Osmotic drag

A disadvantage of methanol, however, is the phenomenon of electro-osmotic drag" in which protons moving through the... 

MeOH is transported through the membrane by two modes diffusion and electro-osmotic drag. ° When MeOH comes into contact with the membrane, it diffuses through the membrane from anode to cathode and is also dragged along with the hydrated protons under the influence of current flowing across the cell. Therefore, a correlation between the MeOH diffusion coefficient and proton conductivity is observed. The diffusive mode of MeOH transport dominates when the cell is idle, whereas the electro-osmotic drag... 

Ren, X., Springer, T. E., Zawodzinski, T. A. and Gottesfeld, S. 2000. Methanol transport through Nafion membranes— Electro-osmotic drag effects on potential step measurements. Journal of the Electrochemical Society 147 466-474. 

Zawodzinski, T. A., Davey, J., Valerio, J. and Gottesfeld, S. 1995. The water-con-tent dependence of electro-osmotic drag in proton-conducting polymer electrolytes. Electrochimica Acta 40 297-302. 

Ise, M., Kreuer, K. D. and Maier, J. 1999. Electro-osmotic drag in polymer electrolyte membranes An electrophoretic NMR study. Solid State Ionics 125 213-223. 

What are the mechanisms and the transport coefficients of water fluxes (diffusion, convection, hydraulic permeation, electro-osmotic drag) ... 

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). 

Under fuel cell operation, a finite proton current density, 0, and the associated electro-osmotic drag effect will further affect the distribution and fluxes of water in the PEM. After relaxation to steady-state operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces. External conditions defined by temperature, vapor pressures, total gas pressures, and proton current density are sufficient to determine the stationary distribution and the flux of water. 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular d5mamics simulations of protons and water in single iono-mer pores, as reviewed in Section 6.7.2. The hydrod5mamic contribution to n can be studied, at least qualitatively, using continuum approaches. Solution of the Poisson-Boltzmann (PB) equation. 

Below /ps, the membrane performs under uniform saturation conditions, like a linear ohmic resistance. According to Equation (6.53), two modes of water management can be applied to compensate for electro-osmotic drag and keep the membrane in a well-hydrated state. Sufficient replenishment of water in the membrane can be accomplished by (1) providing a steady external water supply j > at the anode side, or (2) applying an external gas... 

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).

The transport properties that are most significantly affected by changes of the water volume fraction are the water/methanol electro-osmotic drag and permeation, both of which have significant contributions from viscous flow (see Section 3.2.1.1). For DMFC applications (where the membrane is in contact with a liquid water/methanol mixture), this type of transport determines the crossover, which is only acceptably low for solvent volume fractions smaller than 20 vol % (see Figures 14 and 15). Consequently, recent attempts have been focused on strengthening... 

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