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

Abstract

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 H₂ 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 H₂O and CO₂ 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 H₂O and CO₂ 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.

1. 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 CO₂ 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 CO₂ 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 O₂, 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 H₂O or CO₂, 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 H₂/CO) can be converted into synthetic liquid hydrocarbon fuels via the Fischer–Tropsch process [2]. The metal oxide is not consumed in the overall H₂O and CO₂ splitting process, and thus, acts as a catalyst in the global reaction.

$${\mathrm{M}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}}\to {\mathrm{M}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}-\delta }+\frac{\delta }{2}{\mathrm{O}}_2$$

(1)

$${\mathrm{M}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}-\delta }+\delta {\mathrm{H}}_2\mathrm{O}\to {\mathrm{M}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}}+\delta {\mathrm{H}}_2$$

(2a)

$${\mathrm{M}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}-\delta }+\delta {\mathrm{CO}}_2\to {\mathrm{M}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}}+\delta \mathrm{CO}$$

(2b)

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 (CeO₂) 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 Li²⁺, Mg²⁺, Sc³⁺, Dy³⁺, La³⁺, Sm³⁺, Gd³⁺, Pr³⁺, Hf⁴⁺, and Zr⁴⁺ [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.

2. 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 $\Delta G°$ represents the standard Gibbs free enthalpy variation, $P_{{\mathrm{O}}_2}$ 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 CO₂ splitting and for La_0.6Sr_0.4MnO₃ during the reduction and oxidation steps. The Gibbs free energy of the reduction reaction is computed with values of ΔH° and ΔS° found in the literature [18]. Concerning the CO₂ 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 CO₂ splitting and of La_0.6Sr_0.4MnO₃ 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].

$$\Delta {G°}_{TR}\left(P_{{\mathrm{O}}_2,TR},T_{TR}\right)<0$$

(3)

$$\Delta {G°}_{WS}\left(P_{{\mathrm{O}}_2,WS},T_{WS}\right)<-\Delta {G°}_{{\mathrm{H}}_2\mathrm{O}}\left(P_{{\mathrm{O}}_2,WS},T_{WS}\right)$$

(4a)

$$\Delta {G°}_{CDS}\left(P_{{\mathrm{O}}_2,CDS},T_{CDS}\right)<-\Delta {G°}_{{\mathrm{CO}}_2}\left(P_{{\mathrm{O}}_2,CDS},T_{CDS}\right)$$

(4b)

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;

$$\Delta {G°}_{TR,T_{TR}}=\Delta {H°}_{red}-T_{TR}\left(\Delta {S°}_{red}+\frac{1}{2}{S}_{T_{TR}}^{{\mathrm{O}}_2}\right)$$

(5)

$$\Delta {G°}_{WS,T_{WS}}=-\Delta {H°}_{red}-\Delta H_{f,T_{WS}}^{{\mathrm{H}}_2\mathrm{O}}-T_{WS}\left(S_{T_{WS}}^{{\mathrm{H}}_2}-S_{T_{WS}}^{{\mathrm{H}}_2\mathrm{O}}-\Delta {S°}_{red}\right)$$

(6a)

$$\Delta {G°}_{CDS,T_{CDS}}=-\Delta {H°}_{red}-\Delta H_{f,T_{CDS}}^{{\mathrm{CO}}_2}+\Delta H_{f,T_{CDS}}^{\mathrm{CO}}-T_{CDS}\left(S_{T_{CDS}}^{\mathrm{CO}}-S_{T_{CDS}}^{{\mathrm{CO}}_2}-\Delta {S°}_{red}\right)$$

(6b)

$$\Delta {H°}_{cycle}=\Delta {H°}_{TR}+\Delta {H°}_{WS}$$

(7)

$$\Delta {S°}_{cycle}=\Delta {S°}_{TR}+\Delta {\mathrm{S}°}_{WS}$$

(8)

where $\Delta H$ and $\Delta S$ 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 $\Delta H_{WS}<0$, $\Delta H_{TR}$ has to be at least higher than $\Delta H_{{\mathrm{CO}}_2}$ in order to have $\Delta H_{cycle}>\Delta H_{{\mathrm{CO}}_2}$ [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:

$$\Delta S_{TR}=\Delta {S°}_{TR}-\frac{1}{2}R\ln \left(\frac{P_{{\mathrm{O}}_2}}{P°}\right)$$

