We present a comprehensive thermodynamic and kinetic analysis of the suitability of cerium oxide (ceria) for thermochemical fuel production. Both portions of the two-step cycle, (i) oxygen release from the oxide at 1773 and 1873 K under inert atmosphere, and (ii) hydrogen release upon hydrolysis at 1073 K, are examined theoretically as well as experimentally. We observe gravimetric fuel productivity that is in quantitative agreement with equilibrium, thermogravimetric studies of ceria. Despite the non-stoichiometric nature of the redox cycle, in which only a portion of the cerium atoms change their oxidation state, the fuel productivity of 8.5–11.8 ml of H2 per gram of ceria is competitive with that of other solid-state thermochemical cycles currently under investigation. The fuel production rate, which is also highly attractive, at a rate of 4.6–6.2 ml of H2 per minute per gram of ceria, is found to be limited by a surface-reaction step rather than by ambipolar bulk diffusion of oxygen through the solid ceria. An evaluation of the thermodynamic efficiency of the ceria-based thermochemical cycle suggests that, even in the absence of heat recovery, solar-to-fuel conversion efficiencies of 16 to 19 per cent can be achieved, assuming a suitable method for obtaining an inert atmosphere for the oxygen release step.
More energy from sunlight strikes the Earth in one hour than all of the energy consumed on the planet in one year (Lewis & Nocera 2006). Thus, the challenge that modern society faces is not one of identifying a sustainable energy source, but rather one of capitalizing on the vast solar resource base. Despite its intermittent supply, solar electricity levels of up to about 20 per cent can be integrated into existing electricity delivery networks through careful management of grid resources (National Academy of Sciences 2009). For significantly greater penetration and an eventual complete transition away from fossil energy, however, the photon energy must be stored and made available for use when and where energy is needed. To enable this objective, several plausible storage solutions are already being pursued in laboratories worldwide, including high-energy-density batteries, hydrogen production via electrolysis, and hydrogen production via direct photolysis. Despite these efforts, large-scale energy storage remains elusive. We pursue in this work an alternative strategy that relies on the capacity of selected non-stoichiometric metal oxides, specifically cerium oxide (ceria), to release and uptake oxygen in response to changes in temperature, where the thermal cycling is, ideally, induced by exposure to solar radiation. The resulting stoichiometry changes can be directly used for fuel production when coupled with the introduction of appropriate reactant gases. For example, for hydrogen production, the reaction cycle for the metal oxide MO2, where M represents Ce and often also a dopant element, can be described as follows. 1.1 An analogous reaction cycle can be written for CO2 reduction, where thermodynamics predicts that the product will be CO rather than C(graphite) when the lower-temperature step is carried out at sufficiently high temperatures (Chueh & Haile 2009b).
This thermochemical approach has its roots in reaction schemes developed in the 1970s aimed at using the heat from nuclear reactors (Funk 2001; Kodama & Gokon 2007). The early schemes typically involved corrosive gases such as H2SO4 and HBr, and cycles with as many as 3–5 individual reaction steps. The concept of using metal oxides as substrates for thermochemical production of hydrogen first appeared in the literature in a publication by Nakamura (1977), in which cycling between Fe3O4 and FeO was demonstrated. The specific reactions employed were 1.2and 1.3 The thermochemistry of this pair of reactions is such that (under standard pressures) the first is favoured at temperatures above 2500 K and the latter at temperatures below about 1000 K. The extremely high temperatures required for the reduction step (which exceeds the melting temperatures of both FeO and Fe3O4) render this specific cycle impracticable, but the approach nevertheless introduced the notion of metal oxides as thermochemical reaction media and a new strategy for thermochemical fuel production. To lower the temperature of the first step, substitution of Fe by more easily reduced metals has been pursued (Tamaura et al. 1995; Steinfeld et al. 1999; Kodama & Gokon 2007). Thermodynamic analyses have shown Co, Ni and Zn to be the most promising. State-of-the-art approaches now use these substitutional compounds, with cycles between the wustite (MO) and spinel (M3O4) phases. An alternative metal oxide approach, the Zn(g)/ZnO cycle, embraces rather than avoids the volatility of the material in the reduced state (Steinfeld 2002). Difficulties arise in this case from the need to quench the Zn from the gaseous state to prevent reoxidation and the need to use nanoparticle Zn in the hydrolysis step to obtain sufficient reaction kinetics (Wegner et al. 2006; Melchior et al. 2009).
In the 30 years since the first report by Nakamura (1977) on the FeO/Fe3O4 cycle, significant efforts have been directed towards practical implementation of the alternatives described. It has been recognized that, for the doped MO/M3O4 systems, stability of the particles—against sintering, vaporization or even melting—is essential for ensuring easy access of the gaseous phase to the entirety of the material. One strategy that has emerged is the use of zirconia as a support to prevent high-temperature coagulation of the active oxide (Kodama et al. 2006; Gokon et al. 2008; Miller et al. 2008). While this approach improves short-term cyclability, it introduces redox-inactive material into the reaction vessel, thereby lowering efficiency and gravimetric fuel productivity, and the long-term stability of such systems is unknown. For the Zn(g)/ZnO system, the challenges of delivering mass quantities of nanoparticles through reactor systems have just begun to be tackled. Thus, despite significant progress, substantial hurdles remain for the thermochemical production of hydrogen using oxides, motivating additional efforts in materials development.
