Nafion water self-diffusion coefficients

Proton mobility (D J and water self-diffusion coefficient (D q) as a function of the water volume fraction (X ) in Nafion and SPEEKK, where X, = volume of water in membrane divided by volume of wet membrane. (From Kreuer, K. D. 2001. Journal of Membrane Science 185 29-39.)... 

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

Figure 12. Water self-diffusion coefficient of Nafion 117 (EW =1100 g/equiv), as a function of the water volume fraction Xy and the water diffusion coefficient obtained from a Monte Carlo (MC) simulation (see text). The proton conductivity diffusion coefficient (mobility) is given for comparison. The corresponding data points are displayed in Figure 14.

Zawodzinski et al. [64] have reported self-diffusion coefficients of water in Nafion 117 (EW 1100), Membrane C (EW 900), and Dow membranes (EW 800) equilibrated with water vapor at 303 K, and obtained results summarized in Fig. 36. The self-diffusion coefficients were deterinined by pulsed field gradient NMR methods. These studies probe water motion over a distance scale on the order of microns. The general conclusion was the PFSA membranes with similar water contents. A, had similar water self-diffusion coefficients. The measured self-diffusion coefficients in Nafion 117 equilibrated with water vapor decreased by more than an order of magnitude, from roughly 8 x 10 cm /s down to 5 x 10 cm /s as water content in the membrane decreased from A = 14 to A = 2. For a Nafion membrane equilibrated with water vapor at unit activity, the water self-diffusion coefficient drops to a level roughly four times lower than that in bulk liquid water whereas a difference of only a factor of two in local mobility is deduced from NMR relaxation measurements. This is reasonably ascribed to the additional effect of tortuosity of the diffusion path on the value of the macrodiffusion coefficient. For immersed Nafion membranes, NMR diffusion imaging studies showed that water diffusion coefficients similar to those measured in liquid water (2.2 x 10 cm /s) could be attained in a highly hydrated membrane (1.7 x 10 cm /s) [69]. 

Fig. 26 Water self-diffusion coefficient (Dh2o) and proton mobility (Da) as a function of the water volume fraction in Nafion and sulfonated polyetherketone [134]...

The water diffusion in the ionomer phase,, as a function of ionomer water content A, has been measured by several groups, including Springer et al. [8], Gong and co-workers [12] also reported water self-diffusion coefficients for Nafion with pulse field gradient NMR. Motupally and co-workers expanded the data from [8] to include changes in temperature [13]. 

Nafion absorbs MeOH more selectively than water, and the MeOH diffusion flow is higher than the osmotic water flow in Nafion membranes. Diffusion coefficients of Nafion 117 determined by different techniques have been reported. Ren et al. measured MeOH diffusion coefficients in Nafion 117 membranes exposed to 1.0 M MeOH solutions using pulsed field gradient (PPG) NMR techniques. The MeOH self-diffusion coefficient was 6 x 10 cm S and roughly independent of concentration over the range of 0.5-8.0 M at 30°C. A similar diffusion coefficient was obtained for Nafion 117 at 22°C by Hietala, Maunu, and Sundholm with the same technique. Kauranen and Skou determined the MeOH diffusion coefficient of 4.9 x 10 cm for Nafion... 

The self-diffusion coefficient of water in Nafion, as measured by PFG is shown in... 

For comparison purposes, the proton mobility. Do (for Nafion solvated with water), which is closely related to the self-diffusion coefficient of water, is also plotted. At low degrees of hydration, where only hydrated protons (e.g., H3O+) are mobile, it has a tendency to fall below the water diffusion coefficient (this effect is even more pronounced in other polymers), which may be due to the stiffening of the water structure within the regions that contain excess protons, as discussed in Section 3.1.1. . Interestingly, the proton mobility in Nafion solvated with methanol (Da(MeOH) in Figure 14a) is even lower than the methanol self-diffusion (Z ieon). This may... 

Figure 14. Solvent (water, methanol) diffusion coefficients of (a) Nafion 117 (EW =1100 g/equiv) and (b) sulfonated poly(arylene ether ketone)s, as a function of the solvent volume fraction. Self-diffusion data (AiaO. T eOi-i) are taken from refs 197, 224, 226, 255—263 and unpublished data from the laboratory of one of the authors) chemical diffusion coefficients (Z>h2o) are calculated from self-diffu-sion coefficients (see text), and permeation diffusion coefficients are determined from permeation coefficients. ...

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

To convert the intra(self-)diffusion coefficients (Dseif) to inter(Fickian)diffusion coefficients (Dchem). Zawodzinski and co-workers [64] have corrected the selfdiffusion coefficients they measured for water activity coefficient variations along the membrane thickness dimension and for the effects of swelling of the polymer [87]. The resulting Dchem for water in the Nafion membrane was 2 x lOr cm /s at 30 °C and did not exhibit a strong dependence on water content (however, recent reevalua-... 

Table 8. Self-diffusion coefficients of water in Nafion 117 (T = 30 °C) as a function of glycerol pre-treatment temperature.

Table III. Self-Diffusion Coefficients of Water in 1200 EW Nafion (7).

