Non-Stoichiometric Redox Active Perovskite Materials for Solar Thermochemical Fuel Production: A Review

: Due to the requirement to develop carbon-free energy, solar energy conversion into chemical energy carriers is a promising solution. Thermochemical fuel production cycles are particularly interesting because they can convert carbon dioxide or water into CO or H 2 with concentrated solar energy as a high-temperature process heat source. This process further valorizes and upgrades carbon dioxide into valuable and storable fuels. Development of redox active catalysts is the key challenge for the success of thermochemical cycles for solar-driven H 2 O and CO 2 splitting. Ultimately, the achievement of economically viable solar fuel production relies on increasing the attainable solar-to-fuel energy conversion efﬁciency. This necessitates the discovery of novel redox-active and thermally-stable materials able to split H 2 O and CO 2 with both high-fuel productivities and chemical conversion rates. Perovskites have recently emerged as promising reactive materials for this application as they feature high non-stoichiometric oxygen exchange capacities and diffusion rates while maintaining their crystallographic structure during cycling over a wide range of operating conditions and reduction extents. This paper provides an overview of the best performing perovskite formulations considered in recent studies, with special focus on their non-stoichiometry extent, their ability to produce solar fuel with high yield and performance stability, and the different methods developed to study the reaction kinetics.


Introduction
World energy requirements are still increasing, and fossil fuels combustion contributes to global warming. Currently, most of the world energy production comes from fossil fuels and nuclear. Fossil fuels are limited resources and their combustion produces carbon dioxide which contributes to the greenhouse effect. By contrast, nuclear energy does not produce CO 2 but radioactive waste whose treatment is very expensive [1]. In this context, solar energy is a valuable solution as it is free, inexhaustible, and does not produce CO 2 emissions. However, solar energy is intermittent, variable, and diffuse. With this in mind, thermochemical cycles using concentrated solar energy permit to convert solar energy into chemical fuels, which can be used on demand, stored, and transported. Thermochemical cycles based on metal oxides encompass two steps. First, a solar-activated thermal reduction (TR) of the material at high temperature creates oxygen vacancies in the oxide lattice, producing O 2 , as represented by the reaction (1). Concentrated solar energy can be used as the external source of high temperature heat to drive the reaction. The second step is an exothermic reaction, in which the material is re-oxidized by H 2 O or CO 2 , represented by the reactions (2a) and (2b), respectively. The hydrogen product can be directly used as a fuel (e.g., in fuel cells), whereas syngas (mixture of H 2 /CO) can be converted into synthetic liquid hydrocarbon fuels via the Fischer-Tropsch process [2]. The metal oxide is not consumed in the overall H 2 O and CO 2 splitting process, and thus, acts as a catalyst in the global reaction.
However, thermochemical cycles currently exhibit low efficiency which prevents commercial use in the short term. To date, the highest solar-to-fuel energy conversion efficiency has reached 5% for ceria reticulated porous foam [3], while the efficiency should at least be of 20% to permit industrialization and to compete with photovoltaic technology combined with electrolysis [4]. In the aim of increasing the efficiency, both the solar reactor thermal efficiency and the material fuel productivity can be improved. Improving the overall process efficiency requires increasing the fuel production yields and rates while decreasing the operating temperature to reduce heat losses. In addition, the reactive materials used in thermochemical cycles should be thermally-stable in order to keep a stable production over repeated redox cycles. Among the investigated candidate materials, ceria has been extensively studied for thermochemical cycles due to several desirable thermodynamic and physico-chemical properties. Ceria (CeO 2 ) is able to maintain its crystal structure over a large range of non-stoichiometry and operating conditions. It exhibits rapid reaction kinetics and fast oxygen diffusion rates, which promotes the reversible phase transitions between the oxidized and partially reduced states in a large range of non-stoichiometry. However, it requires a high reduction temperature to produce substantial reduction extent due to high enthalpy change. The high reduction temperature induces sintering and reactor materials issues, and thus limits the practical use of ceria. Different dopants were investigated to increase fuel production while lowering the reduction temperature, like Li 2+ , Mg 2+ , Sc 3+ , Dy 3+ , La 3+ , Sm 3+ , Gd 3+ , Pr 3+ , Hf 4+ , and Zr 4+ [5][6][7][8][9][10][11][12][13][14], at the expense of lowering the oxidation rate. In spite of the numerous dopants investigated, the relatively low fuel productivity of ceria still limits its future implementation in large-scale processes [5]. Recently, perovskite-structured materials have emerged as promising candidate catalysts for high-temperature thermochemical fuel production [6]. Highly reducible and thermally-stable perovskites with high oxygen exchange and transport properties have been proposed [15][16][17]. The theoretical materials performance is ruled by thermodynamics, but in reality, another limitation to the final fuel production achieved is related to reaction kinetics. In this paper, the first section describes the redox system thermodynamics, then the perovskite formulations that were studied in thermochemical cycles are summarized, and finally the methods used to study the perovskites redox reaction kinetics are described.