Based on the lessons learned from the fully solid-state MO/M3O4 systems, one can surmise that, for realistic implementation of solar-thermal fuel production, materials with excellent thermal stability, a high tendency towards reduction under moderate heating and an ability to maintain open architectures, at both the crystal structure and microstructure levels, under aggressive thermal cycling are desirable. Furthermore, development of thermochemical cycles that produce not only hydrogen but also fuels such as CH4, CH3OH or CO (the latter as a syngas component) using CO2 as an input may have greater immediate acceptability into our energy production and delivery infrastructure. In totality, these considerations suggest that ceria, which undergoes substantial oxygen stoichiometry changes without a change in crystal structure, has an extremely high melting temperature of approximately 2800 K, and displays high catalytic activity towards carbon-containing gases (Jin et al. 1987; Trovarelli 1996; Murray et al. 1999; Park et al. 2000; Sharma et al. 2000; Demoulin et al. 2007), is an attractive material for thermochemical fuel production. Indeed, preliminary reports of the suitability of ceria for this technology have appeared in the recent literature (Abanades & Flamant 2006; Kaneko et al. 2007, 2008; Kang et al. 2007; Miller et al. 2008; Kaneko & Tamaura 2009). Here, the reaction scheme (figure 1) involves a partial reduction at high temperature rather than a stoichiometric phase change. We have recently reported our initial results targeting direct methane and syngas production using samarium-doped ceria, and, despite lower oxygen uptake and release capacity than in stoichiometric cycles (MO/M3O4 and M/MO), we have shown that considerable fuel production rates are possible (Chueh & Haile 2009a). In this work, we provide full documentation of the desirable thermodynamic and kinetic characteristics displayed by ceria for this process.
2. Characteristics of ceria relevant for thermochemical fuel production
Under ambient pressures and from room temperature to the melting point, fully oxidized ceria adopts the ideal cubic fluorite crystal structure (figure 2a). Under reducing conditions, a portion of the Ce converts to the 3+ oxidation state, and these reduced species are charge-balanced by oxygen vacancies, where δ in the stoichiometry CeO2−δ represents the vacancy concentration. A remarkable feature of ceria is that, particularly at high temperatures, exceptionally high vacancy concentrations can be accommodated without a change in crystallographic structure (or phase). Indeed, at temperatures above approximately 1000°C (figure 2b), a δ of 0.25 can occur entirely within the framework of the fluorite phase. Furthermore, under conditions of rapid oxygen loss, vacancy ordering to obtain the CenOm phases may be suppressed and even higher δ values within the fluorite framework appear possible.
While figure 2b shows the phase behaviour of CeO2−δ as a function of oxygen non-stoichiometry, perhaps more relevant for thermochemical cycling is knowledge of the oxygen non-stoichiometry as a function of oxygen partial pressure (or, more strictly, oxygen activity) and temperature, as this determines the maximum quantity of fuel that can be produced in a single cycle for a given quantity of ceria. The thermodynamics embodied in the equilibration between ceria and gas-phase oxygen furthermore provides the basis for evaluating material behaviour during cycling. In the case of undoped ceria, direct measurements of the oxygen non-stoichiometry have been carried out over a wide range of conditions (Panlener et al. 1975), including those relevant for thermochemical fuel production (figure 3). Where such extensive measurements have not been carried out, the high-temperature behaviour can be approximated from an extrapolation of properties measured at more accessible conditions.
The governing reaction establishing the oxygen non-stoichiometry is the equilibration of ceria and gas-phase oxygen, i.e. the redox reaction, written in Kröger–Vink notation as 2.1 where the species is equivalent to a small polaron (a localized, mobile electron). Physically, this is equivalent to an infinitesimal change in non-stoichiometry, expressed (on a per mole atomic oxygen basis) as 2.2 where M is the trivalent dopant and x is the doping level.
In the limit of ideal solution behaviour, the equilibrium constant for the redox reaction (explicitly for the oxidation direction) is given by 2.3 where ΔG0oxd, ΔH0oxd and ΔS0oxd are, respectively, the standard Gibbs free energy, enthalpy and entropy of oxidation, R and T have their usual meanings, p*O2 is the oxygen partial pressure relative to the standard state (1 atm), and square brackets indicate the defect concentrations relative to the standard concentrations (defined as the density of crystallographic sites). Applying electroneutrality ( and crystal site conservation ( and , one obtains an explicit equation relating oxygen non-stoichiometry to the standard oxidation enthalpy and entropy, temperature, oxygen partial pressure and doping level: 2.4 This expression applies both to the electrolytic regime, in which the dopant concentration greatly exceeds the polaron concentration, and to the electronic regime, in which the reverse is true. The assumption of ideal solution behaviour required for ready application of equation (2.4) is equivalent to the statement that the oxidation enthalpy is, to a first approximation, independent of defect concentration, and that the configurational entropy describes a solution with random and non-interacting defects. It has been shown that ideal solution behaviour is obeyed in 15–20% samarium-, gadolinium- and yttrium-doped ceria for δ as large as 0.03–0.05 (Wang et al. 1997; Kobayashi et al. 1999; Otake et al. 2003). In contrast, undoped ceria deviates from ideal solution behaviour for δ greater than 0.01 (Panlener et al. 1975; Duncan et al. 2007; Bishop et al. 2009). Non-idealities typically result from the formation of intrinsic defect complexes, with the effects generally being more pronounced at higher δ and lower temperatures (Otake et al. 2003; Duncan et al. 2007; Bishop et al. 2009).