Membrane Diffusion in Nonaqueous Solvent Environments. Self-diffusion coefficients of Na+ and Cs+ for 1200 EW Nafion membranes in dilute methanol and acetonitrile solutions have been measured (5). Arrhenius plots of these results are shown in Figure 7 along with corresponding results for aqueous experiments activation energies of diffusion are listed in Table IV. Diffusion coefficients of Na+ in methanol and water-equilibrated membranes are very similar, and the activation energy of diffusion for the methanol system is only slightly higher than the respective value for Na+ in pure methanol solvent, 12.9 kJ mol 1 (27). Thus a solution-like diffusion mechanism is inferred for both solvent systems. Cesium ion diffusion in the methanol equilibrated membrane is much slower than sodium ion diffusion in fact the... 

Water, sodium ion, and hydroxide ion concentrations have been measured within the membrane phase as a function of bulk caustic solution concentration and temperature. These internal membrane concentrations are important because of their influence on the membrane polymer morphology, structural memory, plasticity and the resultant effects on its internal resistance, viscoelasticity and material transport. In addition, the self-diffusion coefficient of the sodium ions in various Nafion membranes has been measured as a function of temperature and external caustic concentration... 

Figure 12.10. Computed and experimentally determined proton self-diffusion coefficients in Nafion 117 and 65% sulfonated PEEKK membranes plotted as a function of water content expressed as the number of water molecules per sulfonic add group. The comparison to the experimental measurements indicates the generally remarkable agreement (within 15%) range of membrane hydration. Taken from Ref. [23].

Compared to Nafion , a stronger confinement of water in the narrow channels of the sulfonated aromatic polymers leads to a significantly lower dielectric constant of the waters of hydration (20 compared to 64 in fully hydrated Nafion [185,186]). Of particular relevance to macroscopic models are the diffusion coefficients of water. As the amount of water sorbed by the membrane increases and molecular-scale effects are reduced, the properties approach those of bulk water on the molecular scale. Figme 26 shows the trend in proton mobility. Da, and water self-diffusion, Dh20. for Nafion and the sulfonated polyetherketone membrane [134]. 

FIGURE 9.13 Self-diffusion coefficients Ds(T) of water in Nafion. Open symbols are for temperature domains where water concentration is constant, full symbols are for temperature domains where concentrations decrease (0, ) X = 14.6, (O) X = 9.6, ( ) X = 6.65, and (A) X. = 5.4. Ds(T) is also shown for water in sulfuric acid (+). (Reprinted with permission from Guillermo, A. et al. 2009. NMR and pulsed field gradient NMR approach of water sorption properties in Nafion at low temperature. /. Phys. Chem. B 113 6710-6717. Copyright (2009). American Chemical Society Publications.)... 

FIGURE 5.4 Computed and experimentally determined proton self-diffusion coefficients in Nafion 117% and 65% sulfonated PEEKK membranes as a function of water content [20]. 

FIGURE 5.23 Self-diffusion coefficient of water in Nafion as a function of the extent of membrane hydration [69]. 

The proton transport was further probed by NMR using water as a standard, and the number of water molecules was determined by H spin counting. It was determined that the number of waters per H, 2, varied between 6 and 8 from 20 to 100°C. This compares to a 2 = 22 for Nafion 117 [179] showing that this P (SiWll-75 V-co-BA-co-HDDA) film requires less water per H" " to achieve a higher (7 at 100% RH. However, on a functional group basis the film uptakes the same amount of water as a PFSA ionomer. Pulsed-field gradient spin echo (PGSE) NMR [180] was used to determine the self-diffusion coefficients, D, of protons in the polymer. For the P(SiWll-75 V-co-BA-co-HDDA) film at 100% RH and 20°C... 

Radiotracer and electrochemical techniques, developed by Ver-brugge and coworkers [14], which resulted in self-diffusion coefficient of water in the range of 6-10 x 10 cm s in fully hydrated Nafion membranes at room temperature. 

Pulsed field gradient neutron magnetic resonance (NMR) used by Slade et al. [15] and Zawodzinski et al. [16] resulted in self-diffusion coefficients of water close to 10 x 10 cm s for fully hydrated Nafion samples. Zawodzinski et al. [16] also measured the selfdiffusion coefficients in Nafion membranes equilibrated with water vapor and found that the diffusion coefficient decreases from 6 x 10 cmV to 0.6 X 10" cmV ... 

Zelsmann and co-workers [88] have reported tracer diffusion coefficients for water in Nafion membranes exposed to water vapor of controlled activity. These were determined by various techniques, including isotopic exchange across the membrane. They reported apparent self-diffiision coefficients of water much lower than those determined by Zawodzinski et al. [64], with a weaker dependence on water content, varying from 0.5 x 10 cm to 3 x 10 cm /s as the relative humidity is varied from 20 to 100%. It is likely that a different measurement method generates these large differences. In the experiments of Zelsmaim et al., water must permeate into and through the membrane from vapor phase on one side to vapor phase on the other. Since the membrane surface in contact with water vapor is extremely hydrophobic (see Table 7), there is apparently a surface barrier to water uptake from the vapor which dominates the overall rate of water transport in this type of experiment. 

At the opposite side of the timescale (in the range of seconds to minutes), the macroscopic diffusion coefficient of water in swollen Nafion membranes, as determined by the diffusion of tritiated water through the membrane, is lower by a factor of 10 compared to the local diffusion coefficient or the self-diffusion in bulk water. This high value integrates all the restricted motions, which shows that the Nafion morphology is favorable to obtain a high ionic conductivity [160]. One important issue is the identification of the typical... 

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