Thermodynamics of Thermochemical Cycles
Investigating perovskite thermodynamics allows predicting the theoretical maximum fuel production that can be reached in thermochemical cycles, as a function of reduction and oxidation temperatures and partial pressure of oxygen. In order to achieve spontaneous reactions, it is required to satisfy criteria (3) and (4), where ∆G • represents the standard Gibbs free enthalpy variation, P O 2 the oxygen partial pressure, T the temperature, and the subscripts TR, WS, and CDS refer to the thermal reduction, the water splitting, and the carbon dioxide splitting, respectively [16]. The Figure 1 represents the Gibbs free energy in standard conditions for CO 2 splitting and for La 0.6 Sr 0.4 MnO 3 during the reduction and oxidation steps. The Gibbs free energy of the reduction reaction is computed with values of ∆H • and ∆S • found in the literature [18]. Concerning the CO 2 splitting, its Gibbs free energy comes from the thermochemical database of HSC chemistry software. The Gibbs free energy of oxidation corresponds to the difference between the Gibbs free energies of CO 2 splitting and of La 0.6 Sr 0.4 MnO 3 reduction. It can be seen that the thermal reduction is favorable for temperature higher than T high and the oxidation step is promoted for temperature lower than T low [8]. and of La0.6Sr0.4MnO3 reduction. It can be seen that the thermal reduction is favorable for temperature higher than Thigh and the oxidation step is promoted for temperature lower than Tlow [8].
Δ ° ( , , ) < 0 Δ ° ( , , ) < −Δ ° ( , , ) Δ ° ( , , ) < −Δ ° ( , , ) (4b) Figure 1. Schematic plot of the Gibbs energy for carbon dioxide splitting, water splitting, and twostep thermochemical redox cycling of La0.6Sr0.4MnO3 in standard conditions. The Gibbs energy variation for the reduction and the oxidation steps are defined by Equations (5) and (6), respectively, whereas Equations (7) and (8) define the enthalpy and entropy variation of the overall cycle; where Δ and  correspond to the standard enthalpy and entropy variation, is the temperature during the WS or TR reaction. From the Equation (6), the oxidation step is exothermic because the oxidation step is entropically unfavorable and the two steps have to be exergonic. Due to Δ < 0, Δ has to be at least higher than Δ in order to have Δ > Δ [19][20][21]. At non-standard pressures, the effect of oxygen partial pressure on the entropy variation can be expressed as Equation (9), where ° is the reference pressure: The enthalpy variation can be considered as pressure-independent, which conducts to express the Gibbs free enthalpy variation in non-standard pressures, as Equation (10) [22].
When the reduction step is at equilibrium, the Gibbs free enthalpy is nil which allows writing the Equation (5) in the form of Equation (11) for a given value of . The Gibbs energy variation for the reduction and the oxidation steps are defined by Equations (5) and (6), respectively, whereas Equations (7) and (8) define the enthalpy and entropy variation of the overall cycle; where ∆H and ∆S correspond to the standard enthalpy and entropy variation, T i is the temperature during the WS or TR reaction. From the Equation (6), the oxidation step is exothermic because the oxidation step is entropically unfavorable and the two steps have to be exergonic. Due to ∆H WS < 0, ∆H TR has to be at least higher than ∆H CO 2 in order to have ∆H cycle > ∆H CO 2 [19][20][21]. At non-standard pressures, the effect of oxygen partial pressure on the entropy variation can be expressed as Equation (9), where P • is the reference pressure: The enthalpy variation can be considered as pressure-independent, which conducts to express the Gibbs free enthalpy variation in non-standard pressures, as Equation (10) [22]. When the reduction step is at equilibrium, the Gibbs free enthalpy is nil which allows writing the Equation (5) in the form of Equation (11) for a given value of δ.
The oxygen non-stoichiometry is plotted in Figure 2 as a function of the logarithm of the oxygen partial pressure at different temperatures. Then, it is possible to plot the logarithm of the oxygen partial pressure as a function of the inverse of temperature for a constant δ value, and to determine both ∆H red and ∆S red via Equation (11) [6]. For the oxidation step, the contribution of the amount of oxidant gas can be expressed as in Equation (12), where P CO , P CO 2 P H 2 and P H 2 O are the carbon monoxide, carbon dioxide, hydrogen and steam partial pressure, respectively [22]. From Equation (12), it can be evidenced that the increase of the oxidant gas ratio tends to decrease ∆G WS which favors the oxidation reaction. However, increasing the oxidant gas in excess amount may negatively impact the thermochemical cycle efficiency, due to the low conversion yield of the oxidant gas to the splitting products.
Thus, an ideal redox material must have a low enthalpy variation ∆H • red which permits to increase the reduction extent at a lower temperature. In contrast, a high entropy variation ∆S • red is required, thereby allowing smaller temperature variation between the reduction and the re-oxidation steps, which is critical for overall efficiency [6]. The Gibbs free enthalpy variation can be adjusted by changing the operating conditions (lower oxygen partial pressure or oxidant excess) but this induces energy penalty.
The oxygen non-stoichiometry is plotted in Figure 2 as a function of the logarithm of the oxygen partial pressure at different temperatures. Then, it is possible to plot the logarithm of the oxygen partial pressure as a function of the inverse of temperature for a constant value, and to determine both and via Equation (11) [6]. For the oxidation step, the contribution of the amount of oxidant gas can be expressed as in Equation (12), where , and are the carbon monoxide, carbon dioxide, hydrogen and steam partial pressure, respectively [22]. From Equation (12), it can be evidenced that the increase of the oxidant gas ratio tends to decrease Δ which favors the oxidation reaction. However, increasing the oxidant gas in excess amount may negatively impact the thermochemical cycle efficiency, due to the low conversion yield of the oxidant gas to the splitting products.
Thus, an ideal redox material must have a low enthalpy variation Δ ° which permits to increase the reduction extent at a lower temperature. In contrast, a high entropy variation Δ ° is required, thereby allowing smaller temperature variation between the reduction and the re-oxidation steps, which is critical for overall efficiency [6]. The Gibbs free enthalpy variation can be adjusted by changing the operating conditions (lower oxygen partial pressure or oxidant excess) but this induces energy penalty. Oxygen non-stoichiometry of La0.6Sr0.4MnO3 as a function of the logarithm of oxygen partial pressure at different temperatures (adapted from Reference [23]). Pressure-swing vs. temperatureswing thermochemical pathways: isothermal cycle at 1400 °C with pressure swing operation between A and A', two-temperature cycling with quenching (A to C), oxidation at 1000 °C (C to D) and reduction at 1400 °C (D to A) [24].

Perovskite Formulations Investigated for Thermochemical Cycles
Since a few years ago, perovskites have been investigated for solar fuel production from thermochemical cycles [25]. Perovskites have the general formula ABO3, where A and B are cations. The A cation is 12-fold coordinated with oxygen and it is larger than the B cation. The latter is 6-fold coordinated with oxygen anion. Ideal perovskites present a cubic structure with space group Pm3m, as represented in Figure 3 [26]. Different elements can occupy the A and B sites of the perovskite according to their ionic radius. The ionic radius of the A cation is comprised between 1.10 and 1.80 Å, whereas the ionic radius of the B cation is comprised between 0.62 and 1.00 Å [17]. The Goldschmidt tolerance factor (Equation (13)) determines whether the perovskite structure can be  [23]). Pressure-swing vs. temperature-swing thermochemical pathways: isothermal cycle at 1400 • C with pressure swing operation between A and A', two-temperature cycling with quenching (A to C), oxidation at 1000 • C (C to D) and reduction at 1400 • C (D to A) [24].

Perovskite Formulations Investigated for Thermochemical Cycles
Since a few years ago, perovskites have been investigated for solar fuel production from thermochemical cycles [25]. Perovskites have the general formula ABO 3 , where A and B are cations. The A cation is 12-fold coordinated with oxygen and it is larger than the B cation. The latter is 6-fold coordinated with oxygen anion. Ideal perovskites present a cubic structure with space group Pm3m, as represented in Figure 3 [26]. Different elements can occupy the A and B sites of the perovskite according to their ionic radius. The ionic radius of the A cation is comprised between 1.10 and 1.80 Å, whereas the ionic radius of the B cation is comprised between 0.62 and 1.00 Å [17]. The Goldschmidt tolerance factor (Equation (13)) determines whether the perovskite structure can be formed according to the ionic radii. In this equation, r A , r B , and r O are the ionic radii of cation A, cation B, and oxygen anion, respectively. This factor has to be close to one, so that the perovskite can be formed and equals one in the case of an ideal perovskite structure. Rhombohedral perovskites can be formed if t is approximately greater than 1.02. Orthorhombic and tetragonal perovskites can be formed if t < 1.
The large non-stoichiometry of perovskites is a very interesting property for thermochemical cycles [27]. Due to the large number of dopant insertion options (27 possibilities for the A site and 35 possibilities for the B site), their composition can be tuned to optimize fuel production [28,29]. formed according to the ionic radii. In this equation, , , and are the ionic radii of cation A, cation B, and oxygen anion, respectively. This factor has to be close to one, so that the perovskite can be formed and equals one in the case of an ideal perovskite structure. Rhombohedral perovskites can be formed if is approximately greater than 1.02. Orthorhombic and tetragonal perovskites can be formed if < 1.
The large non-stoichiometry of perovskites is a very interesting property for thermochemical cycles [27]. Due to the large number of dopant insertion options (27 possibilities for the A site and 35 possibilities for the B site), their composition can be tuned to optimize fuel production [28,29].

A-site Substituted Materials
Among the lanthanum-manganese perovskites series, the most studied is La1−xSrxMnO3. LaMnO3 presents a very low reduction extent, which prevents the fuel production. The presence of Sr in the A-site increases the oxidation state of Mn, due to the lower charge of Sr 2+ compared to La 3+ . The increase of Mn oxidation state permits to increase the reduction extent. The reduction extent thus increases with the Sr content [23,[30][31][32][33][34][35][36]. In the same conditions, 24 µmol/g of O2 are produced for x = 0.1 versus 215 µmol/g of O2 for x = 0.4. The optimum content for Sr substituting La is comprised between 0.3 and 0. [23,[30][31][32]. The increase of Sr content adversely affects the re-oxidation yield. Demont and Abanades reported a re-oxidation yield of 92% with 35% Sr content, decreasing to 14% with 80% Sr content (at Tred = 1400 °C and Tox = 1050 °C) [37]. The Figure 4 represents the CO production for different Sr contents in La1−xSrxMnO3, and for undoped and Zr-doped CeO2 as reference materials. All the La1−xSrxMnO3 perovskites present a higher CO production than pure ceria during cycles. La0.5Sr0.5MnO3 presents the highest CO production and can compete with (Ce,Zr)O2 [38]. The use of Sr as dopant in the A-site has also an impact on the grain morphology. A low Sr content favors particle agglomeration whereas crystals have sharp edges with high Sr content [39]. The grain size tends to decrease with the increase of Sr content [30,39]. From a kinetic point of view, the characteristic time, defined as the time required to reach 10% of the peak production rate, is not affected by the Sr content during the reduction step. On the contrary, the characteristic time is strongly increased by the increase of Sr content during the oxidation step [30].