(9)

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].

$$\Delta G_{TR}=\Delta {H°}_{TR}-T\Delta {S°}_{TR}+\frac{1}{2}RT\ln \left(\frac{P_{{\mathrm{O}}_2}}{P°}\right)$$

(10)

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 $\delta$.

$$\ln \left(\frac{p_{{\mathrm{O}}_2}}{p°}\right)={\frac{2\Delta S_{red}}{R}-\frac{2\Delta H_{red}}{RT}|}_{\delta =constant}$$

(11)

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 $\delta$ value, and to determine both $\Delta H_{red}$ and $\Delta S_{red}$ via Equation (11) [6]. For the oxidation step, the contribution of the amount of oxidant gas can be expressed as in Equation (12), where $P_{\mathrm{CO}}$, $P_{{\mathrm{CO}}_2}$ $P_{{\mathrm{H}}_2}$ and $P_{{\mathrm{H}}_2\mathrm{O}}$ 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 $\Delta G_{WS}$ 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.

$$\Delta G_{WS}=\Delta {H°}_{WS}-T\Delta {S°}_{WS}+RT\ln \left(\frac{P_{{\mathrm{H}}_2}}{P_{{\mathrm{H}}_2\mathrm{O}}}\right)$$

(12a)

$$\Delta G_{CDS}=\Delta {H°}_{CDS}-T\Delta {S°}_{CDS}+RT\ln \left(\frac{P_{\mathrm{CO}}}{P_{{\mathrm{CO}}_2}}\right)$$

(12b)

Thus, an ideal redox material must have a low enthalpy variation $\Delta {H°}_{red}$ which permits to increase the reduction extent at a lower temperature. In contrast, a high entropy variation $\Delta {S°}_{red}$ 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.

3. 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 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 $t<1$.

$$t=\frac{r_A+r_O}{\sqrt{2}(r_B+r_O)}$$

(13)

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].

3.1. Lanthanum–Manganite Perovskites

3.1.1. A-Site Substituted Materials

Among the lanthanum–manganese perovskites series, the most studied is La_1−xSr_xMnO₃. 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 Sr²⁺ compared to La³⁺. 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 T_red = 1400 °C and T_ox = 1050 °C) [37]. The Figure 4 represents the CO production for different Sr contents in La_1−xSr_xMnO₃, and for undoped and Zr-doped CeO₂ as reference materials. All the La_1−xSr_xMnO₃ perovskites present a higher CO production than pure ceria during cycles. La_0.5Sr_0.5MnO₃ 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].

The Ca²⁺ cation can also be used to substitute lanthanum. La_1−xCa_xMnO₃ has a lower lattice parameter than La_1−xSr_xMnO₃ due to the lower Ca²⁺ ionic radius ($r_{{\mathrm{Ca}}^{2+}}=1.34\AA$) than Sr²⁺ ($r_{{\mathrm{Sr}}^{2+}}=1.58\AA$) [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 Ca²⁺ compared to Sr²⁺ [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, La_1−xCa_xMnO₃ seems more sensitive to the sintering than La_1−xSr_xMnO₃, which can have a negative impact on the oxidation step [50].

Another possible dopant for the A-site in the lanthanum–manganese perovskites is Ba²⁺, leading to the La_1−xBa_xMnO₃ series. The lattice parameter is higher than for La_1−xSr_xMnO₃ perovskite, due to a higher ionic radius of Ba²⁺ ($r_{{\mathrm{Ba}}^{2+}}=1.61\AA$) compared to Sr²⁺ ($r_{{\mathrm{Sr}}^{2+}}=1.44\AA$). The presence of Ba²⁺ 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 La_0.5Ba_0.5MnO₃, 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].

