Proton current density

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operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces.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. 

Here, the electroosmotic flow is proportional to the proton current density jp with a drag coefficient n (wx). D Arcy flow as the mechanism of water backflow proceeds in the direction of the negative gradient of liquid pressure, which (for A P% = 0) is equal to the gradient of capillary pressure. The density of water, cw, and the viscosity, /1, are assumed to be independent of w. The transport coefficient of D Arcy flow is the hydraulic permeability K wx). 

Fig. 10 Membrane resistance in H2/O2 fuel cell as a function of proton current density. Experimental data, normalized to the resistance 9ts of the saturated membrane at various temperatures have been extracted from Ref. 94. They are compared to the values calculated in the hydraulic permeation model (main figure) and to the results of the diffusion model, taken from Ref. 7 (inset).

Here, the oxygen partial pressure p is normalized to the absolute O2 -partial pressure Po2 the interface between catalyst layer and GDL (at x = 1), P = Poj/Poj- D is an effective oxygen diffusion constant (in cm2s-1). j-p(x) is the local proton current density (in A cm-2) and jo = jv(x = 0) is its value at the interface with the membrane, where jo is equal to the total current density through the cell. 

The maps of methanol and oxygen concentrations, electrochemical reaction rates, membrane phase potential and proton current density are shown in Fig. 24. The mean current density is 0.3 A cm-2. Several interesting features are seen. 

Let us calculate the proton current density of I due to hopping (at room temperature). On calculating I, we apply the method based on the usage of the statistical operator, proposed earlier by Hattori [173] for another type of systems. Setting J(R, ) kBT where kBT 300 K, with accuracy to terms of order J2(Rm) we have for the current density... 

In Ref. 176 the estimation of anharmonicity on the proton conductivity, neglecting the bilinear phonon-phonon interaction, has been calculated. The proton current density is obtained from expression (219) in this formula we... 

The resulting proton current density (which includes the drift activation current), considered in the two previous subsections and photocurrent (281) is... 

Let us apply expression (317) for the calculation of the proton current density associated with the hopping mobility of protons. Neglecting the dispersion in expression (317) and assuming that the applied electric field is small, we can write the hopping current density as follows ... 

Perry, Newman and Cairns [5] obtained a numerical solution to a problem and provided asymptotic solutions for large and small proton current densities Jo - However, they did not present the expressions for the voltage current curve valid in the whole range of jo, nor the relations for the profiles of basic parameters across the CCL. Eikerling and Komyshev [7] used a similar approach and derived an analytical solution in the case of small overpotentials. In the general case they presented numerical results. 

This is the explicit form of proton current density profile across the catalyst layer. Figure 6.5 shows the profiles j x) for three values of mean current... 

Figure 6.5. The profiles of proton current density across the catalyst layer for three indicated values of dimensionless current density j q. The membrane is at x = 0.

Section 6.2 local proton current density in the catalyst layer in the other sections local current density in a cell (A cm )... 

O2 diffusion versus proton conductivity, g = I jab Characteristic parameter of O2 diffusion, A cm Exchange current density parameter, A cm Local proton current density, A cm Proton... 

Shown are the shapes of ion (proton) current density j, eiec-tron current density je, feed moiecuies concentration c, and overpotentiai rj. The CL poiarization curve is t]o jo). 

To illustrate the use of the Tafel equation, consider the following simple problem. Let the proton current density jo enter the cathode catalyst layer from the membrane. In the CCL, this current is converted into the electron current and at the CCL/GDL interface the proton current = 0. The proton current conservation equation reads... 

Consider for definiteness the cathode catalyst layer. Proton current density jp obeys a conservation equation djpjdx = -Q. Using this relation in (1.64) we get... 

In the CL, the electron conductivity of the carbon phase is much greater than the proton conductivity of the electrolyte phase. Since maximal electron and proton current densities in the CL are equal, the major proportion of Joule heat there is released in the electrolyte phase. 

Figure 2.1 Schematic of the cathode catalyst layer and the dimensionless shapes of the proton current density j and oxygen concentration c. Note that in Chapter 1 j is denoted as jp.

ORR participants arrive at the CCL from different sides protons come from the polymer electrolyte membrane, while electrons and oxygen come from the gas-diffusion layer (GDL, Figure 2.1). Let the proton current density entering the CCL be jo (note that this value coincides with the cell current density) and the axis x be directed from the membrane to the CCL/GDL interface (Figure 2.1). Due to the ORR, proton current j decreases along x and at the CCL/GDL interface, j = 0 (Figure 2.1). 

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. 

Figure 2.2 The shapes of the dimensionless proton current density j and overpotential f across the cathode catalyst layer for the two indicated values of parameter e and jo = 0.1.

Figure 2.12 (a) Polarization curves of the anode catalyst layer for cja = 10 and indicated values of = Wa/w. Sohd lines Eq. (2.132), and dashed lines—numerical calculations for the general case. At fji > 0.1, analjdical and numerical curves are indistinguishable. Numerical curve for V = 10 is emphasized in red. (b) Numerical polarization curves of the catalyst layer for Wo = 0.1 and indicated values of Dashed hne analjdical solution (2.141) for 1. Local overpotential and proton current density in the points indicated by filled circles are shown in Figures 2.13 and 2.14. 

The exact boundary condition for external problems can be obtained from Eq. (2.145) using the following assumptions. Suppose that the feed molecule concentration does not vary significantly across the CL, the cell operates in the low-current regime and the reaction penetration depth is large (these assumptions are discussed in detail in Sections 2.1-2.4). In that case, the electron and proton current densities vary linearly with the distance across the CL ... 

Proton current density in the catalyst layers linearly depends on the distance across the layer. 

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