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The ceramic materials exhibiting MIEC properties that are considered for constituting OTMs because of their good O₂ permeation properties are known since the 1970s [35–37]. OTMs typically consist of dense layer(s) of multimetallic oxides comprising alkali, alkali earth, rare earth, or transition metals together in the same crystalline structure. The O₂ permeation through a ceramic membrane comprises several steps, which are depicted in Figure 3.4a,b.

As can be seen in Figure 3.4a,b, O₂ permeation depends on two main processes: oxygen bulk diffusion (step 5) and oxygen surface reactions (steps 2–4 and 6–8). Figure 3.4c depicts O₂‐bulk diffusion through oxygen vacancies in the material's cristal lattice. Typically, O₂ permeation is described by using Wagner's equation (Eq. (3.4))

(3.4)

where J(O₂) is the O₂ flux through the membrane, R is the gas constant, T is the temperature, F is Faraday's constant, L is the membrane thickness, pO₂″ and pO₂′ stand for the O₂ partial pressures at feed and permeate sides, respectively, and σ_el and σ_ion are the electronic and ionic conductivities of the considered membrane material, respectively. Wagner's equation describes the O₂ permeation through the material bulk (step 5 in Figure 3.4a,b), when the membrane is thicker than the value known as the characteristic thickness L_c [38], which is distinctive of every material.

Figure 3.4 (a, b) Steps involved in the oxygen permeation through an oxygen transport membrane and (c) representation of the oxygen anion diffusion through the oxygen vacancies present in a perovskite's crystal lattice and (d) fracture cross.

Source: (c) Bouwmeester and Burggraaf [38].

For thinner membranes and for temperatures typically lower than 800 °C, J(O₂) does not depend on O²⁻ bulk diffusion but on oxygen surface exchange kinetics. These surface reactions involve a number of steps that may include O₂ adsorption, O₂ dissociation into O²⁻ and electrons, charge transfer, surface diffusion of intermediate species, and finally O²⁻ incorporation into the material crystal lattice [39, 40]. A general expression for describing J(O₂) can be obtained by assuming linear kinetics of the relevant rate laws when both surface exchange reactions and bulk diffusion are governing the O₂ permeation and then J(O₂) [41] can be expressed by means of the following expression:

(3.5)

where is the total O₂ chemical potential difference across the membrane.

Therefore, the O₂ permeation of an OTM depends on temperature, membrane thickness, pO₂ gradient between the two membrane sides, and the MIEC properties of the considered material. Then, higher O₂ fluxes can be achieved by operating at higher temperatures and larger pO₂ gradients (use of pressurized feeding or high vacuum or sweeping flows), by using thinner membranes (material brittleness will require the use of porous supports for ensuring mechanical stability as depicted in Figure 3.4d where a thin supported membrane is shown) and by selecting materials with high ionic and electronic conductivities.

The most considered materials for being used as OTMs are those with perovskite and fluorite crystal structures [38]. In addition to these materials, other compounds that also exhibit interesting properties are pyrochlore (A₂B₂O₇), brownmillerite (A₂B₂O₅), Ruddlesden–Popper series (A_n+1B_nO_3n+1), orthorhombic K₂NiF₄‐type structure materials, and Sr₄Fe_6−xCo_xO₁₃ [42–45]; nevertheless, the performance of this materials is very low in comparison with fluorites and perovskites. Among the mentioned structures, the perovskite with composition Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCF) is that presenting the highest O₂ permeation up to date, achieving an O₂ production of up to 67.7 ml min⁻¹ cm⁻² at 1000 °C for a 70 μm thick membrane [46]. Nevertheless, the unpractical stability under certain environments (especially when exposed to CO₂ atmospheres) makes BSCF‐based membranes unsuitable for most of the industrial applications if a direct contact between flue gases and membranes is considered. Fluorites, on the contrary, exhibit outstanding chemical and mechanical stability when exposed to oxyfuel and reaction atmospheres, but their low electronic conductivity averts them for being considered for practical applications because of the low O₂ permeation performance. One solution is then the use of dual‐phase structures consisting of a mixture of ionic‐conductive and electronic conductive materials. These materials with good O₂ permeation and stability when subjected to harsh environments have attracted a lot of interest within the past years in studies focused on oxyfuel applications [47–51], achieving interesting O₂ fluxes of c. 3 ml min⁻¹ cm⁻² at 925 °C under full CO₂ environments [51].