3.1.2. 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)MnO₃ perovskites, the presence of Al³⁺ cation in the B-site permits to increase the reaction kinetics. The introduction of Al³⁺ 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−xSr_xMn_1−yAl_yO₃ has an onset temperature 300 °C, lower than CeO₂ revealing a lower reduction enthalpy, which promotes the reduction extent [51]. The presence of Al³⁺ enables the reduction of Mn⁴⁺ to Mn³⁺ but prevents the reduction of Mn³⁺ to Mn²⁺ [54]. The enthalpy variation of La_0.2Sr_0.8Mn_0.8Al_0.2O₃ and La_0.4Sr_0.6Mn_0.8Al_0.2O₃ decreases when increasing the $\delta$, as shown by Ezbiri et al. [55]. McDaniel et al. [51] performed 80 cycles with La_0.6Sr_0.4Mn_0.6Al_0.4O₃ 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−xSr_xMn_1−yAl_yO₃ 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−xSr_xMn_1−yAl_yO₃ 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: $1.8\mathrm{eV}<E_V<2.4\mathrm{eV}$ (with experimental conditions used by McDaniel et al. [51]). The reduction is promoted by $E_V<2.4\mathrm{eV}$ whereas the oxidation is promoted by $E_V>1.8\mathrm{eV}$ [56]. Deml et al. [56] studied three perovskites (La_0.6Sr_0.4Mn_0.6Al_0.4O₃; La_0.4Sr_0.6Mn_0.6Al_0.4O₃; and La_0.6Sr_0.4Mn_0.4Al_0.6O₃) that were selected by McDaniel et al. [51] for their ability to be used in thermochemical cycles. These perovskites have a predicted $E_V$ (2.6, 1.4, and 2.2 ± 0.2 eV, respectively) that corresponds to a favorable reduction. Furthermore, La_0.6Sr_0.4Mn_0.6Al_0.4O₃ and La_0.6Sr_0.4Mn_0.4Al_0.6O₃ have a predicted $E_V$ > 1.8 that promotes oxidation. However, La_0.4Sr_0.6Mn_0.6Al_0.4O₃ produces less H₂ than La_0.6Sr_0.4Mn_0.6Al_0.4O₃ whose $E_V$ < 1.8, this is due to lower oxidation yield caused by the lower $E_V$ of La_0.4Sr_0.6Mn_0.6Al_0.4O₃. Finally, Deml et al. [56] presented La_0.6Sr_0.4Mn_0.6Al_0.4O₃ 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_0.6Sr_0.4Mn_0.4Al_0.6O₃ [41]. A low H₂ 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−xSr_xMnO₃ perovskites The Al³⁺ cation was also used as B-site dopant in La_1−xCa_xMnO₃. Takacs et al. [18] found that the O₂ production of La_1−xCa_xMn_1−yAl_yO₃ was superior to the one of La_1−xCa_xMnO₃ and La_1−xSr_xMn_1−yAl_yO₃. 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_0.6Ca_0.4Mn_0.6Al_0.4O₃ 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−xCa_xMnO₃ and La_1−xSr_xMnO₃ 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−xCa_xMnO₃. The introduction of Ga³⁺ allowed increasing O₂ and CO production. The La_0.6Ca_0.4Mn_0.8Ga_0.2O₃ perovskite produced 212 µmol/g of O₂, 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 H₂ 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 Mg²⁺ cation as dopant in the B-site of La_1−xSr_xMnO₃ was also highlighted [41]. Mg²⁺ 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_0.6Sr_0.4Mn_0.4Al_0.6O₃ produced the highest CO amount while La_0.6Sr_0.4Mn_0.83Mg_0.17O₃ 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].

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 La_0.5Sr_0.5MnO₃, 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.

The La_1−xSr_xMn_1−yFe_yO₃ 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_0.6Sr_0.4Mn_0.8Fe_0.2O₃ produced 286 µmol/g of O₂ at 1350 °C while La_0.6Sr_0.4Mn_0.2Fe_0.8O₃ produced 333 µmol/g. The CO amount produced tended to decrease with the increase of the Fe content. For instance, La_0.6Sr_0.4MnO₃ doped with 20% Fe produced 329 µmol/g of CO while La_0.6Sr_0.4MnO₃ doped with 60% Fe produced 277 µmol/g [61].

In order to improve the fuel production during the re-oxidation step, Mn substitution by Cr ion was investigated. La_0.7Sr_0.3Mn_0.7Cr_0.3O₃ was reported by Sugiyama et al. [57] to yield a similar O₂ production as La_0.7Sr_0.3Mn_0.7Al_0.3O₃ but a higher H₂ production. The presence of Cr in the B-site permits to increase the oxidation extent when compared to Al.