A-Site Substituted Materials
Among the lanthanum-manganese perovskites series, the most studied is La 1−x Sr x MnO 3 . LaMnO 3 presents a very low reduction extent, which prevents the fuel production. The presence of Sr in the A-site increases the oxidation state of Mn, due to the lower charge of Sr 2+ compared to La 3+ . The increase of Mn oxidation state permits to increase the reduction extent. The reduction extent thus increases with the Sr content [23,[30][31][32][33][34][35][36]. In the same conditions, 24 µmol/g of O 2 are produced for x = 0.1 versus 215 µmol/g of O 2 for x = 0.4. The optimum content for Sr substituting La is comprised between 0.3 and 0. [23,[30][31][32]. The increase of Sr content adversely affects the re-oxidation yield. Demont and Abanades reported a re-oxidation yield of 92% with 35% Sr content, decreasing to 14% with 80% Sr content (at T red = 1400 • C and T ox = 1050 • C) [37]. The Figure 4 represents the CO production for different Sr contents in La 1−x Sr x MnO 3 , and for undoped and Zr-doped CeO 2 as reference materials. All the La 1−x Sr x MnO 3 perovskites present a higher CO production than pure ceria during cycles. La 0.5 Sr 0.5 MnO 3 presents the highest CO production and can compete with (Ce,Zr)O 2 [38]. The use of Sr as dopant in the A-site has also an impact on the grain morphology. A low Sr content favors particle agglomeration whereas crystals have sharp edges with high Sr content [39]. The grain size tends to decrease with the increase of Sr content [30,39]. From a kinetic point of view, the characteristic time, defined as the time required to reach 10% of the peak production rate, is not affected by the Sr content during the reduction step. On the contrary, the characteristic time is strongly increased by the increase of Sr content during the oxidation step [30].
The Ca 2+ cation can also be used to substitute lanthanum. La 1−x Ca x MnO 3 has a lower lattice parameter than La 1−x Sr x MnO 3 due to the lower Ca 2+ ionic radius (r Ca 2+ = 1.34 A) than The Ca 2+ cation can also be used to substitute lanthanum. La1−xCaxMnO3 has a lower lattice parameter than La1−xSrxMnO3 due to the lower Ca 2+ ionic radius ( = 1.34 Å) than Sr 2+ ( = 1.58 Å) [40]. The increase of Ca content decreases the lattice parameter due to the increase of the Mn ionic radius induced by the change in the oxidation state. Similarly, to the Sr dopant, Ca permits to increase the reduction extent. Furthermore, this increase is more pronounced than with Sr, because of the larger decrease of the Gibbs' free enthalpy [41][42][43][44]. This can be attributed to the smaller ionic radius of Ca 2+ compared to Sr 2+ [18,[45][46][47]. The substitution of lanthanum by calcium also permits to diminish the reduction temperature [48]. However, a decrease of the re-oxidation yield is reported by Demont and Abanades: substituting La with 35% of Ca results in a re-oxidation yield of 63% which falls to 33% in the same conditions when the amount of Ca is 50% [41]. Furthermore, the CO production is lower when Ca is used as dopant (210 µmol/g) instead of Sr (269 µmol/g) [41,49]. This can be explained by a larger standard Gibbs free enthalpy [41]. In addition, La1−xCaxMnO3 seems more sensitive to the sintering than La1-xSrxMnO3, which can have a negative impact on the oxidation step [50].
Another possible dopant for the A-site in the lanthanum-manganese perovskites is Ba 2+ , leading to the La1-xBaxMnO3 series. The lattice parameter is higher than for La1-xSrxMnO3 perovskite, due to a higher ionic radius of Ba 2+ ( = 1.61 Å) compared to Sr 2+ ( = 1.44 Å). The presence of Ba 2+ does not show any benefic effect on the reduction extent when compared with Sr and Ca dopants. For instance, an O2 production of 203 µmol/g was measured for La0.5Ba0.5MnO3, while Sr and Ca containing materials produced 248 µmol/g and 311 µmol/g, respectively ( Figure 5). Another point is that the re-oxidation yield is also reduced compared with Sr or Ca-doped lanthanum-manganese perovskites [41]. Another possible dopant for the A-site in the lanthanum-manganese perovskites is Ba 2+ , leading to the La 1−x Ba x MnO 3 series. The lattice parameter is higher than for La 1−x Sr x MnO 3 perovskite, due to a higher ionic radius of Ba 2+ (r Ba 2+ = 1.61 A) compared to Sr 2+ (r Sr 2+ = 1.44 A). The presence of Ba 2+ does not show any benefic effect on the reduction extent when compared with Sr and Ca dopants. For instance, an O 2 production of 203 µmol/g was measured for La 0.5 Ba 0.5 MnO 3 , while Sr and Ca containing materials produced 248 µmol/g and 311 µmol/g, respectively ( Figure 5). Another point is that the re-oxidation yield is also reduced compared with Sr or Ca-doped lanthanum-manganese perovskites [41].  The Ca 2+ cation can also be used to substitute lanthanum. La1−xCaxMnO3 has a lower lattice parameter than La1−xSrxMnO3 due to the lower Ca 2+ ionic radius ( = 1.34 Å) than Sr 2+ ( = 1.58 Å) [40]. The increase of Ca content decreases the lattice parameter due to the increase of the Mn ionic radius induced by the change in the oxidation state. Similarly, to the Sr dopant, Ca permits to increase the reduction extent. Furthermore, this increase is more pronounced than with Sr, because of the larger decrease of the Gibbs' free enthalpy [41][42][43][44]. This can be attributed to the smaller ionic radius of Ca 2+ compared to Sr 2+ [18,[45][46][47]. The substitution of lanthanum by calcium also permits to diminish the reduction temperature [48]. However, a decrease of the re-oxidation yield is reported by Demont and Abanades: substituting La with 35% of Ca results in a re-oxidation yield of 63% which falls to 33% in the same conditions when the amount of Ca is 50% [41]. Furthermore, the CO production is lower when Ca is used as dopant (210 µmol/g) instead of Sr (269 µmol/g) [41,49]. This can be explained by a larger standard Gibbs free enthalpy [41]. In addition, La1−xCaxMnO3 seems more sensitive to the sintering than La1-xSrxMnO3, which can have a negative impact on the oxidation step [50].
Another possible dopant for the A-site in the lanthanum-manganese perovskites is Ba 2+ , leading to the La1-xBaxMnO3 series. The lattice parameter is higher than for La1-xSrxMnO3 perovskite, due to a higher ionic radius of Ba 2+ ( = 1.61 Å) compared to Sr 2+ ( = 1.44 Å). The presence of Ba 2+ does not show any benefic effect on the reduction extent when compared with Sr and Ca dopants. For instance, an O2 production of 203 µmol/g was measured for La0.5Ba0.5MnO3, while Sr and Ca containing materials produced 248 µmol/g and 311 µmol/g, respectively ( Figure 5). Another point is that the re-oxidation yield is also reduced compared with Sr or Ca-doped lanthanum-manganese perovskites [41]. Figure 5. (a) O2 production rates derived from thermogravimetric analysis (TGA) data for La0.5Ca0.5MnO3, La0.5Ba0.5MnO3, Y0.5Sr0.5MnO3, and La0.5Sr0.5MnO3, (b) TGA of the same materials during reduction at 1400 °C under Ar, followed by oxidation with CO2 at 1050 °C (two cycles) [41].

