Reaction penetration depth

Eor illustration purposes, we consider here a simple scenario of this interplay. We evaluate the effectiveness factor at a fixed cell voltage and thus at a fixed rig. We can express the corresponding current density as a two-variable function, jg =f f, Sqi), where the reaction penetration depth, CL/ depends on rjg. This function can be used to determine the effectiveness factor, rcL- In the case of severely limited oxygen diffusion, the following relations for local oxygen partial pressure and current density can be obtained ... 

The existence of a maximum thickness beyond which the performance deteriorates is due to the concerted impact of oxygen and proton transport limitations. Considered separately, each of these limitations would only serve to define a minimum thickness below which performance worsens due to an insufficient electroactive surface. The thickness of the effective layer, in which current density is predominantly generated, is given by the reaction penetration depth ... 

A simple analytical solution can be obtained, when the renormalized reaction-penetration depth Lp is large compared to l. Indeed, for this case the variation of r](x) with x can be neglected, that is, the electrolyte phase in the electrode is equipotential. Therefore, the dynamic response in the Tafel regime is given by a similar expression as in the linear regime,... 

Several approximations for the calculation of the effect of 02-transport limitations on the complex impedance response of the electrode have been studied [144]. In one of these approximations, only oxygen diffusion limitations were considered, whereas proton transport limitations were neglected (equipotential electrolyte phase), cf. Sect. 8.2.3.4.4. The stationary solution for this case provides the definition of a gas-diffusion-limited reaction-penetration depth,... 

Equation (6.22) contains CCL thickness It, whereas Eq. (6.23) contains reaction penetration depth / (6.12). 

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 ... 

A feature of the anode-supported SOFC design is its large anode thickness It — 1 mm). Experiments show that the reaction penetration depth into the anode is in the order of 10 [xm (Mogensen and Hendriksen, 2003). Thus, for the anode-supported SOFC, is a small parameter s 0.01. 

Length of the Nusselt number relaxation in the chaimel (m) Length of the domain exposed to degradation, Section 4.4 (m) Damping length of the disturbance in the stack Reaction penetration depth (2.14) and (4.158) (m)... 

As discussed above, f is a static materials property. It is the product of the specific electrocatalytic activity of the catalyst surface times statistical factors that arise at all scales due to the random morphology and distribution of the catalyst in the composite CL, as considered in Equation 8.2. The reaction penetration depth is a steady state property, which is mainly determined by the nonlinear coupling between transport of oxygen and protons and exchange current density. Together, both parameters, f and, determine the overall effectiveness of catalyst utilization. 

Note that in either case, the reaction penetration depth is proportional to the poor transport coefficient, and it is inversely proportional to the cell current density (cf. Equations 1.86 and 1.87). 

Note that both Ip and Id are independent of the exchange current density f. Physically, the dependence on f appears in the problem if both Ip and Id are much larger than Icl- This case corresponds to a small current regime discussed in the section Small Cell Current Density. If one of Id and Ip is less than Icl, the ratedetermining process is the transport of the respective reactant, and the reaction penetration depth is independent of the catalyst active surface, which is incorporated in/. 

This chapter will cover major topics of CL research, focusing on (i) electrocatalysis of the ORR, (ii) porous electrode theory, (iii) structure and properties of nanoporous composite media, and (iv) modern aspects in understanding CL operation. Porous electrode theory is a classical subject of applied electrochemistry. It is central to all electrochemical energy conversion and storage technologies, including batteries, fuel cell, supercapacitors, electrolyzers, and photoelectrochemi-cal cells, to name a few examples. Discussions will be on generic concepts of porous electrodes and their percolation properties, hierarchical porous structure and flow phenomena, and rationalization of their impact on reaction penetration depth and effectiveness factor. 

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