Surface Exchange Model for MIEC Membrane in Transient Stage
Usually, to model, the membrane is divided into three zones: the bulk, where oxygen bulk diffusion takes place and the two surfaces where oxygen exchanges between atmosphere and membrane take place. Oxygen bulk diffusion is well described by the Wagner theory . The surface exchanges include the adsorption/desorption, dissociation/association and incorporation/exclusion of oxygen. A consensus has not yet emerged regarding the oxygen surface exchange models proposed in the literature. Two categories of models are reported: one corresponds to an extension of the Wagner theory to the surface  and the second corresponds to a chemical approach by kinetic laws [1, 5].
Different experiments have been performed to characterize the surface exchange and bulk diffusion parameters. The measures reported by Geffroy et al. on membrane surfaces during steady oxygen flow exhibits a large chemical potential gap between the membrane surfaces and the surrounding gases . From our knowledge, this experimental data cannot be reproduced by a single model from literature. Moreover, although the combination of Wagner extension approach on the high oxygen side and kinetic approach on the low oxygen side makes it possible to reproduce results in steady state, it does not allowed to investigate transient stage.
The proposed talk deals with a new macroscopic surface exchange model describing both oxidizing and reducing surface for transient stage. This model assumes that the oxygen flow is governed by the association/dissociation of adsorbed oxygen and by the high energetic cost of oxygen reduction/oxidation. Then, the balance of a transient species at the membrane surface is introduced to account for these two phenomena. The first results obtained are in accordance with oxygen semi-permeation measurements reported by Geffroy et al. . The computation of isothermal expansion tests realized by Adler  in transient stage, using the proposed exchange model and the chemical expansion model proposed by Valentin et al. , present also a good correlation with experimental results.
 S.B. Adler et al, Mechanisms and rate laws for oxygen exchange on mixed-conducting oxide surfaces, J Catal, (245), 91-109, 2007.
 O. Valentin et al, Chemical expansion of La0.8Sr0.2Fe0.7Ga0.3O3-δ, Solid State Ionics, (193), 23-31, 2011.
 C. Wagner, Equations for transport in solid oxides and sulfides of transition metals, Prog Solid State Ch, (10), 3-16, 1975.
 H.J.M. Bouwmeester et al, Importance of the surface exchange kinetics as rate limiting step in oxygen permeation through mixed-conducting oxides, Solid States Ionics, (72), 185-194, 1994.
 S. J. Xu et al, Oxygen permeation rates through ion-conducting perovskite membranes, Chem Eng Sci, (54), 3839-3850, 999.
 P.M. Geffroy et al, Influence of oxygen surface exchanges on oxygen semi-permeation through La(1-x)SrxFe(1-y)GayO3-δ dense membrane, J Electrochem Soc, (158), 1-9, 2011.
 S.B. Adler, Chemical expansivity of electrochemical Ceramics, J. Am. Ceram. Soc., (84), 2117-2119, 2004.
 O. Valentin et al., Thermo-Chemo-Mechanical Modelling of Mixed Conductors in Transient Stages, Adv. Sci. Rech., (65), 232-237, 2010.