Proton diffusion coefficient

The mobilities of H+ and OH- ions in these aqueous mixtures are of some importance but their understanding presents problems. It is recalled that in ice the mobility of H+ dramatically exceeds that of H+ in water, and that in water the proton mobility is dependent on the ability of water molecules to rotate into a configuration which allows ready proton transfer (Hills et al., 1965). It is therefore noteworthy that addition of t-butyl alcohol to H+ in water lowers the proton diffusion coefficient, a trend expected if this co-solvent enhances water-water interactions (Lannung et al., 1974). 

Figure 8. Proton diffusion coefficient in slab pores (see Fig. 7) as a function of water content A for 4 different temperatures as indicated. The density of SO3 groups on the pore surfaces is 1/58 A2.

Going beyond an atomistic description of the aqueous phase and the membrane, Paddison and coworkers [79-88] employed statistical mechanical models, incorporating solvent friction and spatially dependent dielectric properties, to the calculation of the proton diffusion coefficient in Nation and PEEKK membrane pores. They concluded from their studies that, in accordance with NMR based evidence [50], the mechanism of proton transport is more vehicular (classical ion transport) in the vicinity of the pore surface and more Grotthus-like in the center. 

In contrast to the well studied molecular diffusion, proton diffusion is less well understood. Protons can move in the hydrogen-bonded network of water molecules by transfer in a hydrogen bond and a successive jump into another hydrogen bond by molecular rotation, as illustrated in Fig. 24.3. This diffusion processis oversimplified but well highlights the dominant proton motions involved. Although the model was proposed a half century ago [12], its process has eluded experimental investigation. The competitive molecular diffusion shades the protonic diffusion. The protonic diffusion coefficient is estimated to be the order of... 

The protonic diffusion coefficients measured for ice VII in a pressure range... 

Figure 24.10 Variation of the protonic diffusion coefficient with pressure measured for ice VII. Open and solid circles represent those obtained from reflection spectra measured for the HjO and D O back surfaces of HjO/DjO bilayer, respectively. (From Ref [25].)...

Figure 7. The variation of the rate of proton dissociation from excited hydroxypyrene trisulfonate on the molar concentration of the salt (O, ) time-resolved fluorescence measurements ( , ) steady-state fluorescence measurements (A) proton diffusion coefficient, normalized for pure water (data from Glietenberg et al. 1968). Open symbols, MgCl2 closed symbols, LiC104.

This value is definitely smaller that the value given by Prats et al. (9), who estimated the proton diffusion coefficient on a lipid interface to be 20 times larger than in bulk water (see also reference 10). 

We use Bruggemann formula to relate the effective diffusion coefficient of protons in micropores, to the relative volume portion of micropores in agglomerates and the proton diffusion coefficient in water. 

Figure 12.11. Computed proton diffusion coefficients as a function of the length of intrusion of the side chain (1) and as a function of the number ( ) of axially positioned arrays of fixed sites for an arbitrary membrane pore with fixed length, diameter, total number of anionic groups, and water content. The plots show the substantial sensitivity (i.e. varying over more than 3 orders of magnitude) of the computed diffusion coefficient to these parameters and suggest that the most uniform distribution of anionic groups (i.e. where = 9) results in the highest proton diffusion notwithstanding the protrusion of the anionic groups. Taken from Ref. [26].

Using this extended model they computed the radial dependence of the proton diffusion coefficient for a Nafion membrane pore at a hydration level of 6 H20/S03 with inclusion of the two different formulations for the shielding. The results are shown in Figure 12.12 and show that the Attard formulation for the screening parameter results in higher proton diffusion particularly in the center of the pore (i.e. more efficient screening of the sulfonate anions). By comparing it to the experimental diffusion coefficient (6.0 X 10 ° the authors estimated that the hydrated protons reside... 

Proton diffusion coefficients for ETFE-g-PSSA membranes (Scheme 2e) have been calculated and compared to those of Nafion 117 (Fig. 27) [189] as well as PTFSSA (Scheme 2h) [190]. Fully hydrated ETFE-g-PSSA and PTFSSA membranes exhibit much higher proton diffusion coefficients than hydrated Nafion 117 due to their high water content. This is in agreement with the higher conductivities observed for fully hydrated ETFE-g-PSSA and, in general, PTFSSA membranes (Fig. 14). However, when proton diffusion coefficients are compared where the three polymer series overlap (e.g., Xy = 0.1-... 

Fig. 27 Proton diffusion coefficients of ETFE-g-PSSA (Scheme 2e) and Nafion 117 membranes as a function of water volume fraction, Xy...

Proton conductivity (ctjj+ ) can be related to the proton diffusion coefficient D + using the Nernst-Einstein equation [179] ... 

Table 38.1. Conductivity and proton diffusion coefficient into WO3 and MoO films prepared by different techniques...

The triblock membranes exhibited relatively good proton diffusion coefficient values of about 2.0 X lO cm /s even at 30% RH, which was comparable to that of Nafion 112 (2.67x lO cm /s). At 90% RH, the proton diffusion coefficients of the... 

Recendy, Song et al. measured the local water diffusion coefficient and proton diffusion coefficient Dp within 5—10 A of spin probes that are partitioned into selectively different local environments of the swollen NAFION using Overhauser dynamic nuclear polarization relaxometry (ODNP) for nuclei of water at 9.8 GHz. This experiment concluded that... 

The PA-doped /m-PBI fuel cell membrane maintains thermal and physical stability while operating at high temperature. To illuminate the fundamental differences in polymer film architecture, polymers with similar physical characteristics were prepared by the conventional PPA Process (Table 13.1). Even though the ratio of phosphoric acid-to-polymer repeat unit (PA/PRU) achieved by both processes were nearly identical, the PPA Process produces membranes with much higher proton diffusion coefficients and conductivities. The higher protmi diffusion coefficients of membranes produced by the PPA... 

Vehicular proton diffusion coefficients were calculated, which - for the higher hydrations - account for only 20% of the total diffusion. This finding... 

Assuming that surface exchange (Eqs. (14.57) and (14.59)) and bulk diffusion (Eq. (14.58)) for H2 permeation show a comparable resistance to the overall mass transfer, a generalized equation can be obtained by assirniing that ionic conductivity rules the charge transfer within the membrane, and the proton diffusion coefficient is constant. An expression similar to Eq. (14.55) for H2 permeation within the single-phase perovskite membranes can be proposed [44] ... 

In spite of diverging predictions of surface proton diffusion coefficients, the studies quoted above provide consistent accounts of the impact of monolayer composition, reduced dimensionality, and interfacial ordering on proton dynamics. Altogether, there is ample evidence for efficient surface proton transport, which is sensitive to the packing density and chemical nature of acid headgroups. Surface pressure, surface electrostatic potential, and lateral proton conductivity increase dramatically upon monolayer compression below a critical area with typical values in the range of 25 to 40 K per SG. This critical area corresponds to a nearest-neighbor separation distance of SG of 6.5-7 A (Leite et al., 1998 Mitchell, 1961). 

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