Thermodynamic and First-principles Assessments of Materials for Solar-driven CO2 Splitting Using Two-step Thermochemical Cycles

FENG Qingying, LIU Dong, ZHANG Ying, FENG Hao, LI Qiang

Thermodynamic and First-principles Assessments of Materials for Solar-driven CO2Splitting Using Two-step Thermochemical Cycles

FENG Qingying, LIU Dong, ZHANG Ying, FENG Hao, LI Qiang

(School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China)

Carbon-neutral fuel production by solar-driven two-step thermochemical carbon dioxide splitting provides an alternative to fossil fuels as well as mitigates global warming. The success of this technology relies on the advancements of redox materials. Despite the recognition of the entropic effect, usually energy descriptors (enthalpy of formation or energy of oxygen-vacancy formation) were used for computational assessment of material candidates. Here, in the first step, the criteria was derived based on the combination of solid-state change of entropy and formation enthalpy, and was used to thermodynamically assess the viability of material candidates. In the thermodynamic map, a triangular region, featuring large positive solid-state changes of entropy and small enough solid-state changes of formation enthalpy, was found for qualified candidates. Next, a first-principles DFT+method was presented to fast and reasonably predict the solid-state changes of entropy and formation enthalpy of candidate redox materials, exemplified for pure and Samaria-doped ceria, so that new redox materials can be added to the thermodynamic map. All above results highlight the entropic contributions from polaron-defect vibrational entropy as well as ionic (oxygen vacancies) and electronic (polarons) configurational entropy.

carbon dioxide splitting; two-step thermochemical cycle; first principles; entropy; solar fuel

Using solar energy to convert carbon dioxide (CO2) into carbon-neutral fuels provides an alternative to fossil fuels and mitigates global warming. In analogy to conv-entional chemical plants, a solar-fuel plant is able to operate overnight addressing the intermittency of solar energy. Regarding this, concentrated solar thermochem-ical CO2splitting holds promise because cost-effective and high-density heat storage can be integrated into this technology[1]. Direct CO2splitting by thermolysis, req-uires temperature as high as 3000 ℃ except for separa-tion of oxygen from fuel products. Therefore, research converged to the two-step redox cycles based on partial reduction (or non-stoichiometric, oxygen-vacancy) and oxidation of non-volatile oxides (or redox materials), because this type of cycles features the combinations of practical operation temperature and high thermodynamic efficiency[1-3].

Although considerable materials[4]have been examined including ceria[5-8], ferrites[9-11]and perovskites[12-14], the state-of-the-art solar-to-chemical energy conversion effi-c-i-ency was as low as ～5% for solar thermochemical CO2splitting[5]. Therefore, computational assessments of mat-e-rials are still of great importance[15-17]. Intuitively, the the-rmodynamically suitable redox materials can be ide-ntified based on the fundamental concept that the change in the Gibbs free energy, Δ, should be negative for the two cycle steps (Reactions (2) and (3)). Thereby, solid-state enthalpy and entropy of reduction excluding the contri-butions from gaseous species (whose thermodynamic pro-perty data is available for a wide range of conditions) can be used as the descriptors for thermodynamic assess-ments of redox materials. Particularly, Meredig[18]and Shah,.[19]raised the importance of entropic effects. Unfortunately, obtaining reliable thermodynamic data, esp-ecially the reduction entropy, of redox material candida-tes, either computationally or experimentally is often challenging[11-12,20-24]. For example, Bork,.[12]used CALPHAD models to access or extrapolate needed the-rmodynamic properties of perovskites, but models with this level of sophistication are not available for many redox material candidates[2]. Michalsky,.[22]found that the Gibbs free energy for formation of many bulk oxides (equivalent to solid-state enthalpy and entropy of reduction) scaled with their oxygen-vacancy formation energy at their most stable surfaces. However, this sca-ling feature was only demonstrated in the stoichiometric regime. Muhich,.[11]developed an assessment method where only the enthalpy of reduction was used, but this method only worked for the assessments within the same class of materials (hercynite in their work) because the reduction entropy is approximately the same for the her-cynite family.

Therefore, this study provided general descriptors and criteria for thermodynamic assessments of proposed or newly discovered redox materials, and to provide first- principles methods for fast predictions of these descriptors. Here, pure and Samaria-doped ceria were taken as benc-h-mark materials because they own fast splitting kinetics, excellent high-temperature and cycling stability[5-8], and also provide a platform for first-principles investigations of the effects of typical defects including oxygen vacan-cies, polarons and dopant ions[25].

