Gas Permeation Models for Perovskite Membranes

The conductivity in perovskites is a direct function of the concentration of ionic species, especially vacancies, Q, and the concentration of mobile electrons, n, and holes, p, available in the material. The concentration of vacancies is often related to the crystal structure of the material, whereas the electronic bandgap conditions to the concentration of mobile electrons and holes. Overall, the total conductivity of a perovskite, 7t can be expressed as follows  

The conductivity can in turn be expressed as a function of the solid-state diffusion coefficient D for each conductive species through the Nernst-Einstein relation  

Noteworthy, for species that migrate with mechanisms different from diffusion (i.e., itinerant electrons and holes), the diffusion coefficient is undefined, and instead one uses mobilities with temperature dependencies typical of polaron-limited transport, involving electron hopping between cations with different valence states. 

In the case of vacancy diffusion, the conductivity can be expressed as follows  

Knowing that there are three oxygen sites per unit cell in a perovskite, the lattice oxygen ion concentration can be directly linked to the vacancy concentration  

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In Section 14.3 we concentrate our attention on the formulation of equations for modeling gas semipermeation within perovskite membranes for high-tem-perature CO2 capture applications. In such derivations, we assume that external diffusion at both the feed/membrane and permeate/membrane sides of the membrane (steps 1 and 2, respectively) can be neglected. In such a situation, bulk diffusion (step 3) and surface exchange kinetics (steps 2 and 4) are expected to contribute only to the permeation process. 

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