B-Site Substituted Materials
As shown previously, lanthanum-manganese perovskites do not show complete re-oxidation. In order to improve the re-oxidation yield, the B-site was doped with aluminum element. The presence of Al also permits to increase the reduction extent [18,41,45,[50][51][52] In the case of (La,Sr)MnO 3 perovskites, the presence of Al 3+ cation in the B-site permits to increase the reaction kinetics. The introduction of Al 3+ in the structure leads to strong atomic interaction due to the decrease of the unit cell volume, which leads to a better stability. Nevertheless, it also diminishes the amount of Mn cation, thus reducing the redox capacity [53]. In addition, reduction of La 1−x Sr x Mn 1−y Al y O 3 has an onset temperature 300 • C, lower than CeO 2 revealing a lower reduction enthalpy, which promotes the reduction extent [51]. The presence of Al 3+ enables the reduction of Mn 4+ to Mn 3+ but prevents the reduction of Mn 3+ to Mn 2+ [54]. The enthalpy variation of La 0.2 Sr 0.8 Mn 0.8 Al 0.2 O 3 and La 0.4 Sr 0.6 Mn 0.8 Al 0.2 O 3 decreases when increasing the δ, as shown by Ezbiri et al. [55]. McDaniel et al. [51] performed 80 cycles with La 0.6 Sr 0.4 Mn 0.6 Al 0.4 O 3 and they obtained a constant CO production, proving that the material was not deactivated. Deml et al. [56] studied the oxygen vacancy formation energy (E V ) of 18 perovskites from La 1−x Sr x Mn 1−y Al y O 3 series. They highlighted that the E V decreases with the Sr ratio increase and it increases or stays nearly constant with the Mn ratio increase. It was also shown that La 1−x Sr x Mn 1−y Al y O 3 has a large range of E V , from 0 to more than 3 eV, which promotes the vacancy formation, thus the redox activity. The optimal range of E V for reduction and oxidation reaction is: 1.8 eV < E V < 2.4 eV (with experimental conditions used by McDaniel et al. [51]). The reduction is promoted by E V < 2.4 eV whereas the oxidation is promoted by E V > 1.8 eV [56]. Deml et al. [56] studied three perovskites (La 0. 6 [56] presented La 0.6 Sr 0.4 Mn 0.6 Al 0.4 O 3 as the optimal composition for thermochemical cycles. In an experimental study using the same material composition, the fuel production was not stable and the re-oxidation yield dropped from 57% to 35% between the first and second cycle for La 0.6 Sr 0.4 Mn 0.4 Al 0.6 O 3 [41]. A low H 2 production for this material was also highlighted by Sugiyama et al. [57]. Furthermore, Nair and Abanades [49]. found that the use of Al did not improve the reactivity compared to La 1−x Sr x MnO 3 perovskites The Al 3+ cation was also used as B-site dopant in La 1−x Ca x MnO 3 . Takacs et al. [18] found that the O 2 production of La 1−x Ca x Mn 1−y Al y O 3 was superior to the one of La 1−x Ca x MnO 3 and La 1−x Sr x Mn 1−y Al y O 3 . However, the oxidation temperature must be lower than 850 • C for a complete re-oxidation, which induces energy penalty due to the necessity to reheat the material [50]. The optimal composition was found to be La 0.6 Ca 0.4 Mn 0.6 Al 0.4 O 3 which produces more hydrogen (429 µmol/g) than ceria (56 µmol/g) in similar experimental conditions (reduction at 1400 • C, oxidation at 1000 • C) [58]. For both La 1−x Ca x MnO 3 and La 1−x Sr x MnO 3 with Al dopant on the B-site, it was also proved that the presence of the dopant in the B-site avoids the carbonate formation at low temperature during the carbon dioxide splitting [39].
Gallium was also considered as B-site dopant in La 1−x Ca x MnO 3 . The introduction of Ga 3+ allowed increasing O 2 and CO production. The La 0.6 Ca 0.4 Mn 0.8 Ga 0.2 O 3 perovskite produced 212 µmol/g of O 2 , while the undoped perovskite produced only 167 µmol/g (at T red = 1300 • C). During the oxidation step at 900 • C, the Ga-doped perovskite produced 401 µmol/g of H 2 whereas the undoped perovskite produced 339 µmol/g. The fuel production was promoted by the high specific surface area of the perovskite, as it favors solid-gas interactions. However, the substitution of Mn by Ga was limited to 30% in the Sr-doped lanthanum-manganese perovskite [59].
The beneficial effect of the Mg 2+ cation as dopant in the B-site of La 1−x Sr x MnO 3 was also highlighted [41]. Mg 2+ does not participate to the redox reactions, but it improves the resistance to sintering and the thermal stability. It can be noticed in Figure 6 that during the first cycle La 0.6 Sr 0.4 Mn 0.4 Al 0.6 O 3 produced the highest CO amount while La 0.6 Sr 0.4 Mn 0.83 Mg 0.17 O 3 kept the highest CO production during the second cycle, showing a stable fuel production upon two cycles (209 and 207 µmol/g, respectively). Furthermore, the use of Mg permits to reduce grain growth during cycles and to obtain smaller grain size compared to the undoped perovskite. Smaller grain sizes induce higher specific surface areas, and thus, promotes the oxidation step. Notwithstanding this effect, the use of Mg dopant is limited to~15-20% due to its low solubility [41]. 207 µmol/g, respectively). Furthermore, the use of Mg permits to reduce grain growth during cycles and to obtain smaller grain size compared to the undoped perovskite. Smaller grain sizes induce higher specific surface areas, and thus, promotes the oxidation step. Notwithstanding this effect, the use of Mg dopant is limited to ~15-20% due to its low solubility [41]. Scandium was also considered as B-site dopant in Sr-doped lanthanum-manganese perovskite, but its content was limited to 10% due to its low solubility. Despite this, the introduction of only 5% of Sc increases the O2 production by a factor of two when compared with La0.5Sr0.5MnO3, according to Dey et al. [60]. However, the authors also present an almost full and very fast re-oxidation whatever the investigated materials, which may be due to flaws in the experimental procedure given that the re-oxidation with either H2O or CO2 is never complete for such materials (as opposed to the re-oxidation with O2). Accordingly, the presence of residual oxygen in the system when switching the gas atmosphere must be avoided in order to prevent the swift material re-oxidation. The observed mass gain may thus not be attributed to the CO2 splitting, and quantifying the amount of produced CO by gas analysis would be necessary to confirm the results.
In order to improve the fuel production during the re-oxidation step, Mn substitution by Cr ion was investigated. La0.7Sr0.3Mn0.7Cr0.3O3 was reported by Sugiyama et al. [57] to yield a similar O2 production as La0.7Sr0.3Mn0.7Al0.3O3 but a higher H2 production. The presence of Cr in the B-site permits to increase the oxidation extent when compared to Al.

Lanthanum-Cobalt Perovskites
Lanthanum-cobalt perovskites were studied in thermochemical cycles. LaCoO3 presents a high O2 production (369 µmol/g at Tred = 1300 °C) during the first reduction step. However, the CO production is low and it decreases quickly over cycles: 86 and 22 µmol/g of CO during the first and second cycles, respectively [38]. Scandium was also considered as B-site dopant in Sr-doped lanthanum-manganese perovskite, but its content was limited to 10% due to its low solubility. Despite this, the introduction of only 5% of Sc increases the O 2 production by a factor of two when compared with La 0.5 Sr 0.5 MnO 3 , according to Dey et al. [60]. However, the authors also present an almost full and very fast re-oxidation whatever the investigated materials, which may be due to flaws in the experimental procedure given that the re-oxidation with either H 2 O or CO 2 is never complete for such materials (as opposed to the re-oxidation with O 2 ). Accordingly, the presence of residual oxygen in the system when switching the gas atmosphere must be avoided in order to prevent the swift material re-oxidation. The observed mass gain may thus not be attributed to the CO 2 splitting, and quantifying the amount of produced CO by gas analysis would be necessary to confirm the results.
The La 1−x Sr x Mn 1−y Fe y O 3 perovskite was also investigated [61]. The starting reduction temperature of this perovskite was reduced when increasing the Fe content, which in turn promoted the reduction extent. As an illustration, La 0. 6  .
In order to improve the fuel production during the re-oxidation step, Mn substitution by Cr ion was investigated. La 0.7 Sr 0.3 Mn 0.7 Cr 0.3 O 3 was reported by Sugiyama et al. [57] to yield a similar O 2 production as La 0.7 Sr 0.3 Mn 0.7 Al 0.3 O 3 but a higher H 2 production. The presence of Cr in the B-site permits to increase the oxidation extent when compared to Al.