1 Thermodynamic derivation of desc--ri--ptors and criteria

In this section, the descriptors was proposed, and then the criteria was derived for thermodynamic assessments of the viability of material candidates. In the derivation, complementary constraints were presented in considera-tion of non-stoichiometric reaction mechanism, theoretical efficiency and practical operating conditions of the solar- driven two-step thermochemical process to extend the thermodynamic framework described by Meredig and Wolvertor[18].

This study starts with the fundamental concept that the change in the Gibbs free energy, Δ, should be negative for the two cycle steps (Reactions (2) and (3)) so that they are thermodynamically favorable. This gives Eq. (1–2).

where Δfrepresents the enthalpy of formation,represents entropy,represents pressure (kPa) andis the ideal gas constant. Solid-state entropy and solid-state enthalpy of formation are assumed to be temperature- independent. Observed from Eq. (1) and (2), solid-state change of entropy, Δsolid, and change of enthalpy of formation, Δsolid

depend on the redox material, while the rest quantities for gaseous species are independent and were well docu-mented[26]. Therefore, Δsolidwith unit of J?(0.5 mol O2)–1?K–1and Δsolidwith unit of kJ?(0.5 mol O2)–1, defined in Eq. (3), were used as descriptors for thermodynamic assessments in this work. By substituting Eq. (3) into Eq. (1) and (2), Eq. (4–5), two of the assessment criteria, are obtained.

In the next step, thermodynamic principles are applied to analyse the solar-to-chemical (STC) energy conversion efficiency of the two-step thermochemical process to provide complementary criteria. STC efficiency,STC=STT×TTC, whereSTTis solar-to-thermal efficiency, andTTCis thermal-to-chemical efficiency. Ideally,TTC=Δ1298K/ Δsolid, where Δ1298K(～256 kJ?(0.5 mol O2)–1) is the cha-nge in the Gibbs free energy at 298 K for CO2ther-molysis (Reaction 1). By assuming an achievableSTTof 70%, a targetTTCof 28.6% is required to achieve a practicalSTCof 20%, which is competitive to the technology that a solar photovoltaic device coupled with an electrolyser[27]. Miller,.[2]analysed that potential redox materials should be able to achieve a theoretical thermal-to-chemical efficiency which is twice of the targetTTC(Eq. (6)).

Therefore, Eq. (4) to (6) were used to calculate the boundary values of (Δsolid, Δsolid). Eq. (4) and (5) tell that the (Δsolid, Δsolid) boundary varies with operating temperatures (HandL) and operating pressure (O2). For the thermal reduction step of a practical solar ther-mochemical reactor,H=2000 K[18]andO2=0.101 kPa[2]were used as the upper limit for the reduction tempera-ture and the lower limit for the pressure respectively. For the oxidation step, the exothermic reaction is thermody-namically favorable for low temperatures, but suffers fromslow kinetics. Thus,Lof 1000 K[18]was used as the lower limit for the oxidation temperature. Now, the criteria is summarized as Eq. (7) with the descriptors, Δsolidand Δsolid, defined in Eq. (3).

As shown in Fig. 1, the (Δsolid, Δsolid) area below the purple curve features theoretical thermal-to-chemical efficiency which is twice higher than the target. (Δsolid, Δsolid) below the green curve and above the blue curve are thermodynamically favorable for thermal reduction step (Reaction (2)) and CO2splitting step (Reaction (3)) res-pectively. Therefore, the combination of Δsolidand Δsolidof qualified redox material should fall in the shaded triangular region.

These results highlight the importance of accurate predictions of Δsolidand Δsolid, which are investigated in Section 2. Fig. 1 also shows that a positive Δsolidopensthe favorable region, so redox materials with large positive Δsolidbenefits reaction thermodynamics. However, this is non-trivial for redox materials in the stoichiometric regime, because the reduced oxide has fewer atoms and thereby, fewer vibrational degrees of freedom.