For the specific case of 15 per cent samarium-doped ceria (Sm0.15Ce0.85O1.925−δ, or SDC15), the experimentally determined standard enthalpy and entropy of the oxidation reaction are −4.18±0.05 eV and −1.15 ± 0.05 meV K−1, respectively (Lai & Haile 2005; Chueh & Haile 2009b). Using these values and equation (2.4), the computed non-stoichiometry in this material varies as shown in figure 3. From the two sets of data provided in figure 3, it is evident that, at TH=1773 K under inert gas with an oxygen partial pressure of 10−5 atm, a non-stoichiometry in the range of δ=0.03–0.05 is expected for SDC15 (accounting for the uncertainty in the enthalpy and entropy values), whereas the measured value is 0.06 for undoped ceria. In turn, these values are equivalent to the release in the reduction half-cycle at TH of 2–3 ml of O2 per gram of fully oxidized SDC15 and to 4 ml of O2 per gram of fully oxidized CeO2 (hereafter reported simply in units of ml g−1, irrespective of doping).
Turning to the fuel production half-cycle at TL, and the particular case of hydrogen production, the overall reaction can be expressed as the sum of the ceria oxidation reaction and the steam dissociation reaction (reaction (1.1)). 2.5 If the reaction is run with excess steam, thermodynamics predicts the ultimate complete reoxidation of the reduced ceria, and the quantity of fuel produced will be exactly equal, within a stoichiometric factor, to the non-stoichiometry achieved at TH. However, operation of the system in such a mode implies tremendous energy penalties, as excess quantities of gas must be heated and cooled in each cycle. A more realistic scenario is one in which the quantity of gas-phase reactant is fixed at some value that appropriately balances the available oxygen non-stoichiometry. The quantity of fuel produced in this scenario depends not only on the oxygen non-stoichiometry attained at TH, but also on the relative reducing potential of the ceria, and can be computed, much as in the case of the reduction half-cycle at TH, from a knowledge of the thermodynamic parameters.
The equilibrium constant for the overall reaction (equation (2.5)) of reduced ceria with steam, K′, is simply given as KWKoxd, where KW is the equilibrium constant for steam dissociation and Koxd is as given in equation (2.4). Taking the system comprising reduced ceria plus steam to be closed and hence to obey mass conservation, one finds 2.6 where δf=δi−α/nCeOy, δi is the initial non-stoichiometry attained in the high-temperature reduction step, nCeOy is the number of moles of ceria, nH2O,i is the initial number of moles of water, and α is the extent of reaction in moles. Solving for α yields the amount of hydrogen produced at equilibrium. Gaseous oxygen, which is assumed to take on a very low concentration during fuel production, is excluded here from the mass balance for computational simplicity. If the defect model and hence Koxd are not well known, one can alternatively predict the equilibrium fuel productivity from knowledge of the partial molar free energy of lattice oxygen, ΔGO, as a function of temperature and non-stoichiometry according to the relationship: 2.7 In the case where the input reactant is carbon dioxide (rather than water), an expression analogous to equation (2.6) or equation (2.7) can be obtained. Here one begins with the reduction of CO2, where both CO and C(graphite) are considered as possible products through the following two reactions. 2.8 2.9 Again, the extent of reaction yields the equilibrium quantity of CO and/or C produced. Taking the process one step further, one can consider the simultaneous dissociation of CO2 and H2O to yield methane as a product through the reaction 2.10 where the water-gas-shift equilibrium is taken into account implicitly.
With this formalism, the equilibrium gas-phase compositions were computed for δi=0.05 and (i) nH2O,i=δinCeOy, (ii) , and (iii) , with details provided in the Methods section below (§5). While the quantity of reactant supplied under this set of conditions is stoichiometrically sufficient for full reoxidation of the ceria, thermodynamic considerations indicate that the reoxidation will not proceed to completion and instead the ceria will attain, upon system equilibration, a non-zero non-stoichiometry, δf. The fuel production capacity in the oxidation half-cycle is given in such a case not by the initial non-stoichiometry achieved at high temperature, δi, but by the change in oxygen non-stoichiometry: 2.11 Each mole of stoichiometry change in bulk oxygen content corresponds to either 1 mole of H2, 1 mole of CO, 0.5 mole of C(graphite) or 0.25 mole of CH4 produced. The results of the computation (figure 4) show that the amount of fuel produced increases as TL is lowered, consistent with the greater driving force for ceria oxidation at lower temperatures relative to hydrogen or carbon oxidation. The implication of this behaviour on overall solar-to-fuel conversion efficiency, which at first glance might be considered to benefit from a small temperature swing between TH and TL, is discussed below (see §4).
