents of = 0.1, 0.2, 0.3, and 0.4. The curves were obtained for O2 diffusing through the membrane at T = 40 °C.
The calculated H2, N2, and O2 permeability as function of ϕ in Naf1200. Calculations were performed for (a) T = 40 °C (b) T = 55 °C (c) T = 70 °C. Assumed pure component diffusion constants are given by Eqs. (15a–f) and the solubilities are given by Eqs. (18a–c) and Eqs. (19a–c). Solid lines are fits obtained for H2 and O2 over the window 0.1 ⩽ ϕ ⩽ 0.7.
as a function of water volume fraction, ϕ. Filled symbols were obtained from KMC calculations for T = 40 °C (diamonds), T = 55 °C (squares) and T = 70 °C (triangles). Calculated values according to Eq. (27) for G = 0 (filled lines) and G = inf. (dashed lines) at T = 40 °C (open diamonds) and T = 70 °C (open triangles) are shown.
(a)–(c) Calculated gas permeability at T = 55 °C vs ϕ. (a) H2, (b) O2, (c) N2. (d) Gas permeability in EW800, 1000, and 1200 membranes relative to EW1400 membrane vs Q.
Calculated gas permeability obtained at T = 55 °C for several EW membranes vs R pore. (a) H2, (b) O2, and (c) N2. Dashed arrows in (b) and (c) serve as eye guides connecting data obtained for water contents ϕ = 0.35.
Calculated gas permeability at T = 55 °C obtained for several EW membranes vs D Bragg. (a) H2, (b) O2, and (c) N2. Lines are linear fits through data points obtained for similar EW membranes. The arrows in (b) and (c) serve as eye guides and connect data points obtained for water contents ϕ = 0.35.
General picture of differences in pore networks for low and high EW membranes at equal water contents.
Comparison between K(O2) values measured by Zhang et al. (Ref. 57) with (interpolated) values derived from the work of Sakai et al. (Ref. 53).
DPD repulsions used here (from Ref. 36).
Parameter values used in Eq. (13) (from Ref. 51)
Values for the parameters used in Eq. (16) to calculate the molar solubility of gasses within pure water at partial gas pressure of 1 atm. Values are taken from Ref. 55.
Calculated and in EW1200 compared with interpolated values from Ref. 53. The gas permeability is expressed in barrer (10−10 cm2.cm.cm−2.cm.Hg−1). Values given in parenthesis were obtained by assuming given by Eq. (28).
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