Mixed conduction model

A deterministic model for corrosion under SCW conditions was developed based on the model for oxide film growth on stainless steels in high-temperature, high-pressure aqueous environments proposed by Bojinov et al. [70—74]. The mixed conduction model (MCM) emphasizes the coupling between ionic and electronic defects in quasisteady-state passive films. It allows determination of the electronic properties of the oxide layer, the main kinetic and transport parameters needed to calculate the steady-state current density, the oxide film impedance response, and the thickness versus time relationship on many alloys. Such a model can provide insights into the effects of alloying elements on SCW oxidation resistance [70,75]. 

I. Betova, M. Bojinov, P. Kinnunen, K. Lundgren, T. Saario, Mixed-conduction model for stainless steel in a high-temperature electrolyte estimation of kinetic parameters of inner layer constituents, J. Electrochem. Soc. 155 (2) (2008) C81—C92. 

M. Bojinov, G. Fabricius, P. Kinnunen, T. Laitinen, K. Makela, T. Saario, G. Sundholm, Electrochemical study of the passive behaviour of Ni-Cr alloys in a borate solution — a mixed conduction model approach, J. Electroanal. Chem. 504 (1) (2001) 29-44. 

Figure 24. Models illustrating the source of chemical capacitance for thin film mixed conducting electrodes, (a) Oxygen reduction/oxidation is limited by absorption/de-sorption at the gas-exposed surface, (b) Oxygen reduction/ oxidation is limited by ambipolar diffusion of 0 through the mixed conducting film. The characteristic time constant for these two physical situations is different (as shown) but involves the same chemical capacitance Cl, as explained in the text.

Figure 25. Adler s ID macrohomogeneous model for the impedance response of a porous mixed conducting electrode. Oxygen reduction is viewed as a homogeneous conversion of electronic to ionic current within the porous electrode matrix, occurring primarily within a distance A from the electrode/electrolyte interface (utilization region). (Adapted with permission from ref 28. Copyright 1998 Elsevier.)...

One limit of behavior considered in the models cited above is an entirely bulk path consisting of steps a—c—e in Figure 4. This asymptote corresponds to a situation where bulk oxygen absorption and solid-state diffusion is so facile that the bulk path dominates the overall electrode performance even when the surface path (b—d—f) is available due to existence of a TPB. Most of these models focus on steady-state behavior at moderate to high driving forces however, one exception is a model by Adler et al. which examines the consequences of the bulk-path assumption for the impedance and chemical capacitance of mixed-conducting electrodes. Because capacitance is such a strong measure of bulk involvement (see above), the results of this model are of particular interest to the present discussion. 

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

Figure 28. Svensson s macrohomogeneous model for the i— 1/characteristics of a porous mixed-conducting electrode, (a) The reduction mechanism assuming that both surface and bulk diffusion are active and that direct exchange of oxygen vacancies between the mixed conductor and the electrolyte may occur, (b) Tafel plot of the predicted steady-state i— V characteristics as a function of the bulk oxygen vacancy diffusion coefficient. (Reprinted with permission from ref 186. Copyright 1998 Electrochemical Society, Inc.)...

Several models have been proposed to estimate the thermal conductivity of hydrate/gas/water or hydrate/gas/water/sediment systems. The most common are the classical mixing law models, which assume that the effective properties of multicomponent systems can be determined as the average value of the properties of the components and their saturation (volumetric fraction) of the bulk sample composition. The parallel (arithmetic), series (harmonic), or random (geometric) mixing law models (Beck and Mesiner, 1960) that can be used to calculate the composite thermal conductivity (kg) of a sample are given in Equations 2.1 through 2.3. 

M.H.R. Lankhorst and H.J.M. Bouwmeester, Determination of oxygen nonstoichiometry and diffusivity in mixed conducting oxides by oxygen coulometric titration. Part 11 Oxygen nonstoichiometry and defect model for Lao.8Sro.2Co03-8. J. Electrochem. Soc. submitted... 

There are many examples of PK/PD exposure-response analyses conducted subsequent to population PK model development using a traditional statistical package such as SAS (8) either with or without the use of a mixed effects model (9-11). As Yano et al. (12) have demonstrated in their simulations, this approach may be perfectly adequate in many circumstances and the assumed gain in precision of the fixed effect estimates through the use of a mixed effects model is either marginal... 

The objective of this analysis was to integrate all of the above information for making a hnal recommendation on optimal therapeutic dose of Botani. Nonlinear mixed effects modeling analyses were conducted only on dose-response data from study 2 because of its completeness at multiple dose levels and larger number of subjects. A total of 374 subjects with 1816 observations were included in the data analyses. An inhibitory effect model describes the response-time relationship (at a given... 

Despite this, PPC is inherently suited for nonlinear mixed effect modeling of pharmacokinetic data as it utilizes the posterior distribution of parameter estimates to examine whether the salient features of the original data are observed in the derived (replicated) data. Berin and Rubin applied this approach to mixture models of reaction time based on visual tracking experiments conducted in patients with and without schizophrenia. Their application of PPC was directed in the modelbuilding stage and not implemented to validate their final model per se. This technique has appeal in both settings as it can serve as a metric in the establishment of a credible model. 

Although a variety of protonceramic materials has been found in the past decade, only very limited studies have dealt with experimental measurements of H2 flux, and little effort has been made to model the experimentally measured data in these studies. H2 permeation flux data on more perovskite-based membranes are needed so that the mathematical models can be verified with experimental data. Such models, when rigorous and accurate, can provide essential guidance in the design and understanding of the mixed conducting materials. Fundamental study should be conducted to understand the stractural,... 

What is clearly needed is a working model for multicomponent, mixed-conducting electrolytes, one which would be applicable to closed as well as open circuit conditons and yet would be relatively... 

A. Haffehn, J. Joos, M. Ender, et al., Time-Dependent 3D Impedance Model of Mixed-Conducting Solid Oxide Fuel Cell Cathodes, Journal of the Electrochemical Society, vol. 160, no. 8, F867-F876, 2013. 

Formal Graph An isolated moving body with an inductance (the inertial mass) and with a conductance (modeling the friction) constitutes a mixed pole in the Formal Graph theory. 

Wade J L and Lackner K S (2007), Transport model for a high temperature, mixed conducting CO2 separation membrane , 5o/t[Pg.603]

It is important to note that the geometry associated with porous electroplated coatings can result in significant deviation from the uniform potential distribution associated with the simple mixed potential model described above [9]. In reality, the distributed nature of the pores may yield a highly nonuniform potential distribution. Furthermore, the occluded geometry of the pores, like that associated with pitting corrosion, may result in local solution chemistry markedly different from that of the bulk electrolyte. Likewise, the conductivity of the electrolytic medium is also... 

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