An arguably more common method for assessing the thermodynamic suitability of a potential thermochemical reaction medium is through a direct consideration of ΔGoxd in comparison to ΔGrxn for hydrogen oxidation (figure 5) for standard state conditions (pgas=1 atm). A subtlety arises here in that the initial and final δ values in the calculation of ΔGoxd of ceria are inherently arbitrary. For simplicity, the reaction is considered in the limit in which the non-stoichiometry change is infinitesimal (as in the case of equation (2.2)), and several selected values of δ are considered. The data are also compared to the stoichiometric reaction , which has no contribution from defect configurational entropy, and is directly analogous to a reaction such as . The figure reveals graphically the thermodynamic underpinnings of the thermochemical reaction approach. In general, where ΔGoxd of ceria lies below ΔG0rxn of hydrogen oxidation, i.e. at low temperatures, the ceria has sufficient reducing power that it will induce dissociation of steam as the ceria becomes oxidized. At high temperatures, the reducing power of ceria decreases, as indicated by the decrease in magnitude of ΔGoxd, and where ΔGoxd becomes positive, ceria releases oxygen (under 1 atm pO2). The clear dependence of ΔGoxd on δ results from the dependence of both the cerium–oxygen bond enthalpy and the configurational entropy on defect concentrations. As evident from figure 5, the dependence is such that, at a given temperature, TH, it is increasingly more difficult to liberate additional oxygen from ceria (ΔGoxd becomes increasingly more negative with increasing δ). Similarly, at a given TL, it is increasingly more difficult to reoxidize ceria because the difference ΔGoxd−ΔGrxn becomes less negative with decreasing δ. These considerations thus reveal subtle differences in the manner in which the redox thermodynamics of non-stoichiometric compounds and stoichiometric reactions apply to thermochemical reactions.
Turning from the thermodynamics to the kinetics of thermochemical fuel production, both the oxygen release (TH) and the water or carbon dioxide dissociation (TL) portions of the cycle require serial steps of heterogeneous surface reaction and oxygen bulk diffusion. In principle, either reaction step may be rate-limiting. The time for bulk diffusion can be estimated from knowledge of the chemical (or ambipolar) diffusion coefficient, , describing the coupled migration of oxygen vacancies and electrons under an oxygen chemical potential gradient. For a mixed oxide-ion and electron conductor, depends on the individual oxide vacancy and electron diffusion coefficients, Dion and Deon, respectively, according to 2.12 where kB is Boltzmann’s constant, μion and μeon are the chemical potentials of oxygen vacancies and electrons, respectively, and cion and ceon are the volumetric concentrations of vacancies and polarons, respectively. In the ideal solution limit, the ambipolar diffusion coefficient becomes 2.13 where the pO2-dependent oxygen vacancy and polaron concentrations are as given from the thermodynamic treatment provided above. If not directly available, the diffusivities may be obtainable from the electrical mobilities, , through the Nernst–Einstein relationship 2.14 where ezi is the charge of species i. Using the mobility data reported for SDC15 (Lai & Haile 2005), such an analysis yields the ambipolar diffusion coefficient presented in figure 6, where both the directly measured (Lai & Haile 2005) and the computed values for a range of temperatures and oxygen partial pressures are presented. The slight deviations between the two sets of values are due to slight dependences of the mobilities on carrier concentrations, a consideration not explicitly accounted for in the calculation.1 Under the limiting conditions in which the doped material is held deep in the electrolytic regime such that Deonceon≪Dioncion (requiring ceon≪cion/10 because of the higher mobility of electrons), equation (2.13) reduces to . Deep in the electronic regime in which 2cion≅ceon, the ambipolar diffusion coefficient reduces to . For fixed mobilities, of acceptor-doped ceria decreases with increasing defect concentrations (increasing δ, decreasing pO2) as the transport process transforms from one that is determined entirely by the electron mobility to one that is an appropriately weighted average of both the electron and vacancy mobilities. More significant is the overall remarkably high value of , falling within the range of 1.7×10−5 to 1.1×10−4 cm2 s−1 at 1073 K and within 2.1×10−4 to 3.6×10−4 cm2 s−1 at 1773 K.
For undoped ceria, the electron and oxygen ion vacancy concentrations are related according to 2cion=ceon under all relevant oxygen partial pressures and temperatures and, accordingly, the latter limiting expression for applies under all conditions. This consideration implies, in turn, that the ambipolar diffusion coefficient is independent of defect concentration under the ideal solution limit. Assuming that the vacancy and polaron mobilities are the same in doped and undoped ceria, the value for this fixed ambipolar diffusion coefficient corresponds to the minimum value encountered in doped ceria, i.e. that at high δ. At low oxygen non-stoichiometry (close to ambient oxygen partial pressures) the chemical diffusion coefficient in SDC15 is substantially higher than it is in undoped ceria. The difference is about one order of magnitude at 923 K and increases at lower temperature owing to the larger enthalpy of vacancy ion migration than electron migration.
With the diffusion coefficient in hand, it is possible to obtain the characteristic time, t, for a diffusion-limited process from the expression , where l is the diffusion length. Using the smallest value of for each temperature in the 773–1073 K range and a diffusion length of 5 μm (a typical grain size in porous ceria), the characteristic diffusion time falls in the range of only 4–0.3 ms. A more rigorous calculation that takes into the account the temporal and positional variations of as the reaction proceeds gives values within the range of 2–0.1 ms. This estimate indicates that bulk diffusion is unlikely to be rate-limiting in thermochemical fuel production unless the surface reaction rate is exceptionally rapid, or reaction substrates with extremely unfavourable geometric configurations and/or morphological characteristics are used.
