CCL, proton conductivity

On the cathode side of a PEFC under normal operating conditions, one is concerned about excessive amounts of liquid water and flooding of gaseous supply charmels due to a net electroosmotic flux through the PEM and the production of water. Under these conditions, it is reasonable to assume full hydration of the ionomer phase in the CCL. Proton conductivity of the layer is, thus, eonsidered constant. Due to the assumption of capillary equilibrium in pores, pore-filling is... 

With Cdi in hand, the CCL proton conductivity Op can be determined from the slope of the high-frequency straight line Zre versus as discussed in the sec-... 

Equation 5.128 gives the last undefined parameter, the CCL proton conductivity Gp. Thus, Equations 5.123 and 5.124 and one of Equations 5.127 and 5.128 allow characterizing the CCL from a single low-current impedance curve without fitting. 

Concentrating on the operation of the so-called membrane electrode assembly (MEA), E includes irreversible voltage losses due to proton conduction in the PEM and voltage losses due to transport and activation of electrocatalytic processes involved in the oxygen reduction reaction (ORR) in the cathode catalyst layer (CCL) ... 

With this extension, the complex impedance response of the CCL could be calculated. The model of impedance amplifies diagnostic capabilities— for example, providing the proton conductance of the CCL from the linear branch of impedance spectra (in Cole-Cole representation) in the high-frequency limit. 

The challenge for modeling the water balance in CCL is to link the composite, porous morphology properly with liquid water accumulation, transport phenomena, electrochemical kinetics, and performance. At the materials level, this task requires relations between composihon, porous structure, liquid water accumulation, and effective properhes. Relevant properties include proton conductivity, gas diffusivihes, liquid permeability, electrochemical source term, and vaporizahon source term. Discussions of functional relationships between effective properties and structure can be found in fhe liferafure. Because fhe liquid wafer saturation, 5,(2)/ is a spatially varying function at/o > 0, these effective properties also vary spatially in an operating cell, warranting a self-consistent solution for effective properties and performance. 

Intrinsic rate constant of evaporation Evaporation-penetration depth Liquid water viscosity Ratio of the distributed liquid vapor interfacial area to the apparent electrode surface area Active site fraction effective proton conductivity in CCL... 

Fig.l (a) Principal layout of a PEM fuel cell with the main functional components, viz. proton-conducting polymer-electrolyte membrane (PEM), catalyst layers on anode (ACL) and cathode sides (CCL), gas-diffusion layers (CDL) and flow fields (FF). (b) Disciplines in fuel cell research and how they are connected by the theory. 

PEMFGs use a proton-conducting polymer membrane as electrolyte. The membrane is squeezed between two porous electrodes [catalyst layers (CLs)]. The electrodes consist of a network of carbon-supported catalyst for the electron transport (soHd matrix), partly filled with ionomer for the proton transport. This network, together with the reactants, forms a three-phase boundary where the reaction takes place. The unit of anode catalyst layer (ACL), membrane, and cathode catalyst layer (CCL) is called the membrane-electrode assembly (MEA). The MEA is sandwiched between porous, electrically conductive GDLs, typically made of carbon doth or carbon paper. The GDL provides a good lateral delivery of the reactants to the CL and removal of products towards the channel of the flow plates, which form the outer layers of a single cell. Single cells are connected in series to form a fuel-cell stack. The anode flow plate with structured channels is on one side and the cathode flow plate with structured channels is on the other side. This so-called bipolar plate... 

At the anode of a PEMFC, hydrogen is oxidized, creating protons and electrons. The polymer membrane provides proton-conducting pathways, whereas the electrons are forced through an external circuit by a potential difference between the anode and cathode. Within the CCL, oxygen is reduced to water in the presence of protons and electrons. The respective half-cell reactions, typically catalyzed by cost-intensive platinum, are... 

Figure 1.3 Schematic for the calculation of voltage loss in a fuel cell (for discussion see text). ACL and CCL are the abbreviations for the anode and cathode catalyst layers, respectively. Yellow shaded areas indicate the local polarization voltage r]. For simplicity, the proton conductivity of catalyst layers is taken to be equal to the proton conductivity of the bulk membrane (otherwise the curve loses smoothness at the membrane interfaces). Note that the half-cell voltage loss is given by the value of the overpotential at the catalyst layer/membrane interface.