3.2. Lanthanum–Cobalt Perovskites

Lanthanum–cobalt perovskites were studied in thermochemical cycles. LaCoO₃ presents a high O₂ 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_0.8Ca_0.2CoO₃ and 1213 µmol/g for La_0.2Ca_0.8CoO₃ 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 La_0.6Ca_0.4CoO₃ 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 La_0.8Sr_0.2CoO₃ perovskite presents a mass loss (1.5%) higher than La_0.8Sr_0.2MnO₃ (0.1%), meaning a higher reduction extent [63]. Furthermore, La_0.6Sr_0.4CoO₃ offers higher H₂ production (514 µmol/g) than La_0.6Sr_0.4MnO₃ (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 La_0.8Sr_0.2CoO₃ 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].

$$2\left(\mathrm{La},\mathrm{Sr}\right){\mathrm{CoO}}_3\to {\left(\mathrm{La},\mathrm{Sr}\right)}_2{\mathrm{CoO}}_4+\mathrm{CoO}+1/2{\mathrm{O}}_2$$

(14)

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 LaFe_0.75Co_0.25O₃ 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 La_0.6Sr_0.4Co_0.2Fe_0.8O₃ at 1200 °C) compared to perovskite with the B-site only occupied by Fe (337 µmol/g O₂ for La_0.6Sr_0.4FeO₃ 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−xSr_xCo_1−yCr_yO₃ 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: La_0.6Sr_0.4Co_0.2Cr_0.8O₃. 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 La_0.6Sr_0.4Co_0.2Cr_0.8O₃ 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 La_0.6Sr_0.4Co_0.2Cr_0.8O₃ to be used in thermochemical cycles.

3.3. Yttrium–Manganese Perovskites

Strontium was studied as a B-site dopant in yttrium manganese perovskites. Y_0.5Sr_0.5MnO₃ shows a reduction extent higher (539 µmol/g of O₂ produced) than La_0.5Sr_0.5MnO₃, (256 µmol/g of O₂ produced) in similar conditions [49]. The improvement of the reduction extent can be explained by a smaller ionic radius of Y³⁺ ($r=1.08\AA$ [40]) than La³⁺ ($r=1.36\AA$ [40]). This smaller ionic radius has for effect an increase of the MnO₆ octahedron inclination and an increase of the lattice distortion, which promotes oxygen departure [46]. Demont and Abanades [41] observed that the O₂ production peak was reached at 1315 °C (Figure 5a), suggesting that the reduction temperature can be lowered without diminishing the O₂ 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 O₂ instead of CO₂. 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 CO₂ 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−xCa_xMnO₃ perovskite. Both yttrium and calcium tend to increase the reduction extent in comparison with lanthanum and strontium, respectively. The O₂ production was 573 µmol/g for Y_0.5Ca_0.5MnO₃ (at T_red = 1400 °C) while it was only 312 µmol/g and 481 µmol/g for La_0.5Ca_0.5MnO₃ and Y_0.5Sr_0.5MnO₃, respectively [46].

3.4. 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−yCe_yO₃. It was highlighted that the BaCe_0.25Mn_0.75O₃ 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 La_0.6Sr_0.4Mn_0.6Al_0.4O₃ perovskite, BaCe_0.25Mn_0.75O₃ 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. La_0.6Sr_0.4Mn_0.6Al_0.4O₃ showed a rapid decrease of H₂ production with the decrease of H₂O:H₂ ratio and hydrogen production stopped for H₂O:H₂ < 500, whereas BaCe_0.25Mn_0.75O₃ 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 La_0.6Sr_0.4Mn_0.6Al_0.4O₃, BaCe_0.25Mn_0.75O₃, and ceria under various H₂O:H₂ ratios are illustrated in Figure 8. Thus, BaCe_0.25Mn_0.75O₃ 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_0.5A_0.5MnO₃ (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 Y_0.5Ca_0.5MnO₃ (573 µmol/g) and Y_0.5Sr_0.5MnO₃ (481 µmol/g), because yttrium has the smallest ionic radius among the rare-earth tested. As a comparison, La_0.5Ca_0.5MnO₃ and La_0.5Sr_0.5MnO₃ produced 312 µmol/g and 198 µmol/g of O₂, 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 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 Y_0.5Sr_0.5MnO₃). The very low re-oxidation extent for Y_0.5Sr_0.5MnO₃ in comparison with La_0.5Sr_0.5MnO₃ and La_0.5Ca_0.5MnO₃ can be observed in Figure 9.