3. Experimental demonstration
With these expectations in hand, CeO2−δ was exposed to thermochemical cycling, from which the thermodynamics, kinetics and stability of fuel production were examined. Procedural details are provided below (§5). The results (figures 7–10) indicate that ceria is remarkably well suited as a thermochemical reaction medium. On aggressive heating (1000 K min−1) to 1773 K under an inert atmosphere (pO2=10−5 atm), almost immediate release of oxygen is observed (figure 7a). The total quantity of oxygen detected by mass spectrometry, 4.3±0.3 ml g−1, corresponding to δ=0.066±0.005, is within error of the value of 4 ml g−1 determined via thermogravimetry (Panlener et al. 1975). An identical oxygen release amount, within experimental error, was obtained for lower ramp rates (e.g. 100 K min−1). Moreover, the oxygen release reaches 70 per cent completion within 5 min of the initiation of the heating and largely keeps pace with the rate of temperature rise throughout heating. Upon lowering the temperature to 1073 K and introducing steam (pH2O=0.25–0.27 atm), rapid hydrogen production is observed, with 90 per cent of the fuel produced within 1.8 min of initiation. Furthermore, the total amount of hydrogen produced, 8.5±0.6 ml g−1, implies complete reoxidation of the reduced ceria and hence full use of the available non-stoichiometry. Together, these values correspond to an average hydrogen production rate of 4.6 ml min−1 g−1 (instantaneous reaction rate averaged over the time required to reach 90 per cent of the extent of reaction).
Raising the temperature of the oxygen release step is expected, on thermodynamic grounds, to increase the extent of oxygen non-stoichiometry (figure 3), and indeed experimentally such behaviour is observed (figure 7b). Ceria reduction at 1873 K increases oxygen release from 4.3 to 5.9±0.4 ml g−1, or to δ=0.091±0.006. After cooling and steam injection at 1073 K, the entirety of the structural non-stoichiometry is again used in the fuel production step, with 11.8±0.8 ml g−1 now produced. The rate, 6.2 ml min−1 g−1, is higher than that for the less reduced material, possibly as a result of increased surface vacancy concentrations leading to higher reaction rates.
While the kinetics of thermochemical fuel production using ceria are seen here to be relatively facile, it is noteworthy that, in comparison to the expectations for a bulk-diffusion-limited process (with characteristic time estimated at 0.3–4 ms above), the rates are, in fact, rather slow, indicating that some other step must limit the overall reaction kinetics. Under non-isothermal conditions, the oxygen release process is largely limited by the rate at which the ceria can be heated using the furnace employed, as evidenced by the oxygen release behaviour on heating, already noted above, and by the further observation that the oxygen release rate depends on the heating rate (for experiments performed at heating rates as low as 100 K min−1). Under isothermal conditions, heat transfer is unlikely to be rate-limiting because the quantities of heat generated or consumed by the reaction are small relative to the heat input from the furnace. A remaining possibility as the rate-limiting step is the surface reaction, and, indeed, the experimental evidence points in this direction. The hydrogen production over Rh-decorated SDC15 was found to be substantially faster than over neat SDC15 (figure 8). The reaction was examined in this instance under kinetically unfavourable conditions of low overall water partial pressure in order to capture the influence of the catalyst. The almost fivefold increase in hydrogen production rate upon introduction of Rh indicates that a step involving the surface must be rate-limiting and that bulk, ambipolar oxygen diffusion is much too rapid to have any detrimental impact on fuel production rates.
Beyond suitability for hydrogen production (both thermodynamically and kinetically), ceria has the characteristic of rapidly dissociating CO2 to CO and lattice oxygen (figure 9). Once again, the fuel productivity matches precisely that expected for complete use of the structural oxygen non-stoichiometry, and at 1073 K the average reaction rate is 1.6 ml min−1 g−1 (pCO2=0.032 atm). As discussed in greater detail in our previous study (Chueh & Haile 2009a), CO2 dissociation at temperatures below approximately 940 K would be anticipated to yield solid carbon (at least in transient form), as shown in figure 4. However, no carbon deposition has been observed on neat ceria, even at a very low gas space velocity of 4300 h−1. The situation is altered by the introduction of a catalyst such as Ni that enables transient carbon deposition under thermodynamically favourable conditions. The carbonaceous species produced in this step provides a path to direct methane formation when CO2 and H2O are simultaneously reacted with reduced ceria. Again, the details have been discussed previously.
In any technologically significant thermochemical process, fuel productivity (fuel per unit of oxide, ml g−1) and production rates (fuel per unit of time per unit of oxide, ml min−1 g−1) must remain high over thousands of cycles. What is evident from the long-term cycling behaviour in figure 10 (TH=1773 K, TL=1073 K) is that the hydrogen production rate decreases by about 50 per cent over the first 100 cycles, then maintains a stable value of 1.3 ml min−1 g−1 for the remaining 400 cycles. The hydrogen and oxygen productivities mirror the hydrogen production rate, decreasing, respectively, from initial values of 8 and 4 ml g−1 to stable values of 6 and 3 ml g−1 after about 100 cycles. Most significant is that for all cycles all of the non-stoichiometry created in the ceria during high-temperature reduction is subsequently used in the low-temperature water dissociation step, despite the clear loss in rate for this reaction. That is, the volumetric ratio of hydrogen to oxygen produced remains at approximately 2 throughout cycling. The overall decrease in productivity (of both oxygen and hydrogen) can be understood to be a result of the decreased reaction rates in combination with a fixed cycle time (10 min for each half-cycle) that is no longer sufficient for complete reaction. At the conclusion of the cycling experiment, it was verified that an oxygen release amount of 4 ml g−1 can indeed be obtained if the reaction is allowed to proceed to completion.