Lanthanum-Cobalt Perovskites
Lanthanum-cobalt perovskites were studied in thermochemical cycles. LaCoO 3 presents a high O 2 production (369 µmol/g at T red = 1300 • C) during the first reduction step. However, the CO production is low and it decreases quickly over cycles: 86 and 22 µmol/g of CO during the first and second cycles, respectively [38].
Lanthanum-cobalt perovskites substituted in the A or/and B-site were investigated. Regarding the impact of Ca dopant in the A-site, the increase of Ca content promoted oxygen production (715 µmol/g for La 0.8 Ca 0.2 CoO 3 and 1213 µmol/g for La 0.2 Ca 0.8 CoO 3 at 1300 • C). Figure 7a reveals that the increase of Ca content increases the O 2 production rate. Nonetheless, the hydrogen production dropped for Ca content above 40%, as shown in Figure 7b. For example, the hydrogen production was 587 µmol/g for 40% Ca content versus only 204 µmol/g for 80% Ca content at 900 • C. Wang et al. [62] selected La 0.6 Ca 0.4 CoO 3 as the most promising material among Ca-doped lanthanum-cobalt perovskites according to both O 2 and CO production. Lanthanum-cobalt perovskites substituted in the A or/and B-site were investigated. Regarding the impact of Ca dopant in the A-site, the increase of Ca content promoted oxygen production (715 µmol/g for La0.8Ca0.2CoO3 and 1213 µmol/g for La0.2Ca0.8CoO3 at 1300 °C). Figure 7a reveals that the increase of Ca content increases the O2 production rate. Nonetheless, the hydrogen production dropped for Ca content above 40%, as shown in Figure 7b. For example, the hydrogen production was 587 µmol/g for 40% Ca content versus only 204 µmol/g for 80% Ca content at 900 °C. Wang et al. [62] selected La0.6Ca0.4CoO3 as the most promising material among Ca-doped lanthanum-cobalt perovskites according to both O2 and CO production. Substitution of lanthanum by Sr in lanthanum-cobalt perovskites was also considered. The La0.8Sr0.2CoO3 perovskite presents a mass loss (1.5%) higher than La0.8Sr0.2MnO3 (0.1%), meaning a higher reduction extent [63]. Furthermore, La0.6Sr0.4CoO3 offers higher H2 production (514 µmol/g) than La0.6Sr0.4MnO3 (234 µmol/g) [64]. However, Orfila et al. [63] tested the stability of this perovskite, highlighting a decrease of the production after four consecutive cycles. This is due to the formation of a pure Co oxide phase that impairs both O2 and CO/H2 production [63]. In addition, Demont et al. [32] pointed out a partial decomposition of the La0.8Sr0.2CoO3 perovskite to form a Ruddlesden-Popper phase according to reaction (14). However, Ruddlesden-Popper phases are subjected to topotactic oxygen release which can be suitable for thermochemical cycles [32].

2(La, Sr)CoO → (La, Sr) CoO + CoO + 1/2 O
Iron was also investigated as another dopant in lanthanum-cobalt perovskites. It appears that the presence of Fe decreases the oxygen production. For example, LaCoO3 releases 369 µmol/g of O2 at 1300 °C, whereas LaFe0.75Co0.25O3 releases 59 µmol/g. In addition, the oxidation step was not enhanced by the introduction of Fe. Nair and Abanades [38] emphasized that the use of Fe as dopant in LaCoO3 neither improves the perovskite stability, nor the re-oxidation yield. In addition to the use of Fe dopant in B-site, the introduction of Sr in the A-site was tested. The mix Co/Fe tends to increase the reduction extent (465 µmol/g O2 for La0.6Sr0.4Co0.2Fe0.8O3 at 1200 °C) compared to perovskite with the B-site only occupied by Fe (337 µmol/g O2 for La0.6Sr0.4FeO3 at 1200 °C). However, the produced amount of CO is low (90 µmol/g during the 1 st cycle) and decreases over cycles (51 µmol/g during the 2 nd cycle) due to sintering [32,38].
La1−xSrxCo1−yCryO3 was also studied for fuel production. Above 50% of Co, the powder grain size increased. Bork et al. [65] noticed that the increase of Co content promoted the O2 production. In addition, increasing the Co content up to 20% increased the CO production. An optimum composition was thus deduced for fuel production: La0.6Sr0.4Co0.2Cr0.8O3. This perovskite offered a CO production of 157 µmol/g with a reduction temperature of 1200 °C and an oxidation temperature of 800 °C. This performance is similar to ceria (CO production: 168 µmol/g) with reduction and oxidation temperatures of 1500 °C and 1000 °C, respectively. Thus, comparable CO production as ceria can be obtained with La0.6Sr0.4Co0.2Cr0.8O3 at lower temperatures. In addition, Bork et al. [65] demonstrated the absence of carbonate formation during the oxidation step in presence of CO2, confirming the ability of La0.6Sr0.4Co0.2Cr0.8O3 to be used in thermochemical cycles. Substitution of lanthanum by Sr in lanthanum-cobalt perovskites was also considered. The La 0.8 Sr 0.2 CoO 3 perovskite presents a mass loss (1.5%) higher than La 0.8 Sr 0.2 MnO 3 (0.1%), meaning a higher reduction extent [63]. Furthermore, La 0.6 Sr 0.4 CoO 3 offers higher H 2 production (514 µmol/g) than La 0.6 Sr 0.4 MnO 3 (234 µmol/g) [64]. However, Orfila et al. [63] tested the stability of this perovskite, highlighting a decrease of the production after four consecutive cycles. This is due to the formation of a pure Co oxide phase that impairs both O 2 and CO/H 2 production [63]. In addition, Demont et al. [32] pointed out a partial decomposition of the La 0.8 Sr 0.2 CoO 3 perovskite to form a Ruddlesden-Popper phase according to reaction (14). However, Ruddlesden-Popper phases are subjected to topotactic oxygen release which can be suitable for thermochemical cycles [32].

2(La, Sr)CoO 3 → (La, Sr) 2 CoO 4 +
Iron was also investigated as another dopant in lanthanum-cobalt perovskites. It appears that the presence of Fe decreases the oxygen production. For example, LaCoO 3 releases 369 µmol/g of O 2 at 1300 • C, whereas LaFe 0.75 Co 0.25 O 3 releases 59 µmol/g. In addition, the oxidation step was not enhanced by the introduction of Fe. Nair and Abanades [38] emphasized that the use of Fe as dopant in LaCoO 3 neither improves the perovskite stability, nor the re-oxidation yield. In addition to the use of Fe dopant in B-site, the introduction of Sr in the A-site was tested. The mix Co/Fe tends to increase the reduction extent (465 µmol/g O 2 for La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3 at 1200 • C) compared to perovskite with the B-site only occupied by Fe (337 µmol/g O 2 for La 0.6 Sr 0.4 FeO 3 at 1200 • C). However, the produced amount of CO is low (90 µmol/g during the 1st cycle) and decreases over cycles (51 µmol/g during the 2nd cycle) due to sintering [32,38]. La 1−x Sr x Co 1−y Cr y O 3 was also studied for fuel production. Above 50% of Co, the powder grain size increased. Bork et al. [65] noticed that the increase of Co content promoted the O 2 production. In addition, increasing the Co content up to 20% increased the CO production. An optimum composition was thus deduced for fuel production: La 0.6 Sr 0.4 Co 0.2 Cr 0.8 O 3 . This perovskite offered a CO production of 157 µmol/g with a reduction temperature of 1200 • C and an oxidation temperature of 800 • C. This performance is similar to ceria (CO production: 168 µmol/g) with reduction and oxidation temperatures of 1500 • C and 1000 • C, respectively. Thus, comparable CO production as ceria can be obtained with La 0.6 Sr 0.4 Co 0.2 Cr 0.8 O 3 at lower temperatures. In addition, Bork et al. [65] demonstrated the absence of carbonate formation during the oxidation step in presence of CO 2 , confirming the ability of La 0.6 Sr 0.4 Co 0.2 Cr 0.8 O 3 to be used in thermochemical cycles.

