Overpotential transport diffusion

It shonld be noted that high utilization factors measnred with cyclic voltammetry by no means warrant the assnmption that nnder dynamic conditions of fnel cell operation the CLs deliver the same cnrrent as they wonld without mass transport and ohmic constraints. To acconnt for the latter, Gloagnen et al. [185] employed the effectiveness factor the ratio of the actnal reaction rate to the rate expected in the absence of mass and ionic transport limitations. The effectiveness factor is a fnnction of the total catalyst area, the exchange cnrrent density, the overpotential, the diffusion coefficient D, the concentration of electroactive species Co, the thickness of the CL, and the proton conductivity of the electrolyte, and drops sharply below 100% with increased exchange current density and decreased the product DCq. 

This chapter is a practical summary of how to create CFD models, and how to interpret results. A review of recent literature on PEM fuel cell modeling was presented. A fiill three-dimensional computational fluid d5mamics model of a PEM fuel cell with straight flow channels has been developed. This model provides valuable information about the transport phenomena inside the fuel eell such as reactant gas concentration distribution, liquid water saturation distribution, temperature distribution, potential distribution in the membrane and gas diffusion layers, activation overpotential distribution, diffusion overpotential distribution, and local current density distribution. In addition, the hygro and thermal stresses in membrane, which developed during the cell operation, were modeled and investigated. 

It is quite clear from the above that diffusion overpotential gives no information at all on the kinetic parameters of an electrode reaction. Thus if we want to measure kinetics, but find curves which exhibit diffusion characteristics, then the technique must be changed to a faster one, so that the electrode reaction itself would not have time to reach equilibrium. It is the reaction which reaches virtual equilibrium that is mass-transport (diffusion) controlled and where the overpotential gives no information on the kinetic parameters. 

At higher current densities, the primary electron transfer rate is usually no longer limiting instead, limitations arise tluough the slow transport of reactants from the solution to the electrode surface or, conversely, the slow transport of the product away from the electrode (diffusion overpotential) or tluough the inability of chemical reactions coupled to the electron transfer step to keep pace (reaction overpotential). 

Electroplating passive alloys Another application of strike baths reverses the case illustrated in the previous example. The strike is used to promote a small amount of cathode corrosion. When the passivation potential of a substrate lies below the cathode potential of a plating bath, deposition occurs onto the passive oxide film, and the coating is non-adherent. Stainless steel plated with nickel in normal baths retains its passive film and the coating is easily peeled off. A special strike bath is used with a low concentration of nickel and a high current density, so that diffusion polarisation (transport overpotential) depresses the potential into the active region. The bath has a much lower pH than normal. The low pH raises the substrate passivation potential E pa, which theoretically follows a relation... 

Concentration (diffusion or transport) Overpotential change of potential of an electrode caused by concentration changes near the electrode/solution interface produced by an electrode reaction. 

A correlation between the spacing of striae and convection downstream of protrusions does not fully describe the process. The initial protrusions arise far from transport control and cannot be attributed to a diffusive instability of the type described in the previous section. Jorne and Lee proposed that striations formed on rotating electrodes by deposition of zinc, copper and silver are generated by an instability that arises only in systems in which the current density at constant overpotential decreases with increasing concentration of metal ion at the interface [59]. 

In a PEMFC, the power density and efficiency are limited by three major factors (1) the ohmic overpotential mainly due to the membrane resistance, (2) the activation overpotential due to slow oxygen reduchon reaction at the electrode/membrane interface, and (3) the concentration overpotential due to mass-transport limitations of oxygen to the electrode surfaced Studies of the solubility and concentration of oxygen in different perfluorinated membrane materials show that the oxygen solubility is enhanced in the fluorocarbon (hydrophobic)-rich zones and hence increases with the hydrophobicity of the membrane. The diffusion coefficient is directly related to the water content of the membrane and is thereby enhanced in membranes containing high water content the result indicates that the aqueous phase is predominantly involved in the diffusion pathway. ... 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

Bulk path at moderate to high overpotential. Studies of impedance time scales, tracer diffusion profiles, and electrode microstructure suggest that at moderate to high cathodic over potential, LSM becomes sufficiently reduced to open up a parallel bulk transport path near the three-phase boundary (like the perovskite mixed conductors). This effect may explain the complex dependence of electrode performance on electrode geometry and length scale. To date, no quantitative measurements or models have provided a means to determine the degree to which surface and bulk paths contribute under an arbitrary set of conditions. 

In the assumptions that were made in this chapter up to the beginning of this section, it was assumed that transport of charge carriers to and from the electrode played no part in rate control because it was always plentiful. Thus, in the evolution of hydrogen from acid solutions, the current density in most experimental situations is less than 10 times the limiting diffusion current and for this reason there is a negligible contribution to the overpotential due to an insufficiency of charge carriers. Like water from the tap in a normal city, the rate of supply of carriers is both tremendously important but seldom considered, for there is always plenty available. 

Mass transport processes are involved in the overall reaction. In these processes the substances consumed or formed during the electrode reaction are transported from the bulk solution to the interphase (electrode surface) and from the interphase to the bulk solution. This mass transport takes place by diffusion. Pure diffusion overpotential t]A occurs if the mass transport is the slowest process among the partial processes involved in the overall electrode reaction. In this case diffusion is the rate-determining step. 

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... 

With the evaluated site coverage and pore blockage correlations for the effective ECA and oxygen diffusivity, respectively, and the intrinsic active area available from the reconstructed CL microstructure, the electrochemistry coupled species and charge transport equations can be solved with different liquid water saturation levels within the 1-D macrohomogeneous modeling framework,25,27 and the cathode overpotential, q can be estimated. 

Figure 13 shows the potential and concentration distributions for different values of dimensionless potential under conditions when internal pore diffusion (s = 0.1) and local mass transport (y = 10) are a factor. As expected the concentration and relative overpotential decrease further away from the free electrolyte (or membrane) due to the combined effect of diffusion mass transport and the poor penetration of current into the electrode due to ionic conductivity limitations. The major difference in the data is with respect to the variation in reactant concentrations. In the case when an internal mass transport resistance occurs (y = 10) the fall in concentration, at a fixed value of electrode overpotential, is not as great as the case when no internal mass transport resistance occurs. This is due to the resistance causing a reduction in the consumption of reactant locally, and thereby increasing available reactant concentration the effect of which is more significant at higher electrode overpotentials. 

Because the kinetic and mass-transport phenomena occur in a thin region adjacent to the electrode surface, this area is treated separately from the bulk solution region. Since kinetic effects are manifested within 100 A of the electrode surface, the resulting overpotential is invariably incorporated in the boundary conditions of the problem. Mass transport in the boundary layer is often treated by a separate solution of the convective diffusion equation in this region. Continuity of the current can then be imposed as a matching condition between the boundary layer solution and the solution in the bulk electrolyte. Frequently, Laplace s equation can be used to describe the potential distribution in the bulk electrolyte and provide the basis for determining the current distribution in the bulk electrolyte. 

---