Potential electrolyte phase

Equations (11), (12), and (13) can be solved for three unknowns 0e,Power, e.Load, and s,cath with reference to (ps>an = 0 (set arbitrarily) when the difference in electrolyte phase potential between anode and cathode electrodes is negligible, which is a good assumption at a very low current density. However, anode and cathode electrolyte phase potentials can be differentiated by adding two more equations, namely... 

Here / is the current density with the subscript representing a specific electrode reaction, capacitive current density at an electrode, or current density for the power source or the load. The surface overpotential (defined as the difference between the solid and electrolyte phase potentials) drives the electrochemical reactions and determines the capacitive current. Therefore, the three Eqs. (34), (35), and (3) can be solved for the three unknowns the electrolyte phase potential in the H2/air cell (e,Power), electrolyte phase potential in the air/air cell (e,Load), and cathode solid phase potential (s,cath), with anode solid phase potential (Sjan) being set to be zero as a reference. The carbon corrosion current is then determined using the calculated phase potential difference across the cathode/membrane interface in the air/air cell. The model couples carbon corrosion with the oxygen evolution reaction, other normal electrode reactions (HOR and ORR), and the capacitive current in the fuel cell during start-stop. 

S0l., So2 and SHlo refer to the respective source terms owing to the ORR, e is the electrolyte phase potential, cGl is the oxygen concentration and cHlo is the water vapor concentration, Ke is the proton conductivity duly modified w.r.t. to the actual electrolyte volume fraction, Dsa is the oxygen diffusivity and is the vapor diffusivity. The details about the DNS model for pore-scale description of species and charge transport in the CL microstructure along with its capability of discerning the compositional influence on the CL performance as well as local overpotential and reaction current distributions are furnished in our work.25 27,67... 

Figure 4. Distribution of electrolyte phase potential as a function of discharge time at various interfaces (discharged at 1C rate).

Figure 13.11, illustrating the various voltage loss contributions in a typical fuel cell, shows solid-phase cp) and ionomer (electrolyte)-phase potential distributions as current (0 flows. The solid-phase potential drops within the BPs, DMs, and electrodes are negligible thanks to their high electrical conductivity. Noticeable potential drops are seen at the BP/DM and DM/electrode interfaces due to electrical contact resistances between components. Engineering efforts continue to... 

FIGURE 13.11 Solid-phase and electrolyte-phase potential distributions across a fuel cell. The solid lines are potentials within the solid phases through which electrons are transported. The dotted hnes are for potentials within the electrolyte, where charge conduction occurs via hydrogen ions (protons). The BP potential on the anode side is set to be zero as a reference point. Reprinted with permission from Ref [4], John Wiley Sons. 

The driving forces for charged particles in this environment are modelled by two continuous potentials the electrolyte phase potential and the carbon phase potential ip. The gradient of (pm drives protons in the electrol de phase while the gradient of cp induces electron current in the Pt-carbon phase. 

If an electrical current jo > 0 is drawn from the cell, the shape of the potential profile changes. Figure 1.8b is obtained under the assumptions of (i) ideal kinetics of the anode reaction and (ii) ideal proton conductivity of the electrolyte. The first assumption implies that the deviation of the potential distribution from eleetrochemi-cal equilibrium is negligible in the anode double layer region. The seeond assumption implies a constant electrolyte phase potential. The only change observed in this case is a shift in the metal phase potential on the cathode side away from equilibrium, caused by the poor kinetics of the cathode reaction it corresponds to a decrease of... 

The characteristic length for the separation of charges at both interfaces is in the order of 10 A. In modeling of fuel cells, the continuous potential distribution in this region is usually not resolved and two potentials are introduced instead the metal phase potential, which drives electrons, and the electrolyte phase potential, which controls the proton current in the ionomer phase. The two potentials are separated by finite jumps at the metal/electrolyte interface (Figure 1.8). 

More specifically, the conventional approach to describe this situation is to introduce a so-called representative elementary volume (REV). The size of an REV has to be small on the scale of the electrode thickness, and large on the scale of microscopic variations in electrode structure and composition. Fluctuations on the scale of the double layer thickness, that is, below 1 nm, are averaged out. The electrochemical properties of an REV are defined by local values of metal and electrolyte phase potentials. These potentials are continuous functions of spatial coordinates. 

In one-dimensional electrode modeling, (x) denotes the metal phase potential and (x) the electrolyte phase potential. The gradient of the metal (carbon) phase potential drives the electron flux, while protons move along the potential gradient of the electrolyte (ionomer) phase. At equilibrium, these gradients are zero and the potentials in the distinct phases are constant, (p (x) = and O (x) = 4) . The potential distribution of a working PEFC with porous electrodes of finite thickness is shown in Figure 1.9. For illustrative purposes, a simple assembly of anode catalyst layer, PEM and cathode catalyst layer is displayed. 

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. 

Since then, other groups have developed similar models (Eikerling and Komyshev, 1998 Perry et al., 1998). The main features of this approach are (i) it relates global performance of CCLs to spatial distributions of reactants, electrolyte phase potential, and reaction rates (ii) it defines a reaction penetration depth, or the active zone and (iii) it suggests an optimum range of current density and catalyst layer thickness, with minimal performance losses and highest utilization of the catalyst. 

The transport properties of water-filled nanopores inside of agglomerates and the properties of the ionomer film at the agglomerate surface define local reaction conditions at the mesoscopic scale. These local conditions, which involve distributions of electrolyte phase potential, proton density (or pH), and oxygen concentration, determine the kinetic regime, under which interfacial electrocatalytic processes must be considered. Combining this information, a local reaction current can be found, which represents the source term to be used in performance modeling of the cathode catalyst layer. 

According to Ohm s law j = —apdr]ldx, rj must grow monotonically toward the membrane to provide a positive proton current in the CL (Figure 4.2). Similarly, Ohm s law should be considered for the electron flux in the electronic conductor phase. However, the conductivity of this phase is usually high so that the potential shape of this phase will be uniform. The shape of the overpotential follows the shape of the electrolyte phase potential. The function r](x) peaks at the membrane interface, and obviously r]o is the total potential loss in the catalyst layer. 

In Chapters 4 and 5, a positively defined ORR overpotential is assumed. Thus the local overpotential r] (jc) corresponds to the difference of electrolyte and metal phase potentials. This convention reverses the definition used in Chapters 1 and 3. Owing to the constancy of the metal phase potential, which is the default case, changes in r] (x) exactly match changes in the electrolyte phase potential, that is, A4> (x) = (x). This makes the redefinition of the overpotential a convenient choice in performance... 

The electrode E serves as a second anode, which converts the flux of methanol in the membrane into useful current. Indeed, if R is small, the carbon phase potential of E is almost equal to the carbon phase potential of the cathode, while the electrolyte phase potential in E is not far from that potential in the anode. Thus, the MOR overpotential in E, would be large, that is, the auxiliary electrode would efficiently convert the flux of methanol in the membrane into the usefiil ionic and electron currents. Moreover, thanks to E, no methanol would arrive at the cathode, thereby no poisoning of the ORR electrode by the MOR products would occur. 

In the single particle model, each electrode is represented by a single spherical particle, the surface area of which is equivalent to that of the active area of the solid phase in the porous electrode [22, 54, 55). This model assumes that the transport limitation due to the electrolyte phase of the cell is negligible. Therefore, the equations for electrolyte phase potential and lithium ion concentration in the electrolyte phase are not solved. 

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