The Ba_1−xSr_xFeO₃ 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].

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_0.6Sr_0.4CoO₃ perovskite can accommodate more oxygen vacancies than La_0.6Sr_0.4BO₃ perovskites (with B = Cr, Mn, Fe, and Ni), which is due to a low energy of oxygen vacancy formation. Furthermore, La_0.6Sr_0.4CoO₃ presents a lower onset temperature (~900 °C) than La_0.6Sr_0.4MnO₃ (~1020 °C) in similar conditions. The reported hydrogen production is also higher for La_0.6Sr_0.4CoO₃ (514 µmol/g) at 900 °C (with T_red = 1300 °C) than for other La_0.6Sr_0.4BO₃ 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. Comparison of the performance of current perovskites studied for thermochemical cycles.

Material	Synthesis Method	Experimental Conditions	Production (µmol/g)		Ref.
			O2	H2/CO
La0.7Sr0.3Mn0.7Cr0.3O3	Modified Pechini	Reduction: 1350 °C under N2 Oxidation: H2O between 50 and 84%; 1000 °C during 60 min	~98	~107	[57]
LaFe0.75Co0.25O3	Solid-state	Reduction: 1300 °C under Ar Oxidation: 50% CO2 in Ar at 1000 °C	59	117	[38]
LaCoO3	Solid-state	Reduction: 1300 °C under Ar Oxidation: 50% CO2 in Ar at 1000 °C	369	123	[38]
Ba0.5Sr0.5FeO3	Solid-state	Reduction: 1000 °C under Ar Oxidation: 50% CO2 in Ar at 1000 °C	582	136	[38]
La0.6Sr0.4Co0.2Cr0.8O3	Pechini	Reduction: 1200 °C under Ar Oxidation: 50% CO2 in Ar at 800 °C	-	157	[65]
La0.4Ca0.6Mn0.6Al0.4O3	Modified Pechini	Reduction: 1400 °C under Ar Oxidation: 40% H2O in Ar at 1000 °C	231	429	[58]
BaCe0.25Mn0.75O3	Modified Pechini	Reduction: 1350 °C under Ar Oxidation: 40% H2O in Ar at 1000 °C	-	135	[67]
La0.5Sr0.5MnO3	Solid-state	Reduction: 1400 °C under Ar Oxidation: H2O at 1000 °C	298	195	[32]
La0.35Sr0.75MnO3	Commercial powder	Reduction: 1400 °C under Ar Oxidation: H2O at 1050 °C	166	124	[32]
La0.5Ca0.5MnO3	Solid-state	Reduction: 1400 °C under Ar Oxidation: 50% CO2 at 1050 °C	311	210	[41]
La0.5Ba0.5MnO3	Solid-state	Reduction: 1400 °C under Ar Oxidation: 50% CO2 at 1050 °C	203	185	[41]
La0.5Sr0.5Mn0.4Al0.6O3	Pechini	Reduction: 1400 °C under Ar Oxidation: 50% CO2 at 1050 °C	246	279	[41]
La0.5Sr0.5Mn0.83Mg0.17O3	Solid-state	Reduction: 1400 °C under Ar Oxidation: 50% CO2 at 1050 °C	214	209	[41]
La0.5Sr0.5MnO3	Pechini	Reduction: 1400 °C under Ar Oxidation: 50% CO2 at 1050 °C	256	256	[49]
Y0.5Sr0.5MnO3	Pechini	Reduction: 1400 °C under Ar Oxidation: 50% CO2 at 1050 °C	539	101	[49]
La0.6Sr0.4Mn0.6Al0.4O3	Modified Pechini	Reduction: 1400 °C under Ar Oxidation: 40% CO2 at 1000 °C	-	307	[51]
La0.6Ca0.4Mn0.6Al0.4O3	Modified Pechini	Reduction: 1240 °C under Ar Oxidation: 50% CO2 at 850 °C	165	230	[50]
La0.6Sr0.4Mn0.6Al0.4O3	Modified Pechini	Reduction: 1240 °C under Ar Oxidation: 50% CO2 at 850 °C	190	245	[50]
La0.6Ca0.4Mn0.8Ga0.2O3	Modified Pechini	Reduction: 1300 °C Oxidation: H2O at 900 °C	212	401	[59]
La0.5Sr0.5Mn0.95Sc0.05O3	-	Reduction: 1400 °C under Ar Oxidation: 40% CO2 at 1100 °C	417	545	[60]
La0.6Sr0.4Mn0.8Fe0.2O3	Modified Pechini	Reduction: 1350 °C under N2 Oxidation: CO2 at 1000 °C	286	329	[61]
La0.6Sr0.4CoO3	Modified Pechini	Reduction: 1300 °C Oxidation: 40% H2O at 900 °C	718	514	[64]
La0.6Ca0.4CoO3	Modified Pechini	Reduction: 1300 °C Oxidation: 40% H2O at 900 °C	715	587	[62]
Y0.5Ca0.5MnO3	Solid state	Reduction: 1400 °C Oxidation: CO2 at 1100 °C	573	671	[46]

