Diffusion coefficients in Nafion

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 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. ... 

Note Numbers in brackets indicate ratio of diffusion coefficient in Nafion 117 over lonac MC 3470. 

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]. 

Journal of the Electrochemical Society Figure 6. Na+ diffusion coefficient in Nafion 295 at 60° C, NaOH external solution and change in water molarity in NaOH solution (24). 

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].

In general, both the O2 solubility and the diffusion coefficient in Nafion membrane or ionomer increase with increasing temperature. The experimental data for Cqj and Dq on Nafion 112, 211, and 117 membranes are summarized in Table 1.9 from different literature. It can be seen that both the values of C02 and D02 are varied with type of the Nafion membranes and the temperature. 

In Chapter 1 of this book, the necessary parameters for both RDE/RRDE analysis in ORR study, such as O2 solubility, O2 diffusion coefficient, and the viscosity of the aqueous electrolyte solutions, are discussed in depth in terms of their definitions, theoretical backgroimd, and experimental measurements. The effects of type/concentration of electrolyte, temperature, and pressure on values of these parameters are also discussed. To provide the readers with useful information, the values of these parameters are collected from the literature, and summarized in several tables. In addition, the values of both the O2 solubility and diffusion coefficient in Nafion membranes or ionomers are also listed in the tables. Hopefully, this chapter would be able to serve as a data source for the later chapters of this book, and also the readers could find it useful in their experimental data analysis. 

The first application of PFGSE NMR for the measurement of water diffusion coefficients in NAFION was carried out by Zawodzinski et al. [67,68]. They determined the diffusion coefficients increased from 0.6 X 10 to 5.8 X 10 cm s as the hydration level of the membrane increased from 2 to 14. At a hydration level of about 20, the diffusion coefficients are 2 X 10 cm s for proton and 6 x 10 cm s for water in NAFION 117. Ochi et al, investigated the proton dynamics in NAFION 117 by comparison of the diffusion coefficient D mr estimated from PFGSE NMR and estimated from electrical conductivity, and concluded that... 

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]. 

Every et al. determined diffusion coefficients of Nafion 117 and BPSH 40 using a modified PFG NMR method. Nafion 117 and BPSH 40 were immersed in a MeOH solution of known concentration, and diffusion coefficients were measured as a function of MeOH concentration. For a Nafion... 

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.

Recently, several interesting studies of the electrochemical properties of electrodes coated with thin films of Nafion have been reported. These chemically modified electrodes are prepared using low-EW polymers which are alcohol soluble, or using a solution of a 1100-EW polymer which has been dissolved at high pressure and temperature. Electrochemical studies for cations such as the Ru(bpy)3 couple yielded estimates of ionic diffusion coefficients in the polymer films. However, results also indicate that these films are far more porous than conventional Nafion membranes, so it is not possible to compare values directly with those discussed above. 

Table II. Ionic Self-Diffusion Coefficients in 1200 EW Nafion (7)...

The last assumption means that local electroosmotic flux of water in membrane is exactly counterbalanced by back diffusion. Recent studies [14,27] have shown that in a wide range of operating conditions total transfer coefficient of water from the anode to the cathode does not exceed 0.2. Since electroosmotic drag coefficient in Nafion is 1.5 [28], we conclude that the average over the cell surface electroosmotic flux in the membrane is almost fully compensated for by back diffusion. Note that the local value of total water flux in the membrane may significantly deviate from the surface-averaged value, e.g. close to the outlet of the oxygen channel [27]. Nevertheless, assumption 5 seems to be a reasonable approximation. 

Scharfer et al. set up a multi-component transport model to describe the diffusion driven mass transport of water and methanol in PEM [170]. For a PEM in contact with liquid methanol and water on one side and conditioned air on the other, the corresponding differential equations and boundary conditions were derived taking into account the polymers three-dimensional swelling. Phase equilibrium parameters and unknown diffusion coefficients for Nafion 117 were obtained by comparing the simulation results to water and methanol concentration profiles measured with confocal Raman spectroscopy. The influence of methanol concentration, temperature and air flow rate was predicted by the model. Although there are indications for an influence of convective fluxes, the measured profiles are ascribed to a Fickean diffusion. Furthermore, the assumption to describe the thermodynamic phase equilibrium as liquid-type equilibrium also at the lower surface of the membrane, which is in contact with a gas phase, can be confirmed by their results. 

To provide electronic coupling between the incorporated CoP(pyH)44+ counterions and the graphite electrode surface it was necessary to add to the coatings suitable redox mediators wiUi much larger diffusion coefficients. In Figive IB is shown the cyclic voltammetric response obtained from a Nafion coating which contained Os(bpy)32+ (bpy = 2,2-bipyridine) and Ru(NH3)e3+ as well as CoP(pyH)44+. The pair of current peaks near —0.25 V arises fix)m the Ru(NH3)63+/2+ couple and the pair near 0.6 V from the Os(bpy)33+/2+ coimle. This pair of mediators was chosen because they both have reasonable diflusional rates in Nafion and their formal potentials lie on either side of the formal potential of the CoP(pyH)4 couple (—O.IV) so that the cobalt center of the porphyrin could be repetitively cycled between its oxidized and reduced states by me mediator counterions which diffused to and from the electrode surface where they were oxidized or reduced. 

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]. 

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 ... 

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 effects of equivalent weight (FW = g polymer/mol SO3H) and water content on diffusion coefficient, solubility, and permeability of oxygen for fully hydrated BAM, S-SEBS, ETFE- -PSSA, Nafion 117, and BPSH membranes have been studied. It has been found that the diffusion coefficients of all the studied membranes decrease with increasing EW, while the solubility correspondingly increases. These trends are the same as found in... 

In comparing the diffusion behavior of these two membranes at low MeOH concentrations, MeOH in BPSH 40 membranes exhibits significantly higher diffusion coefficients than those in Nafion 117. This may be the result of differences in morphology. Tapping mode AFM measurements found that, for dry membranes, the domains for BPSH 40 appeared to be 10-25 nm in diameter for Nafion 117, the domains were smaller, approximately 4-10 nm. Although one would expect restricted diffusion in both cases, it is possible that the smaller domains limit diffusion to a greater extent. 

---