Osmotic drag coefficient

The study of the dynamical behavior of water molecules and protons as a function of the state of hydration is of great importance for understanding the mechanisms of proton and water transport and their coupling. Such studies can rationalize the influence of the random self-organized polymer morphology and water uptake on effective physicochemical properties (i.e., proton conductivity, water permeation rates, and electro-osmotic drag coefficients). 

N effective number of polymer chains in resin N molar flux of liquid water in the membrane number of SO3 groups in the dry membrane ng. electro-osmotic drag coefficient in PEM... 

Figure 15. Electro-osmotic drag coefficients Adras of (a) Nafion 117 (EW — 1100 g/equiv) and (b) sulfonated poly-(arylene ether ketone)s, as a function of the solvent (water and/or methanol) volume fraction 174.212,219,274-281...

There is no quantitative model yet describing the observed electro-osmotic drag coefficients as a function of the degree of hydration and temperature. However, the available data provide strong evidence for a mechanism that is (i) hydrodynamic in the high solvation limit, with the dimensions of the solvated hydrophilic domain and the solvent—polymer interaction as the major parameters and (ii) diffusive at low degrees of solvation, where the excess proton essentially drags its primary solvation shell (e.g., H3O+). 

The cross coefficients are contained in the electro-osmotic drag coefficients ... 

There are actually no experimental measurements of protonic streaming currents (Lu) and coupled water and methanol transport (L23 = L32) however, the first may be related to the hydrodynamic component of the electro-osmotic drag L /Ln, Lis/Lu) (see discussion in Section 3.2.1.1). The second is expected to be qualitatively related to the ratio of the electro-osmotic drag coefficient of water and methanol (L12/Z.13). In the following, the directly accessible transport coefficients o (Do), FH2O, MvieOH,... 

Figure 18 shows the temperature dependence of the proton conductivity of Nafion and one variety of a sulfonated poly(arylene ether ketone) (unpublished data from the laboratory of one of the authors). The transport properties of the two materials are typical for these classes of membrane materials, based on perfluorinated and hydrocarbon polymers. This is clear from a compilation of Do, Ch 20, and q data for a variety of membrane materials, including Dow membranes of different equivalent weights, Nafion/Si02 composites ° ° (including unpublished data from the laboratory of one of the authors), cross-linked poly ary lenes, and sulfonated poly-(phenoxyphosphazenes) (Figure 19). The data points all center around the curves for Nafion and S—PEK, indicating essentially universal transport behavior for the two classes of membrane materials (only for S—POP are the transport coefficients somewhat lower, suggesting a more reduced percolation in this particular material). This correlation is also true for the electro-osmotic drag coefficients 7 20 and Amcoh...

Figure 20. Electro-osmotic drag coefficients of diverse membranes based on perfluorinated polymers (Dow - and Nafion/silica composites ) and polyarylenes (S—PEK/ PSU blends, ionically cross-linked S—PEK/PBP ), as a function of the solvent (water/methanol) volume fraction Xy (see text for references). Lines represent data for Nafion and S—PEK (given for comparison) for data points, see Figure 15. Dashed lines correspond to the maximum possible electro-osmotic drag coefficients for water and methanol, as indicated (see text).

Two other important electrolyte properties for the PEFC system are the water diffusion coefficient and electro-osmotic drag coefficient. These two param-... 

Figure 5. Electro-osmotic drag coefficient and water diffusivity as functions of water content in Nafion membranes.

A) and the water electro-osmotic drag coefficient. In this study, the methanol... 

Table 2.1 lists the measured value of the DMFC current density, the equivalent current density of methanol crossover, the total water flux at a DMFC cathode and the calculated water electro-osmotic drag coefficient from Equation 2.2 at various DMFC operating temperatures. 

Similar values of electro-osmotic drag coefficients for a Nafion 117 membrane in contact with liquid water at both sides and their increase with temperature have been reported previously [10, 12]. 

Most recently, Gallagher et al.21 measured the water uptake of Nafion membrane under subfreezing temperatures, which showed a significant reduction in the maximum water content corresponding to membrane full hydration. The Nafion membrane with 1,100 equivalent weight, for example, uptakes A 8 of water at -25°C when it equilibrates with vapor over ice because of the low vapor pressure of ice compared to supercooled liquid water. They also found the electro-osmotic drag coefficient to be 1 for Nafion membrane under sub freezing temperatures. 

Weng, D. et al.. Electro-osmotic drag coefficient of water and methanol in polymer electrolytes at elevated temperatures, J. Electrochem. Soc., 143, 1260, 1996. 

An electro-osmotic drag due to proton migration is defined as the number of water molecules moved with each proton in the absence of a concentration gradient For comparison, the electro-osmotic drag coefficient for vapor or liquid-equilibrated Nafion membranes ranges from 0.9 to 3.2 at room temperature [146]. For phosphoric acid-doped PBI membranes, however, the water drag coefficient is dose to zero [149,... 

In the formulation of Bernardi and Verbrugge, the membrane is assumed fully hydrated, and the gases are taken to be dissolved in the pore fluid [42]. A more general variant of this hydraulic model was proposed by Eikerling et al. [44] and allows water content variation, and dependence of conductivity, permeability, and electro-osmotic drag coefficient on the local water content. 

An approach that is conceptually simpler and does not require the prescription of transport to hydraulic or diffusion mechanisms was proposed by Janssen [47], and Thampan et al. [22] (hereafter TMT) based on the use of chemical potential gradients in the membrane. More recently, Weber and Newman [27] developed a novel model where the driving force for vapour-equilibrated membranes is the chemical potential gradient, and for liquid-equilibrated membranes it is the hydraulic pressure gradient. A continuous transition is assumed between vapour- and liquid-equilibrated regimes with corresponding transition from 1 to 2.5 for the electro-osmotic drag coefficient. 

Constant in the formula for D below, value 2.1 x 10 m /s. Diffusivity of water in membrane m /s. An empirical function of membrane temperature T and water content c [10]. Electro-osmotic drag coefficient, taken to be 1. 

Luo Z, Chang Z, Zhang Y et al (2010) Electro-osmotic drag coefficient and proton conductivity in Nation membrane for PEMFC. Int J Hydrogen Energy 35 3120-3124... 

---