Here j x) is the local proton current density, is the volumetric exchange current density (the number of charges produced in unit volume per second, A cm ), c is the molar concentration of oxygen, Cref is the reference oxygen concentration, (f> is the conversion function, r] is the local polarization voltage, at is the proton conductivity of the CCL, D is the effective oxygen diffusion coefficient and jo is the cell current. 

Higher diffusivity means higher CCL porosity, which is usually achieved at the cost of lower Nafion content and thus of lower proton conductivity. Equation (2.80) thus gives an optimal oxygen diffusion coefHcient in the CCL, and ) can be used as a reference point for optimal CCL design in terms of porosity and related Nafion content. 

Here AS is the entropy change in the half-cell reaction, rj is the half-cell polarization voltage, j is the mean current density in the cell, I is the thickness of the respective catalyst layer, at is the proton conductivity of the catalyst layer, am is the proton conductivity of the bulk membrane, and A and Am are the thermal conductivities of the catalyst layers and membrane, respectively. Note that the thermal conductivities of the ACL and CCL are assumed to be the same. 

The steps involved in modeling performance and water balance in CCLs are indicated in Figure 8.2 [50, 51]. At the materials level, it requires constitutive relations between random composition, dual porous morphology, liquid water accumulation, and effective physico-chemical properties, including proton conductivity, gas diffusivities, liquid permeabilities, electrochemical source term, and vaporization source term. The set of relationships between structure and physico-chemical properties has been discussed in [3, 47, 50-51]. Since the liquid water saturation S (z) is a spatially var5dng function at jf,>0, these physicochemical properties become spatially varying functions in an operating cell. This demands a self-consistent solution for non-linearly coupled properties and performance. 

FIGURE 1.9 Potential distribution of a PEFC with porous electrodes of finite thickness at (a) equilibrium and (b) under load. The metal phase potentials in the electrodes (horizontal lines below the label 0" in ACL and in CCL) are constant along x, but shifted as a function of current density. The electrolyte phase potential (continuous line in (b) labeled with 4>(jt)) exhibits a continuous decrease from anode to cathode the shape of this profile depends on the proton conductivity in electrodes and PEM. The total potential loss r)tot = VHOR — noRR + RpemJo is the sum of the overpotentials in the anode and cathode, plus the resistive potential loss in the membrane. 

On the cathode side of a PEFC, electro-osmotic influx of water from the PEM and water production in the ORR create an excess of liquid water under normal conditions, even if the reactant at the cathode inlet is dry. Under normal conditions, it is reasonable to assume that primary hydrophilic pores and ionomer in the CCL are well hydrated. The proton conductivity can be assumed to be relatively constant. At high rate of water formation and insufficient water removal, excessive accumulation of water occurs in diffusion media and flow fields, which blocks critical pathways for gas diffusion of reactants. 

The voltage response of the CCL in the intermediate regime is dictated by the double Tafel slope term, -qo 2b In jo. This regime leads to similar expressions for reaction penetration depth and differential CCL resistance in the limiting cases of (i) rapid proton conduction and poor oxygen diffusion (g 1) and (ii) rapid oxygen diffusion and poor proton conduction (g 1). 

Comparing this to the ideal-transport CCL resistivity given in Equation 1.79, shows that Equation 4.115 contains proton conductivity and does not depend on the CL thickness. The latter feature is due to the presence of the internal space scale s in the problem. 

Here, kr is the CCL thermal conductivity and Rreac is the volumetric rate of electrochemical conversion (A cm ). Equation 4.282 says that the variation of conductive heat flux (the left-hand side) equals the sum of the heating rates from the reaction and the Joule dissipation of electric energy. On the other hand, determines the rate of proton current decay along x ... 

The CCL electron conductivity is much larger than the proton conductivity and, hence, the electron Joule heat can be neglected. 

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