. 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 possible perovskite formulations leaves space for the finding of suitable materials for thermochemical cycles.

4. 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),

$$\frac{\mathrm{d}\alpha }{\mathrm{dt}}=A\exp \left(-\frac{E_a}{RT}\right)f\left(\alpha \right)$$

(15)

where $\alpha$ 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 $f\left(\alpha \right)$ is a mathematical representation of the reaction mechanism [68]. Physical reaction processes can be expressed in a mathematical function $f\left(\alpha \right)$, 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.

$$\ln \left(\frac{d\alpha }{dt}\frac{1}{f\left(\alpha \right)}\right)=-\frac{E_a}{RT}+\ln A$$

(16)

A contracting sphere model was used for the reaction model, i.e., $f\left(\alpha \right)=3{\left(1-\alpha \right)}^{\frac{2}{3}}$, 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_0.5Ca_0.5MnO₃, La_0.5Sr_0.5MnO₃, and La_0.5Ba_0.5MnO₃ 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 $\alpha$ = 0.5, as represented by the Equation (17).

$$\frac{\left(\mathrm{d}\alpha /\mathrm{d}t\right)}{{\left(\mathrm{d}\alpha /\mathrm{d}t\right)}_{\alpha =0.5}}=\frac{f\left(\alpha \right)}{{f\left(\alpha \right)}_{\alpha =0.5}}$$

(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_0.7Co_0.3O₃ [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:

• Kinetic rate related to the oxidation reaction itself;
• Time necessary for the oxidant gas to be introduced in the reaction chamber;
• Gas detector delay;
• 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).

$$\frac{\mathrm{d}\alpha }{\mathrm{d}t}=A\exp \left(-\frac{E_a}{RT}\right){\left[Y_{{\mathrm{H}}_2\mathrm{O}}\left(t\right)\right]}^{\gamma }f\left(\alpha \right)$$

(18)

where $Y_{{\mathrm{H}}_2\mathrm{O}}$ is the mole fraction of the oxidant gas in the inlet and $\gamma$ is the factor that rules the relation with the gaseous oxidant concentration. The H₂ 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 H₂ 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; $\gamma$ = 0.89 and $f\left(\alpha \right)=\left(1-\alpha \right)$. 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 La_1−xSr_xMnO₃. Two electrodes (Pt) were placed on the La_1−xSr_xMnO₃ (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 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),

$$\frac{\sigma \left(t\right)-\sigma \left(0\right)}{\sigma (\infty )-\sigma \left(0\right)}=1-\exp \left(\frac{k_s}{a}t\right)$$

(19)

where $\sigma$ 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−xSr_xMnO₃ 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),

$$D_{chem}=D_{V_o}{t}_{el}\left(-\frac{1}{2}\frac{\partial \ln p_{O_2}^{*}}{\partial \ln \left[V_O^{\cdot \cdot }\right]}\right)=D_{V_o}{t}_{el}\Lambda$$

(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 $\left[V_O^{\cdot \cdot }\right]$ 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 $\Lambda$ defined by the Equation (21).

$$\Lambda =-\frac{1}{2}\frac{\partial \ln p_{O_2}^{*}}{\partial \ln \left[V_O^{\cdot \cdot }\right]}$$

(21)