The decrease in reaction rates is most likely due to a loss in ceria surface area (figure 11), which limits the available sites for reaction to occur. Prior to thermochemical cycling, the ceria was formed into a porous monolith with a specific surface area of 0.1 m2 g−1 by sintering in the presence of a fugitive pore former. The resulting material was subsequently annealed for 3 h at 1773 K in an attempt to stabilize the microstructure. By this process, a highly porous structure (approx. 70% porosity) formed of grains with an average size of approximately 5 μm was obtained. After completion of the 500 cycles, coarsening of the microstructure is clearly evident, with the average grain size increasing to approximately 15 μm and each grain becoming significantly more faceted. These results emphasize that any path to higher overall fuel production rates (based on shorter cycle times) should focus on the surface characteristics of ceria. However, it must be noted that the oxygen and hydrogen production rates obtained here are sufficiently high that attention may be more fruitfully directed towards enhancing bulk, thermodynamic efficiency.
4. Efficiency analysis
The thermodynamic efficiency of the thermochemical approach for converting solar radiation and water to hydrogen can be written as 4.1 Where the numerator is the higher heating value (HHV) of one mole of hydrogen and Qsolar is the total heat input to the cycle (required to produce the one mole of hydrogen), consisting of re-radiation losses and three enthalpy terms: that required to heat water from 298 K to TL, that to heat ceria from TL to TH, and that to reduce ceria from CeO2−δf to CeO2−δi at TH. Together, these imply that 4.2 where nH2O is the moles of water heated per mole of hydrogen produced and Cp,j is the molar heat capacity of species j at constant pressure. The absorption efficiency, ηabs, is calculated by assuming a blackbody cavity with an incident radiation flux of 5 MW m−2. The change in ceria non-stoichiometry, Δδ, which, as already noted, for the case of hydrogen production directly yields the quantity of fuel produced, is taken from the closed-system equilibrium calculations described above. For the purposes of evaluating the impact of cycling strategies on the thermodynamic efficiency, and for comparison with other thermochemical approaches, the energy penalty associated with attaining the low oxygen partial pressure required in the reduction half-cycle (fixed here at 10−5 atm) is ignored in this analysis. Furthermore, because of the uncertainties associated with extrapolation of the properties of SDC15 to the very high temperatures of interest for thermochemical cycling, the analysis is limited to undoped ceria, for which high-temperature thermogravimetric data are available. In this case, the dependences of the partial molar thermodynamic terms for lattice oxygen (ΔGO(δ)=ΔHO(δ)−TΔSO(δ)) on non-stoichiometry are treated numerically, as determined from the raw data (figure 3).
For a given material with a fixed set of properties, the efficiency and fuel productivity can be manipulated through selection of the process parameters, TH, TL and rH2O=nH2O,i/δinCeOy, where rH2O is the molar quantity of steam injected into the system at the initiation of the fuel production half-cycle relative to the available ceria non-stoichiometry. A preliminary analysis of the dependence of efficiency on rH2O indicated a peak in efficiency at rH2O=2, and all subsequent computations were performed for this condition. The impact of changing TL and TH on equilibrium fuel productivity and efficiency is summarized in figure 12. As perhaps intuitively expected, the fuel productivity increases (figure 12a) as the temperature swing is widened. That is, Δδ increases as either TH is increased or TL is lowered. This is readily understood as follows. With increasing TH, the amount of oxygen released increases, and with decreasing TL, the reducing power of ceria to dissociate H2O increases. Incomplete reoxidation of the ceria occurs when TL is too high, and as TL is lowered, the fuel productivity rapidly approaches the maximum value of δi attained at TH. Lowering TL below about 1000 K has minimal benefit for fuel productivity, regardless of TH. It is to be emphasized that, by definition of an equilibrium calculation, it is assumed that the kinetics are fully reversible.
In terms of efficiency, a broad maximum is observed as a function of TL for any given TH (figure 12b). If TL is insufficiently low, then the reducing power of the ceria is too low to induce extensive H2O dissociation and the fuel productivity is low relative to a large input heat. If, on the other hand, TL is lower than required, i.e. beyond what is necessary to reoxidize the ceria, the excess thermal cycling is unused and, again, the efficiency decreases. This combination of factors leads to the broad peak displayed in the curves of figure 12b. An important aspect of the data in figure 12 is the fact that both fuel productivity and efficiency increase monotonically with TH for the range examined. This behaviour is highlighted in figure 12c, in which the maximum efficiency at each TH is shown (the TL implied for each of the data points rises somewhat with TH). The monotonic increase in efficiency reflects the decreasing energy cost of heating ceria per unit of fuel productivity or Δδ. That is, with increasing TH, Δδ increases exponentially and hence the second term of equation (4.2) decreases owing to the prefactor (Δδ−1) decreasing much more rapidly than the quasi-linear increase in the heat capacity integral (owing to increased temperature swing). Ultimately, a limiting value is reached because, while the energy cost of heating ceria per mole of fuel decreases with increasing TH, the other terms (reducing the ceria, heating the water to TL, and the re-radiation losses) are relatively fixed on a per mole fuel basis at the conditions examined (figure 12d). The data suggest that, if the practical challenges of achieving a high temperature oxygen release step at 2073 K and operating over a temperature swing of ΔT=940 K (TL=1133 K) can be overcome, an efficiency of almost 22 per cent is attainable, even in the absence of heat recovery. If one considers a less aggressive and arguably more realistic cycle of TH=1873 K and TL=1123 K, the efficiency remains at an attractive value of 19 per cent.