Yttrium-Manganese Perovskites
Strontium was studied as a B-site dopant in yttrium manganese perovskites. Y 0.5 Sr 0.5 MnO 3 shows a reduction extent higher (539 µmol/g of O 2 produced) than La 0.5 Sr 0.5 MnO 3 , (256 µmol/g of O 2 produced) in similar conditions [49]. The improvement of the reduction extent can be explained by a smaller ionic radius of Y 3+ (r = 1.08 A [40]) than La 3+ (r = 1.36 A [40]). This smaller ionic radius has for effect an increase of the MnO 6 octahedron inclination and an increase of the lattice distortion, which promotes oxygen departure [46]. Demont and Abanades [41] observed that the O 2 production peak was reached at 1315 • C (Figure 5a), suggesting that the reduction temperature can be lowered without diminishing the O 2 production. Dey et al. [46] reported a complete re-oxidation, performed with thermogravimetric analysis. Nevertheless, the extremely fast oxidation profile can again be questioning, suggesting possible prompt reaction with residual O 2 instead of CO 2 . Rodenbough and Chan [66] performed a thermochemical cycle in similar conditions as the one used by Dey et al. [46] and they analyzed the output gas with integrated IR-electrochemical sensor to detect CO. They observed a lack of CO and they suggested that the mass uptake observed by Dey et al. [46] was not attributable to the CO 2 splitting [66]. Nair and Abanades [49] also pointed out a low re-oxidation yield (14%), which is in agreement with Rodenbough and Chan [66].
Substitution of yttrium by calcium was also investigated, yielding Y 1−x Ca x MnO 3 perovskite. Both yttrium and calcium tend to increase the reduction extent in comparison with lanthanum and strontium, respectively. The O 2 production was 573 µmol/g for Y 0.5 Ca 0.5 MnO 3 (at T red = 1400 • C) while it was only 312 µmol/g and 481 µmol/g for La 0.5 Ca 0.5 MnO 3 and Y 0.5 Sr 0.5 MnO 3 , respectively [46].

Other Perovskites
The most largely investigated perovskite series were presented in the previous sections. Other perovskites were also investigated as reactive materials in thermochemical cycles such as BaMn 1−y Ce y O 3 . It was highlighted that the BaCe 0.25 Mn 0.75 O 3 formulation haD higher reduction ability than ceria for a temperature below 1400 • C. Furthermore, this perovskite produces three times more hydrogen (140 µmol/g) than ceria with a reduction temperature of 1350  Figure 8. Thus, BaCe 0.25 Mn 0.75 O 3 perovskite is able to perform water splitting under milder conditions in the aim of future large-scale implementation [67].
The influence of the cation in A-site was studied by Dey et al. [46] who tested a set of perovskites in the series Ln 0.5 A 0.5 MnO 3 (Ln = La, Nd, Sm, Gd, Dy, Y, and A = Sr, Ca). They showed that the decrease of the rare-earth ionic size improves the reduction extent. Consequently, the maximal O 2 production was reached by Y 0.5 Ca 0.5 MnO 3 (573 µmol/g) and Y 0.5 Sr 0.5 MnO 3 (481 µmol/g), because yttrium has the smallest ionic radius among the rare-earth tested. As a comparison, La 0.5 Ca 0.5 MnO 3 and La 0.5 Sr 0.5 MnO 3 produced 312 µmol/g and 198 µmol/g of O 2 , respectively, in the same experimental conditions (T red = 1400 • C). The decrease of the rare-earth ionic size leads to a decrease in the tolerance factor. This increases the tilting of the MnO 6 octahedron in the perovskite structure and the lattice distortion, and this favors the oxygen departure. However, the re-oxidation step of perovskites was found to be very fast and almost complete (over 500 µmol/g of produced CO for an oxidation temperature of 1100 • C). On the contrary, Nair and Abanades [38] found that the re-oxidation yield was very low (10% for Y 0.5 Sr 0.5 MnO 3 ). The very low re-oxidation extent for Y 0.5 Sr 0.5 MnO 3 in comparison with La 0.5 Sr 0.5 MnO 3 and La 0.5 Ca 0.5 MnO 3 can be observed in Figure 9.
perovskites were also investigated as reactive materials in thermochemical cycles such as BaMn1−yCeyO3. It was highlighted that the BaCe0.25Mn0.75O3 formulation haD higher reduction ability than ceria for a temperature below 1400 °C. Furthermore, this perovskite produces three times more hydrogen (140 µmol/g) than ceria with a reduction temperature of 1350 °C and an oxidation temperature of 850 °C. Compared with La0.6Sr0.4Mn0.6Al0.4O3 perovskite, BaCe0.25Mn0.75O3 offers similar production, but its oxidation kinetics are faster. Barcellos et al. [67] investigated the ability of this material to produce hydrogen under high-conversion conditions. The H2O:H2 ratio required to drive the thermochemical cycle has to be below 1000:1. To realize this condition, different H2O:H2 ratios were used in the reaction chamber. La0.6Sr0.4Mn0.6Al0.4O3 showed a rapid decrease of H2 production with the decrease of H2O:H2 ratio and hydrogen production stopped for H2O:H2 < 500, whereas BaCe0.25Mn0.75O3 also showed a decrease of H2 production as the H2O:H2 ratio decreased but it still had comparable H2 production as ceria with a H2O:H2 ratio of 285. The fuel productions for La0.6Sr0.4Mn0.6Al0.4O3, BaCe0.25Mn0.75O3, and ceria under various H2O:H2 ratios are illustrated in Figure  8. Thus, BaCe0.25Mn0.75O3 perovskite is able to perform water splitting under milder conditions in the aim of future large-scale implementation [67].  The Ba 1−x Sr x FeO 3 perovskite was also studied for thermochemical cycles. This perovskite showed a high reduction extent (582 µmol/g of O 2 produced) with a low reduction temperature (1000 • C), and it was able to produce CO (136 µmol/g) in an isothermal cycle (1000 • C). Nevertheless, a low stability was observed for this perovskite, with decreasing CO production [38]. The influence of the cation in A-site was studied by Dey et al. [46] who tested a set of perovskites in the series Ln0.5A0.5MnO3 (Ln = La, Nd, Sm, Gd, Dy, Y, and A = Sr, Ca). They showed that the decrease of the rare-earth ionic size improves the reduction extent. Consequently, the maximal O2 production was reached by Y0.5Ca0.5MnO3 (573 µmol/g) and Y0.5Sr0.5MnO3 (481 µmol/g), because yttrium has the smallest ionic radius among the rare-earth tested. As a comparison, La0.5Ca0.5MnO3 and La0.5Sr0.5MnO3 produced 312 µmol/g and 198 µmol/g of O2, respectively, in the same experimental conditions (Tred = 1400 °C). The decrease of the rare-earth ionic size leads to a decrease in the tolerance factor. This increases the tilting of the MnO6 octahedron in the perovskite structure and the lattice distortion, and this favors the oxygen departure. However, the re-oxidation step of perovskites was found to be very fast and almost complete (over 500 µmol/g of produced CO for an oxidation temperature of 1100 °C). On the contrary, Nair and Abanades [38] found that the re-oxidation yield was very low (10% for Y0.5Sr0.5MnO3). The very low re-oxidation extent for Y0.5Sr0.5MnO3 in comparison with La0.5Sr0.5MnO3 and La0.5Ca0.5MnO3 can be observed in Figure 9. The Ba1−xSrxFeO3 perovskite was also studied for thermochemical cycles. This perovskite showed a high reduction extent (582 µmol/g of O2 produced) with a low reduction temperature (1000 °C), and it was able to produce CO (136 µmol/g) in an isothermal cycle (1000 °C). Nevertheless, a low stability was observed for this perovskite, with decreasing CO production [38].
To date, a large number of perovskite formulations have been studied for thermochemical cycles, and some important results are summarized in Table 1. Perovskites can accommodate to a wide range of oxygen non-stoichiometry. However, the high vacancy formation ability is usually associated to a slow re-oxidation step, impeding complete re-oxidation and resulting in low CO/H2 production rates. In other words, a favored reduction capability can be obtained at the expense of lower oxidation extent and vice-versa. A compromise between maximum achievable oxygen non-stoichiometry and fuel production yield has to be considered, and the key outcomes may arise from an optimization of the perovskite's composition. The recent results presented above show that the high number of Wang et al. [64] studied the impact of the cation (Cr, Mn, Fe, Ni, and Co) occupying the B-site of Sr-doped lanthanum perovskites. They reported that the La 0.6 Sr 0.4 CoO 3 perovskite can accommodate more oxygen vacancies than La 0.6 Sr 0.4 BO 3 perovskites (with B = Cr, Mn, Fe, and Ni), which is due to a low energy of oxygen vacancy formation. Furthermore, La 0.6 Sr 0.4 CoO 3 presents a lower onset temperature (~900 • C) than La 0.6 Sr 0.4 MnO 3 (~1020 • C) in similar conditions. The reported hydrogen production is also higher for La 0.6 Sr 0.4 CoO 3 (514 µmol/g) at 900 • C (with T red = 1300 • C) than for other La 0.6 Sr 0.4 BO 3 perovskites (Ni: 368 µmol/g; Fe: 349 µmol/g; Cr: 280 µmol/g and Mn: 234 µmol/g) [64].
To date, a large number of perovskite formulations have been studied for thermochemical cycles, and some important results are summarized in Table 1. Perovskites can accommodate to a wide range of oxygen non-stoichiometry. However, the high vacancy formation ability is usually associated to a slow re-oxidation step, impeding complete re-oxidation and resulting in low CO/H 2 production rates.
In other words, a favored reduction capability can be obtained at the expense of lower oxidation extent and vice-versa. A compromise between maximum achievable oxygen non-stoichiometry and fuel production yield has to be considered, and the key outcomes may arise from an optimization of the perovskite's composition. The recent results presented above show that the high number of possible perovskite formulations leaves space for the finding of suitable materials for thermochemical cycles.