The $\Lambda$ values can be computed as a function of the oxygen partial pressure for the different perovskites. In case diffusion is the limiting step, $\Lambda$ 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:

$$J_O=-k_{surf}\Delta C_o$$

(22)

where $J_o$ is the oxygen flow through the surface, $k_{surf}$ is the surface reaction rate constant, $\Delta C_o$ is the difference between the oxygen surface concentration and the gas oxygen concentration, directly proportional to $\Delta \delta$. The reaction is assumed to be of first order and $k_{surf}$ 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, $\Delta {\mu }_o$, defined by Equation (23).

$$\Delta {\mu }_o={\mu }_{O,solid}\left(interface\right)-{\mu }_{o,gas}\left(interface\right)$$

(23)

$\Delta C_o$ is directly proportional to $\Delta \delta$, while ${\mu }_o={\mu }_o^0+RT\ln p_{O_2}$, $\Delta {\mu }_o$ 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 $\Delta {\mu }_O$ for each perovskite, permit to determine if the surface reaction step is the limiting step. If the oxidation peak production rate increases with the $\Delta {\mu }_O$ increase and the $\Delta \delta$ 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−xSr_xMnO₃ 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 $k_{surf}$ or $k_s$ cannot be computed.

Davenport et al. [24,77,78] developed a thermo-kinetic model. Assuming that O₂ production takes place under quasi-equilibrium conditions, the O₂ 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:

$${\dot{v}}_{O_2}\left(t\right)=\frac{{\dot{V}}_{red}}{m_{Ce{O}_2}}\frac{\left(P_{{\mathrm{O}}_2}\left(\delta ,T\right)-P_{{\mathrm{O}}_2,in}\right)}{\left(P_{tot}-P_{{\mathrm{O}}_2}\left(\delta ,T\right)\right)}$$

(24)

where $V_{red}$ is the volumetric flow rate of reducing gas, $m_{Ce{O}_2}$ is ceria mass used, $P_{tot}$ is the total pressure, $P_{{\mathrm{O}}_2,in}$ is the oxygen partial pressure at the inlet, and $P_{{\mathrm{O}}_2}\left(\delta ,T\right)$ is the oxygen partial pressure in equilibrium at a non-stoichiometry of $\delta$. Concerning the oxidation rate, a similar expression is obtained by applying the mass balance constraints on water, hydrogen and oxygen:

$${\dot{v}}_{H_2}=-\frac{{\dot{V}}_{ox}}{m_{Ce{O}_2}}\frac{(2P_{{\mathrm{O}}_2}\left(\delta ,T\right){\widehat{P}}_{{\mathrm{O}}_2}{\left(\delta ,T\right)}^{\frac{1}{2}}+2P_{{\mathrm{O}}_2}\left(\delta ,T\right)K_{{\mathrm{H}}_2\mathrm{O}}-{\mathsf{\chi }}_{{\mathrm{H}}_{2}O}{K}_{{\mathrm{H}}_2\mathrm{O},T}\left(P_{tot}-P_{{\mathrm{O}}_2}\left(\delta ,T\right)\right)}{\left({\widehat{P}}_{{\mathrm{O}}_2}{\left(\delta ,T\right)}^{\frac{1}{2}}+K_{{\mathrm{H}}_2\mathrm{O},T}\right)\left(P_{tot}-P_{{\mathrm{O}}_2}\left(\delta ,T\right)\right)}$$

(25)

where ${\dot{v}}_{H_2}$ is the normalized flow rate of hydrogen, ${\dot{V}}_{ox}$ corresponds to the volumetric flow rate of oxidant gas; ${\chi }_{H_{2}O}$ is the molar ratio of H₂O in the oxidizing gas; $\widehat{P}$ is $P/P_{ref}$ and $K_{{\mathrm{H}}_2\mathrm{O},T}$ 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 $P_{{\mathrm{O}}_2}\left(\delta ,T\right)$ which can be computed thanks to Equation (26).

$$\frac{1}{2}\ln \left(P_{{\mathrm{O}}_2}(\delta ,T)\right)=\frac{-{\Delta \mathrm{H}}_{red}\left(\delta \right)+T{\Delta \mathrm{S}}_{red}\left(\delta \right)}{RT}$$

(26)

The thermodynamic properties used in Equation (26) can be found in the literature. By this way, the gas flow rates of O₂ and H₂ 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 Ncm³/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.

5. 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.