CeO2 (Alfa Aesar) and Sm0.15Ce0.85O1.925 (Nextech, SDC15) were each ball-milled with 30 wt% starch in ethanol, uniaxially pressed into a pellet, and sintered at 1623 K for 5 h. The porous monolith, typically more than 65 per cent in porosity, was polished into a cylinder measuring 0.25–0.32 g in weight, 7 mm in diameter, and 2–4 mm in thickness. The sample was then loaded into a horizontal alumina tube reactor (9.5 mm diameter), in turn placed inside an infrared furnace (Ulvac-Riko VHT-E44). A thermocouple, enclosed in an alumina sheath, was placed in direct contact with the sample and used to control the furnace. Temperature ramp rates were varied from 100 to 1000 K min−1. During the temperature ramp from TL to TH, the isothermal dwell at TH (reduction half-cycle), and temperature ramp down to TL, digital mass flow controllers delivered 10 ppm O2 (balance N2) gas at 1000 ml min−1 to the reactor. After equilibration at TL, the sample was exposed to humidified N2, achieved by passing 200 ml min−1 dry gas through a bubbler inside a temperature-controlled oven. Effluent humidity was measured using a Rotronic Hygroflex 2 sensor, and dried, effluent gas composition was determined using a Pfeiffer Thermostar GSD301 quadrupole mass spectrometer. Quantification of the mass spectrometry data was achieved by performing, daily, six-point calibrations for both oxygen and hydrogen at the concentrations of interest. A blank run with no sample confirmed that the alumina tube does not release or absorb detectable amounts of oxygen, nor does it dissociate water.
A slightly different set-up was used to examine CO2 dissociation into CO, as well as the effect of metal catalysts. For the CO2 dissociation experiment, the starting powders were ball-milled with starch and pressed into a pellet as described above and sintered at 1773 K for 24 h. To reduce the effect of gaseous mass transport, the pellet was lightly crushed and sieved to obtain particle sizes between 150 and 500 μm. For the catalyst experiment, Rh–SDC15 was prepared via incipient wetness impregnation by dissolving rhodium nitrate. After calcining at 1023 K, the powder was pressed into a pellet, crushed and sieved (same as above), and the agglomerates sintered at 1773 K for 24 h. SDC15 without the catalyst was prepared in the same manner for comparison. Samples containing 1 g of material were loaded into a 10 mm diameter, vertical, packed bed reactor with the particles held in place by a porous quartz frit. Reaction gases were delivered by digital mass flow controllers, and the effluent gas was measured by a Varian CP-4900 gas chromatograph equipped with PoraPak Q and Molecular Sieve 5A columns. H2, CH4, CO and CO2 concentrations were converted to flow rates using an internal N2 standard, which also served as a diluent. In some cases, Ar was also used as a diluent. Gas chromatography calibration curves were established using analytical-grade, premixed gases. The reduction of ceria was achieved by flowing a mixture of H2, H2O and Ar at either pO2=2.0×10−21 atm at 1073 K or 3.8×10−18 atm at 1173 K. Humidification was achieved by bubbling the reaction gas through an H2O bubbler inside a temperature-controlled bath. The pO2 was calculated by assuming gas-phase equilibrium and verified using an oxygen sensor. The oxidation of ceria was achieved by passing diluted water vapour or CO2 over the packed bed of ceria particles. The temperature excursion upon oxidation of the ceria in no case exceeded 6°C.
(i) Undoped ceria
The oxygen enthalpy and entropy measured as a function of oxygen non-stoichiometry (Panlener et al. 1975) were interpolated using appropriate exponential or polynomial functions. The equilibrium fuel productivity was then computed using thermodynamic parameters for H2(g), H2O(g) and O2(g) from JANAF and NASA tables. All computations were carried out in Matlab.
(ii) Samarium-doped ceria
The experimentally measured standard oxygen enthalpy and entropy (Lai & Haile 2005; Chueh & Haile 2009b) were extrapolated to higher temperatures and oxygen partial pressures using the ideal solution model. Furthermore, the temperature dependences of the standard enthalpy and entropy were determined by using the Dulong–Petit law to estimate the heat capacity of lattice oxygen and using NASA tables for the heat capacity of gaseous oxygen. The equilibrium hydrogen fuel productivity and efficiency were calculated in the same way as for undoped ceria. The equilibrium CO, CO2, C(graphite) and CH4 productivities were calculated using the GIBBS Solver (HSC Chemistry). The activity of C(graphite) was taken to be unity.
6. Concluding remarks
The overall evaluation of the thermodynamic and kinetic characteristics of ceria, both undoped and doped, indicates that it is attractive as a thermochemical reaction medium. It is of some importance to compare these characteristics with those of other materials also considered for such an application. The most important figures of merit are the fuel productivity (which determines the amount of reaction medium required and thereby the size of the solar thermochemical power plant, and also influences the efficiency), the fuel production rate (which determines how quickly the cycles can be performed, influencing both the size of the power plant and the efficiency), and the thermodynamic efficiency (computed as described above on the assumption of reversible kinetics). Moreover, the overall ease of implementing the cycling strategy is an additional factor requiring consideration.