Kinetic Studies
Thermodynamic limitations define the theoretical bounds of fuel production, whereas kinetic limitations determine the maximum fuel amount that can be produced in a reasonable duration. Different methods were used to investigate the kinetics of redox reactions involving perovskites. Here, an overview of the methods used is proposed with their advantages and drawbacks.
The kinetic rate of a solid-gas reaction can be expressed with the relation (15), (15) where α is the conversion ratio, A the pre-exponential factor, E a the activation energy, R the gas constant, T the reaction temperature, and f the function representing the reaction model. The activation energy represents the energy barrier that needs to be overcome to initiate the reaction, whereas f (α) is a mathematical representation of the reaction mechanism [68]. Physical reaction processes can be expressed in a mathematical function f (α), supplementary detailed information are available elsewhere [69]. A complete kinetic study is generally required to determine the triplet of the following parameters: E a , A, and f . In their study, Demont and Abanades [17,20] determined the activation energy during the reduction step with linear fits using Arrhenius expression. To determine the conversion fraction, they used the mass variation between the initial state and the mass at the time t over the mass variation between initial and final states. The Equation (16) can be used to determine the kinetic parameters. ln dα dt A contracting sphere model was used for the reaction model, i.e., f (α) = 3(1 − α) 2 3 , which was previously validated by Reference [26]. Thanks to this method, an activation energy of 158, 145, and 174 kJ/mol was obtained for La 0.5 Ca 0.5 MnO 3 , La 0.5 Sr 0.5 MnO 3 , and La 0.5 Ba 0.5 MnO 3 reduction, respectively [41]. Jiang et al. [70] also used this method to determine the activation energy. However, they tested four different reaction models and all the models fit properly to the experimental data, which prevents determining kinetic model. Because each model results in a different activation energy, the authors determined an activation energy range [70]. This simple method allows obtaining the activation energy easily and quickly. Conversely, only a part of the reaction in a given temperature range was taken into account to calculate the activation energy. Furthermore, this method is relevant only if there is one step in the reaction mechanism and it requires knowing the reaction model. Thus, it is suitable to obtain a first estimation of the activation energy.
In order to study the kinetics of the oxidation step in isothermal conditions, Jiang et al. [70] used a master plot method. The conversion rate data in differential form is normalized using a reference point at α = 0.5, as represented by the Equation (17).
A comparison between the normalized experimental data and different theoretical functions of solid-state reaction models, enables to identify the appropriate reaction model, as illustrated in Figure 10. Using this method, Jiang et al. [70] found that the best fitting model at 1000 • C is the first order diffusion model (D1), whereas the first order reaction (F1) is the best model at 1100 • C, for CO production by LaFe 0.7 Co 0.3 O 3 [70]. The master plot method is suited to identify the reaction model with only one experimental test in isothermal condition. However, supplementary kinetic analyses are required to identify the other kinetic parameters [71,72].
10. Using this method, Jiang et al. [70] found that the best fitting model at 1000 °C is the first order diffusion model (D1), whereas the first order reaction (F1) is the best model at 1100 °C, for CO production by LaFe0.7Co0.3O3 [70]. The master plot method is suited to identify the reaction model with only one experimental test in isothermal condition. However, supplementary kinetic analyses are required to identify the other kinetic parameters [71,72].  McDaniel et al. [73] used another approach to study perovskite oxidation kinetics, which was first developed by Scheffe et al. [74] to study cobalt ferrite. It consists in separating the oxidation kinetic rate in different contributions:

