Single-Phase Perovskite Membranes

Equation (14.7) can be rewritten into Eq. (14.8) by decomposing the electrochemical potential into the chemical and electrical potential terms, that is, 

Solution of Eq. (14.9) requires knowledge of the electrostatic potential gradient, which is provided by the Gauss equation  

Since for ceramics the relative permittivities are small (fr = 10), Eq. (14.10) can be replaced by a strict imposition of charge neutrality at each point of the membrane  

The net current density, hot, within the membrane is obtained by adding the partial current densities over all the N species. In the absence of electrodes or an external circuit, 4ot = 0 (open circuit)  

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Figure 14.1 (a) O2 and (b) H2 semipermeation within single-phase perovskite membranes, and (c) chemical activity profile in the presence of a pressure gradient. In this representation, and fifp indicate the chemical potential of the permeating gas (/ = 02, H2) at... 

Equations (14.14) and (14.18) can be used as starting point for generating equations describing O2 and H2 permeation within single-phase perovskite membranes. Key to these equations is the nature of the boundary conditions at the feed/membrane and permeate/membrane surfaces. To this aim, one needs to address appropriate defect point thermodynamics to establish equilibrium and surface exchange relations for all potential species that can play a role during permeation. As a general rule, the law of mass action can be used to predict the concentration of ionic vacancies, protons, electrons, and electron holes in the membrane. Below we describe a series of models that can be deduced for ID steady-state permeation within perovskite and extensively other MIEC membranes. 

Assuming that surface exchange (Eqs. (14.57) and (14.59)) and bulk diffusion (Eq. (14.58)) for H2 permeation show a comparable resistance to the overall mass transfer, a generalized equation can be obtained by assirniing that ionic conductivity rules the charge transfer within the membrane, and the proton diffusion coefficient is constant. An expression similar to Eq. (14.55) for H2 permeation within the single-phase perovskite membranes can be proposed [44] ... 

Of gallium, chromium and titanium B-site cations, only galhum perovskites have substantial oxygen-ion conductivity. Therefore, if chromium or titanium are used as part of a single-phase mixed electronic-ionic conducting membrane, they need to be used in conjunction with iron or small amounts of cobalt [26]. GaUium perovskites, while possessing potential for excellent ionic conductivity, do not have sufficient electronic conductivity and need the addition of iron, cobalt or chromium. 

The development of high-temperature membrane solutions for CO2 capture relying on perovskite membranes requires a proper description of mass transfer within the membranes. To this aim, this chapter provides a compilation of models accounting for mass transfer within single- and dual-phase membranes, as... 

DPMs can also be formulated as composite materials. In this concept, the contact of the two phases at the nanoscale provides materials with improved ionic and electronic conductivities. Examples of composite DPMs encompass the combination of two perovskite and fluorite phases for oxide ion conduction, the latter usually relying on the formula Cei >,Y >,02-5 (Y = Gd, Sm) [11-14]). Perovskites can also be hybridized with metal phases or cermets (most often based on Ni) for promoting the electronic conductivity and stability of cerates for H2 permeation [15-18]. Mass transfer within this membrane family can be described using either a unified permeation model for the two phases as for single-phase membranes or by including the contribution of each phase (Figure 14.2d). 

Figure 39.5 Permeance versus permeability representations for O2 transport within membranes based on single- and dual-phase Co-containing perovskites (PVK-Co and PVK-DF-Co), single- and dual-phase Co-free perovskites (PVK-Co-free and PVK-DF-Co) and...

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