Invited Talk: The Role of Entropy in the Success of Nonstoichiometric Oxides for Solar Thermochemical Water and CO2 Splitting

Owing to their high theoretical efficiency, solar thermochemical water and CO₂ splitting cycles provide a promising pathway to store solar energy in a stable chemical bond. Because direct thermolysis of H₂O and CO₂ proceeds at prohibitively high temperatures, the two-step cycle using a metal oxide intermediate has been extensively investigated as a practical lower-temperature process. In Step 1 of the redox cycle, a metal oxide MO_ox is reduced to MO_red at high temperature T_red using concentrated solar energy to drive the reaction endotherm. In Step 2, the reduced oxide is cooled to T_ox and H₂O and/or CO₂ are introduced. The now oxygen-hungry MO_red is capable of stripping an oxygen from H₂O or CO₂ to produce H₂ or CO fuel, while recovering the initial MO_ox such that the cycle can repeat. The efficiency of the process is highly dependent on the MO_ox/MO_red pair used to facilitate the reaction. To date, the most successful demonstrations have utilized non-stoichiometric oxides, for example CeO_2−δ, a special class of materials capable of continuously transitioning from MO_ox to MO_red without changing their crystallographic phase. The success of non-stoichiometric oxides is typically attributed to their ability to maintain their crystallographic phase, allowing them to be cycled many times without destabilizing. This is a tremendous practical advantage.

In this work, we will present an alternative explanation of the success of non-stoichiometric oxides from a performance perspective. In particular, we first illuminate the importance of entropy as a key driver in the efficiency of the two-step redox cycle. The entropy change ΔS_rxn of the MO_ox → MO_red + O₂ reaction is a gauge of the effect of the temperature swing between Step 1 and Step 2: the higher ΔS_rxn, the lower the ΔT = T_red − T_ox needed to thermodynamically switch between Step 1 and Step 2. Because sensible heating between T_red and T_ox constitutes the major energy loss in the cycle, minimizing ΔT is key to maximizing efficiency. In this light, maximizing ΔS_rxn can be seen as a first step towards finding an optimal redox material.

Stoichiometric most metal/oxide pairs, for example SnO₂ → Sn + O₂, suffer from an inherent flaw: the reduced metal is typically more ordered than its oxide counterpart. The thermodynamic significance of this is paramount. The reaction entropy is ΔS_rxn = S_MOred + S_O2− S_MOox = S_ss + S_O2, where S_ss = S_MOred− S_MOox is the entropy change in the solid state and S_O2 is the entropy associated with the liberated oxygen. In this reaction ΔS_rxn will be a positive quantity, and here we would like to maximize it. Now S_O2 is fixed by the temperature and partial pressure of the system. Holding those operating parameters constant, the only way we can increase ΔS_rxn is by making S_ss positive and as large as possible. However, recall that for a typical stoichiometric pair the reduced metal is more ordered (lower entropy) than its oxide. Therefore, for most stoichiometric pairs S_ss is negative, and so contributes negatively to ΔS_rxn.

For a non-stoichiometric pair, for example CeO₂ → CeO_1.8 + 0.1O₂, the above analysis procedure remains the same, but the result can be starkly different. Oxygen liberation in a non-stoichiometric oxide is concomitant with oxygen vacancy formation in the crystal. Therefore, reduced non-stoichiometric oxides are less ordered than their oxidized counterpart, which can be attributed to the configurational entropy associated with vacancy formation in the lattice. Because of this, S_ss can be positive for non-stoichiometric pairs, thereby giving them the unique capability of boosting to ΔS_rxn above that of S_O2.

In this work, the above phenomenon is investigated from an empirical and statistical thermodynamic approach. In particular, we investigate the potential to maximize ΔS_rxn through the appropriate choice of non-stoichiometric material, and nonstoichiometry, δ, endpoints for both the reduction and oxidation step. We then explore how this unique property of non-stoichiometric can be exploited to maximize the theoretical conversion efficiency of two-step thermochemical water and CO₂ splitting. Ultimately, we hope that this works will shed some light on the role of entropy in redox cycles based on non-stoichiometric oxides, and may pave a path to new materials discovery, guided by a principle of maximizing the solid-state entropy change.