Coupled proton and water transport

Fuller and Newman [4] based their model of coupled proton and water transport in PEFC on the theory of concentrated solutions, wherein the effective diffusion constant was determined from the hydraulic permeability. Based on flux measurements of Fales and Vanderborgh [79], the model of Fuller and Newman used, practically, a -independent permeability. 

Coupled Proton and Water Transport in Polymer Electrolyte Membranes... 

Coupled Proton and Water Transport in Polymer Electrolyte Membranes 137 Table 4.1 Non-dimensional quantities and associated reference values. 

Having determined the transport parameters from the binary membrane conduetivity model, we are now in a position to implement the full BFM2 into a eomplete fuel eell model to solve for coupled proton and water transport. In this Seetion we deseribe briefly the implementation in a fuel cell model and present sample simulations to illustrate features of the BFM2 predictions. 

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). 

Upon the transition from primary polymer architectures to secondary structural units at the mesoscopic scale interactions of solvent-solvent, solvent-polymer, polymer-polymer types are renormalized into effective interactions between sidechains and aqueous domains, as indicated in Fig. 3. These interactions control proton distribution and mobilities as well as the coupling between proton and water transport. At the mesoscopic level of the theory, the hydrophobic polymer phase formed by the backbones can already be considered as an inert, structureless matrix. 

The electro-osmotic coupling of proton and water transport depends on the molecular mechanism of proton transport. It is useful to distinguish a molecular and a hydro-dynamic contribution to the electro-osmotic drag coefficient. The latter contribution increases strongly with water uptake and temperature. 

In reality, this behavior is only observed in the limit of small jg. At currents o 1 A cm-2 that are relevant for fuel cell operation, the electro-osmotic coupling between proton and water fluxes causes nonuniform water distributions in PEMs, which lead to nonlinear effects in r/p M- These deviations result in a critical current density, p at which the increase in r/pp j causes the cell voltage to decrease dramatically. It is thus crucial to develop membrane models that can predicton the basis of experimental data on structure and transport properties. 

Modeling approaches that explore membrane water management have been reviewed in [16]. Overall, the complex coupling between proton and water mobility at microscopic scale is replaced by a continuiun description involving electro-osmotic drag, proton conductivity and water transport by diffusion or hydraulic permeation. Essential components in every model are the two balance equations for proton flux (Ohm s law) and for the net water flux. Since local proton concentration is constant due to local electroneutrality of the membrane, only one variable remains that has to be solved for, the local water content. 

Chapter 2 dwells on all aspects of the structure and functioning of polymer electrolyte membranes. The detailed treatment is limited to water-based proton conductors, as, arguably, water is nature s favorite medium for the purpose. A central concept in this chapter is the spontaneous formation of ionomer bundles. It is a linchpin between polymer physics, macromolecular self-assembly, phase separation, elasticity of ionomer walls, water sorption behavior, proton density distribution, coupled transport of protons and water, and membrane performance. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

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,... 

The initial emphasis on evaluation and modeling of losses in the membrane electrolyte was required because this unique component of the PEFC is quite different from the electrolytes employed in other, low-temperature, fuel cell systems. One very important element which determines the performance of the PEFC is the water-content dependence of the protonic conductivity in the ionomeric membrane. The water profile established across and along [106]) the membrane at steady state is thus an important performance-determining element. The water profile in the membrane is determined, in turn, by the eombined effects of several flux elements presented schematically in Fig. 27. Under some conditions (typically, Pcath > Pan), an additional flux component due to hydraulic permeability has to be considered (see Eq. (16)). A mathematical description of water transport in the membrane requires knowledge of the detailed dependencies on water content of (1) the electroosmotic drag coefficient (water transport coupled to proton transport) and (2) the water diffusion coefficient. Experimental evaluation of these parameters is described in detail in Section 5.3.2. 

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