1.
Kinetic rate related to the oxidation reaction itself; 2.
Time necessary for the oxidant gas to be introduced in the reaction chamber; 3.
Influence of the dispersion of the gas product during the transportation between the reactor outlet and the detector.
The introduction of the oxidant is modeled as a step function (Figure 11a). The step function shape is determined using a numerical simulation of the reactor inlet for different operating conditions. The solid-state reaction is described by a theoretical kinetic model in Equation (18).
where Y H 2 O is the mole fraction of the oxidant gas in the inlet and γ is the factor that rules the relation with the gaseous oxidant concentration. The H 2 production rate is determined thanks to a solid state model as a function of time ( Figure 11b). Afterward, this signal is introduced into a series of ideal continuously-stirred tank reactors (CSTR) to simulate the dispersion and mixing of gas product (( Figure 11c). Kinetic model and associated parameters are obtained thanks to the least-squares method.
The experimental H 2 production rates are fitted to the simulation using different kinetic models, with the least-squares method to obtain the kinetic model and the associated activation energy. If a single kinetic model does not fit correctly with the experimental data, two kinetic models acting in parallel are used [73]. Details about the model have been provided elsewhere [74]. For instance, Arifin and Weimer [75] managed to identify the following parameters for the water splitting with ceria thanks to this method: A = 1 s −1 ; E a = 29 kJ/mol; γ = 0.89 and f (α) = (1 − α). However, they did not manage to compute properly these parameters for carbon dioxide splitting with the same material [75]. This method permits to calculate all the kinetic parameters at the same time, by taking into account the influence of physical processes which depend on the experimental setup. However, numerical simulation of the reactor and calculations to fit the experimental data are required, then providing an appropriate method to precisely study the oxidation kinetics.
splitting with ceria thanks to this method: = 1 s −1 ; = 29 kJ/mol; = 0.89 and ( ) = (1 − ). However, they did not manage to compute properly these parameters for carbon dioxide splitting with the same material [75]. This method permits to calculate all the kinetic parameters at the same time, by taking into account the influence of physical processes which depend on the experimental setup. However, numerical simulation of the reactor and calculations to fit the experimental data are required, then providing an appropriate method to precisely study the oxidation kinetics. Kim et al. [76] studied the surface reaction kinetics and measured the electrical conductivity relaxation of a thin film of La1−xSrxMnO3. Two electrodes (Pt) were placed on the La1-xSrxMnO3 (x=0.1, 0.2, 0.3 and 0.4) coating. The sample was placed in a furnace tube swept by a CO/CO2 mixture. The sample was first heated until thermal equilibrium, and then the oxygen partial pressure was suddenly changed. The oxygen content is related to the plane conductivity in the thin film, which was measured until reaching the new equilibrium of the sample. Measurements were performed for Kim et al. [76] studied the surface reaction kinetics and measured the electrical conductivity relaxation of a thin film of La 1−x Sr x MnO 3 . Two electrodes (Pt) were placed on the La 1−x Sr x MnO 3 (x = 0.1, 0.2, 0.3 and 0.4) coating. The sample was placed in a furnace tube swept by a CO/CO 2 mixture. The sample was first heated until thermal equilibrium, and then the oxygen partial pressure was suddenly changed. The oxygen content is related to the plane conductivity in the thin film, which was measured until reaching the new equilibrium of the sample. Measurements were performed for both reduction and oxidation in order to support the hypothesis of first order surface oxygen exchange reaction and the conductivity varied linearly with the oxygen partial pressure. Experimental data were fitted with Equation (19), where σ represents the conductivity as a function of time, k s is the solid-state constant rate and a is the film thickness. From both Equation (19) and experimental data, the solid-state reaction rate constant k s can be extracted. This method permits to study only surface oxygen exchange and not oxygen diffusion in the bulk, as the coating thickness is much thinner than the critical thickness for bulk diffusion. Thanks to this method, Kim et al. [76] computed the k s values for a set of La 1−x Sr x MnO 3 perovskites with different dopant contents, in order to investigate the effect of Sr concentration, temperature, and oxygen partial pressure on the surface kinetics [76]. This method yields the values of k s constant with good accuracy. Nonetheless, it is necessary to prepare coated samples for this method and a device able to measure the electrical conductivity relaxation. Yang et al. [30] investigated the limiting rate mechanism in the oxidation reaction for different dopant levels in perovskites. They studied the different parameters that can limit the oxidation kinetic including the morphology, the oxygen diffusion rate and the surface reactions. They performed thermochemical cycles in a furnace and analyzed the output gas for a series of perovskites. Concerning the influence of morphology, a comparison was performed between the grain size and the peak production rate evolution. If the grain size decreases, the production rate should increase due to enhanced available surface area for the reaction. Otherwise, the morphology would not limit the oxidation kinetic. Afterward, the authors investigated whether the oxygen diffusion is the limiting step. They checked whether an increase of the oxygen diffusivity due to Sr content change corresponds to an increase of the oxidation rate. The diffusivity is defined as Equation (20), where D chem is the chemical diffusivity; D V O is the vacancy diffusivity, t el is the transference number of electronic species and V ·· O is the fractional oxygen vacancy (with Kröger-Vink notation). D V o and t el are independent from the oxygen partial pressure and the composition. D chem is then directly related to Λ defined by the Equation (21).
The Λ values can be computed as a function of the oxygen partial pressure for the different perovskites. In case diffusion is the limiting step, Λ should increase with the increase of the production rate. Otherwise, it can be assumed that it is not the limiting step. To characterize the surface reaction step, the authors used the oxygen flux through the surface, J o , defined as follows: where J o is the oxygen flow through the surface, k sur f is the surface reaction rate constant, ∆C o is the difference between the oxygen surface concentration and the gas oxygen concentration, directly proportional to ∆δ. The reaction is assumed to be of first order and k sur f independent from the concentration. In Equation (22), the driving force is the difference in concentration. In thermodynamics, driving forces are represented by the difference in oxygen chemical potential, ∆µ o , defined by Equation (23).
∆C o is directly proportional to ∆δ, while µ o = µ 0 o + RT ln p O 2 , ∆µ o is the difference in effective oxygen partial pressure between the quenched state and the oxidized state at the same temperature. Afterward, the plot of the oxidation production peak as function of the non-stoichiometry and the plot of the oxidation production peak as a function of ∆µ O for each perovskite, permit to determine if the surface reaction step is the limiting step. If the oxidation peak production rate increases with the ∆µ O increase and the ∆δ decrease, the oxidation is then limited by the surface reaction step. With this method, Yang et al. [30] revealed that the oxidation step for La 1−x Sr x MnO 3 is limited by the solid-state reaction. The interest of this method is to determine the limiting step during the oxidation reaction and to highlight the effect of the dopant on kinetics. It only requires few materials with different dopant levels. Regarding main drawback, the constants like k sur f or k s cannot be computed.
Davenport et al. [24,77,78] developed a thermo-kinetic model. Assuming that O 2 production takes place under quasi-equilibrium conditions, the O 2 production is entirely governed by the thermodynamic properties. Applying mass balance to the oxygen release and taking in equilibrium, they expressed the oxygen flow rate as: where V red is the volumetric flow rate of reducing gas, m CeO 2 is ceria mass used, P tot is the total pressure, P O 2 ,in is the oxygen partial pressure at the inlet, and P O 2 (δ, T) is the oxygen partial pressure in equilibrium at a non-stoichiometry of δ. Concerning the oxidation rate, a similar expression is obtained by applying the mass balance constraints on water, hydrogen and oxygen: .
where . v H 2 is the normalized flow rate of hydrogen, .
V ox corresponds to the volumetric flow rate of oxidant gas; χ H 2 O is the molar ratio of H 2 O in the oxidizing gas;P is P/P re f and K H 2 O,T is the equilibrium constant for water thermolysis. Details about the method for obtaining the Equations (24) and (25) can be found elsewhere [77]. In Equations (24) and (25), the only unknown remaining is P O 2 (δ, T) which can be computed thanks to Equation (26).
The thermodynamic properties used in Equation (26) can be found in the literature. By this way, the gas flow rates of O 2 and H 2 can be computed by iteration. Using this method, Davenport et al. [24] showed that the oxidation rate of porous ceria is limited by the gas flow introduced in the reactor when the oxidant gas flow is under 600 Ncm 3 /min/g and the oxidation temperature above 1200 • C. This model shows good agreement with the experimental data when at high temperatures and moderate gas flow rates. However, the kinetic study of a reaction with this model requires that the reaction occurs under quasi-equilibrium condition, to assume that the reaction rate is ruled by the thermo-kinetic model.

Conclusions
Thermochemical redox cycles are promising for converting solar energy into chemical energy in the form of sustainable solar fuels that can be stored long-term, transported long-range, and used on-demand. In order to enhance global energy conversion efficiency, the optimization of the reactive material is required. Perovskites represent a promising class of materials for thermochemical fuel production cycles. Such materials have a high thermal stability and can accommodate large oxygen non-stoichiometry in their structure owing to high oxygen exchange properties, thereby allowing for large fuel production. Furthermore, the reduction temperature can be decreased compared with other materials like ceria, while keeping comparable fuel productivities. The main drawback associated with the use of perovskites is generally the incomplete re-oxidation yield due to low kinetics and low thermodynamic driving forces. The large number of possible perovskite formulations and the discovery of novel materials make possible tuning the redox properties to optimize the fuel production. Perovskites based on lanthanum-manganese, lanthanum-cobalt, yttrium-manganese associated with different dopants (Al, Ga, Ba, Mg, Sr, Ca, Ce, Cr, Fe) are the principal materials that were studied for thermochemical cycles application. Moreover, different methods used to study reaction kinetics involving non-stoichiometric perovskites were reported here to provide insights into the different available techniques with their advantages and drawbacks and the related performance data. In showing that perovskites constitute a promising class of materials in the context of solar thermochemical fuel production, further advancements in the discovery and characterization of new and better performing redox materials are of critical importance, while complying with the necessary attributes related to favorable thermodynamics, rapid reaction kinetics, and crystallographic stability over thermochemical cycling.