On first inspection, a non-stoichiometric metal oxide thermochemical cycle might be expected to display a relatively low fuel productivity because of the relatively small change in gravimetric oxygen content between the high and low temperatures of the cycles. The productivity values obtained here for hydrogen are of the order of 9–12 ml g−1 (depending on the specific cycling strategy employed). In contrast, stoichiometric cycles such as FeO/Fe3O4 and Zn(g)/ZnO offer theoretical fuel productivities of 97 and 275 ml g−1, respectively. In practice, however, these productivity values have not been demonstrated. Because use of a redox-inactive support is required in order to achieve cyclability and reasonable kinetics in the ferrites, the gravimetric fuel productivity of the composite system is dramatically reduced, with an experimental value of 12.2 ml g−1 (TH=1673 K, TL=1073 K) having been reported for 20 wt% NiFe2O4/ZrO2 (Kodama & Gokon 2007). Furthermore, because of the low oxygen diffusivity through the stoichiometric phases (tracer diffusion coefficient approx. 10−11 cm2 s−1 at 1473 K) (O’Bryan & DiMarcello 1970), even when the ferrite is supported on zirconia the fuel production rates are rather low. For example, a hydrogen production rate of approximately 10−1 ml min−1 g−1 at 1273 K (pH2O=0.42 atm) has been reported for 20 wt% NiFe2O4/ZrO2 (Kodama & Gokon 2007), significantly lower than the rate demonstrated here. The computed thermodynamic HHV efficiency for the supported nickel ferrite cycle operating between 1673 K and 1273 K is approximately 24 per cent (obtained by the same methodology as in this work), with the heating of the zirconia as the main energy penalty. Additional challenges with the ferrite systems are the tendency towards particle coagulation, which is not entirely alleviated through use of a support—several studies have involved mechanical grinding of the material between each cycle (Kodama et al. 2006; Kodama & Gokon 2007; Gokon et al. 2008)—and the tendency towards volatilization. Slow kinetics are similarly a major challenge for the Zn/ZnO cycle, particularly during the low-temperature metal oxidation (hydrolysis) step. Here, an effectively impermeable oxide layer, with an oxygen tracer diffusion coefficient of 10−14 cm2 s−1 at 1473 K (Haneda et al. 1999), coats the metallic zinc, impeding rapid reaction. As a consequence, the hydrogen production rate is low, with a value of approximately 0.3 ml min−1 m−2 having been reported at 603 K (pH2O=0.4 atm; Ernst et al. 2009). Whether the ambitious strategy of using nanoparticulate Zn to address reaction rates can be realized and its consequences on efficiency remain to be seen.
Beyond suitability for a single solar-thermal reactor, it is important to consider the potential scalability of any thermochemical reaction medium to address world energy demands. Though a rare-earth element, cerium is in fact as similarly abundant as copper (Haxel et al. 2002), and the worldwide reserve of cerium oxide is of the order of 107 tonnes (Hedrick 2007). Based on a fuel productivity of 8×103 l of H2(g) per tonne of CeO2 per cycle, and running 100 cycles per day, approximately 5×102 tonnes are required to construct a 100 MW fuel-cell-based power plant2 that operates for 6 h d−1 (600 MWh capacity). Therefore, ceria’s reserve is sufficient to make a global impact.
While ceria offers several benefits for thermochemical cycling over alternative metal oxide systems, a ceria-based cycle is not without its own set of challenges. The most significant is perhaps the high temperatures required in order to attain high efficiency. Solar concentration to achieve a temperature of 2073 K is not inherently problematic, but it is unclear how one can construct a reactor that is compatible with such a cycling condition. Furthermore, the energy penalty of using gases with low oxygen partial pressure during the oxygen release half-cycle is a challenge that all thermochemical routes to solar fuel production must ultimately address, and if the sweep gas is nitrogen, care may be required to avoid the formation of NOx. In light of the thermodynamic analysis presented here, it is apparent that cycling strategies alone cannot be used to fully address these challenges for the parent compound CeO2−δ. Such an observation then leads one to consider whether targeted doping strategies can be employed to modify the enthalpy and entropy terms of the ceria redox reaction so as to achieve a high sensitivity of oxygen non-stoichiometry to oxygen partial pressure and temperature over any desired operating window (and shift the curves presented in figure 5). Recently, Singh et al. have reported that Ce0.67Cr0.33O2.11 can be reduced in nitrogen at a moderate temperature of 738 K. This result suggests that, indeed, materials optimization can result in a thermochemical cycle based on non-stoichiometric oxides that has even more to offer than one based on known ceria formulations in terms of the key metrics of fuel productivity, production rate, efficiency and ease of cycle operation. Irrespective of the specific composition, with the experimental data reported here, the approach is clearly demonstrated and opens up new avenues for storing solar energy in the form of chemical bonds.
This work was funded by the National Science Foundation (CBET-0829114) and eSolar Inc. The authors are grateful for insightful discussions with Prof. Aldo Steinfeld, Dr Philip Gleckman and Dr Francesco Ciucci.
↵1 In principle, the pO2-dependent mobilities can be directly used for the computation. However, for high temperatures outside of the measurement range of the earlier experiments, the nature of the pO2 dependence is unknown, precluding extrapolation of the measured data to the higher temperatures of interest for thermochemical cycling. As the diffusion coefficient is, overall, relatively insensitive to both oxygen partial pressure and temperature, these subtleties are not explored further here.
↵2 Assuming that the fuel cell operates at 298 K and produces electrical work equivalent to 50 per cent of the ΔGrxn of the hydrogen oxidation reaction.
One contribution of 13 to a Discussion Meeting Issue ‘Energy materials to combat climate change’.
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