The Surface Exchange Coefficient

The oxygen surface exchange coefficient, k, is another important kinetic parameter associated with the measurement of oxygen transport rates in these oxide materials. It is a measure of the neutral oxygen exchange flux crossing the surface of the oxide, at equilibrium, as described by the following 

This flux will be dependent upon the surface vacancy concentration, the surface electron concentration, and the dissociation rate of the dioxygen molecule however, at present, the rate-limiting step has yet to be identified. Kilner et al. [11] have derived a simple relationship for the surface exchange coefficient in terms of the bulk and surface vacancy concentrations, in an attempt to explain the apparent correlation found between the activation enthalpy for the surface exchange coefficient and the diffusion coefficient, in a number of La-based perovskites. Adler et al. [12] have also arrived at a similar relationship for k, by consideration of the AC electrode behavior of symmetrical cells with a double cathode structure. As already mentioned, the exact mechanisms of oxygen surface exchange remain elusive however, the vacancy concentration is clearly a very important parameter. 

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For this estimate, values for the surface diffusion coefficient (D) and the surface exchange coefficient (i) in eq 2 were obtained by linearizing Mitterdorfer s rate expressions for surface transport and adsorption/desorption (ref 84) and re-expressing in terms of the driving forces in eq 2. 

Fig. 6.5 Oxygen permeation flux through LSFG/5M membrane versus oxygen partial pressure on air side for different temperatures lep) and corresponding values of the surface exchange coefficient calculated with Eq. 6.3 (right)...

The surface exchange coefficient or oxygen transfer coefficient k, which describes the kinetics of surface oxygen exchange at the gas-solid interface. 

Table 14.3 compiles a selection of published results on O2 dififusion and surface exchange coefficients in perovskites and perovskite membranes. The last two rows of the table include H2 diffusion and surface exchange coefficients. As can be inferred from Table 14.3, the vacancy diffusion in perovskites falls into the range of 2 X 10 -2 x 10 m /s, whereas the surface exchange coefficients show a broad variety of values depending on the perovskite composition and on the presence of secondary phases. 

The group of Carter and Steele [13] has developed the isotopic 02/ 02 exchange-diffusion profile (lEDP) technique, which allows estimating the surface exchange coefficient k and the diffusion coefficient D [14,15]. This technique is based on surfece thin film analysis by secondary ion mass spectrometry (SIMS) measuring a three-dimensional mapping of the distribution [16-18]. 

These boundary conditions wiU usually include an initial condition, a symmetry condition and a surface flux condition that will depend upon the surface exchange coefficient and a surface, a surface rate constant controlling the rate of exchange between the tracer in the solid and the tracer in the surrounding atmosphere. The tracer diffusion coefficient is related to the diffusion coefficient through a correlation factor or the Haven ratio (the tracer diffusion coefficient is equal to the diffusion coefficient divided by the Haven ratio). 

The constant K, should thus not be confused with the surface exchange coefficient defined by Equation (14.21). Both parameters have the same dimension (cm s ) A general method of regression analysis of data from relaxation experiments using the linear rate law for the surface reaction has been given. Other empirical rate laws for the surface exchange reaction have been proposed by Dovi et al. and Gesmundo et al. °... 

In general, the factors that can sustain the activity and stability of ceria-based electrocatalysts in SOFCs seem to be (i) the flux of oxide ions through the electrolyte (indirectly from the reduction of O2 to 20 at the cathode) (ii) the release of latdce oxide ions from the ceria phase (related to the surface exchange coefficient) (iii) the microstructure of the electrode (electrocatalysts) or the microstructure of the supporting backbone for infiltrated electrocatalysts (iv) current collection or electronic conductivity of the backbone structure and to some extent in the ceria phase as well. 

A cations and one B cation [48]. Furthermore, it has been observed that correlations exist between measured transport parameters, e.g., the relationship between the self-diffusion coefficient and the surface exchange coefficient [11],... 

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