Fig. 1 Thermodynamic assessment map

The combination of Δsolidand Δsolidof redox material candidates should fall in the shaded triangular region. The experimental data points (open scatters) of (Δsolid, Δsolid) were plotted for pure CeO2/CeO2–δand 10% Samaria-doped Ce0.9Sm0.1O1.95/Ce0.9Sm0.1O1.95–δredox pairs (=0.01–0.05)[28-29]. The calculation results (solid scatters) in Section 2 were also plotted for these redox pairs (=0.03). Error bars represent standard deviations. Colourful figure is available on website

Fig. 1 plots the experimental data[28-29]of (Δsolid, Δsolid) for pure CeO2/CeO2–δand 10% Samaria-doped Ce0.9Sm0.1O1.95/Ce0.9Sm0.1O1.95–δredox pairs (=0.01–0.05) as well. Results show that Δsolid, Δsolidof both pure and doped ceria fall in the favorable region except for the pure ceria redox pair with=0.01. These results are reas-o-nable because pure and doped ceria are usually used as benchmark redox materials in literature[5-8].

The favorable region varies with operating temperature and pressure as shown in Fig. 2. Therefore, it is important to recognize that the developed thermodynamic frame-work can further be used for reactor testing to design optimal operating condition of a specific qualified redox pair. For example, results show that thermodynamically favorable thermal reduction step (Reaction (2)) can be per-for-med at lower temperatures (Fig. 2(a)) and higher pre-ssures (Fig. 2(b)) for pure and doped ceria redox pairs with larger Δsolid(smaller). These milder operating con-di-tions can significantly reduce thermal radiation loss and reactor design complexity.

Fig. 2 Variations of the favorable regions with operating conditions of the thermal reduction step (Reaction (2))

(a) Temperature.H=2000 and 1773 K; (b) Pressure.O2=0.101, 1.01 and 101 kPa. Other conditions in (a, b) are the same with those in Fig. 1; Colourful figure is available on website

2 First-principles predictions of desc---riptors

In this section, first-principles calculations were applied to the predictions of the descriptors (Δsolid, Δsolid) so that new redox materials can be added to the thermody-namic assessment map of Fig. 1.

In the first step, fast and reasonable predictions of (Δsolid, Δsolid) were demonstrated. Δsolidin Eq. (8) includes both vibrational (Δvib) and configurational (Δconf) entropic contributions[25].

Vibrational entropic contributions originate from the formations of defects, including oxygen vacancies as well as polarons[28,30], during the partial reduction step (Reaction (4)).

Fig. 3 Supercells for DFT+U calculations

(a) Bulk CeO2supercell; (b) CeO2supercell with a single oxygen- vacancy defect; (c) CeO2supercell with a single polaron defect(The charge density of the polaron is also shown); (d) Sm-doped CeO2supercell (Methods in Supporting Materials)

Δvib, Δconfand Δsolidof the CeO2/CeO2–δand Ce0.9Sm0.1O1.95/ Ce0.9Sm0.1O1.95–δredox pairs (=0.03) were calculated before the comparison of these calculation results with experimentally measured Δsolidand Δsolid[28-29,31]. Table 1 shows that this applied theoretical method can predict Δsolidand Δsolidof pure and Sm-doped ceria pairs, and expectedly other redox materials with reasonable accuracy. Particularly for Δsolidof the CeO2/CeO2–δredox pair (= 0.03), it was demonstrated that the relative differences between calculated and measured values are below 12%, although it is found in references[20, 23] that this method might over-estimate Δsolid. Regarding Δsolidof pure and Sm-doped ceria pairs (=0.03), the relative differences are also below 12%, demonstrating sufficient accuracy of this method which is expected to be more efficient enabled by the advancement and power of high-throughput com-pu-ta-tional tools[15-16].

Table 1 Comparison between calculated and measured values of ΔSsolid and ΔHsolid

Entropy and enthalpy units are J·(0.5 mol O2)–1·K–1and kJ·(0.5 mol O2)–1;Obtained from measured reduction entropy minus 0.5O2

Fig. 4 Variations of , , ΔSvib, and ΔSsolid with temperature

Solid and dash curves are for CeO2/CeO2–δand Ce0.9Sm0.1O1.95/Ce0.9Sm0.1O1.95–δredox pairs (=0.03), respectively; Colourful figure is available on website

3 Discussion

Based on the results of this work, a viable screening approach of materials for solar-driven CO2splitting using two-step thermochemical cycles was proposed as shown in Fig. 5.

The first step is to calculate the descriptors, the com-bination of Δsolidand Δsoliddefined in Eq. (3) by the developed DFT+based first-principles approach. As described in Introduction, despite the recognition of the entropic effect, energy descriptors (enthalpy of formation or energy of oxygen-vacancy formation) were usually used for the screening of material candidates in literature [11-12, 22]. Therefore, (Δsolid, Δsolid) represents a more general descriptor.

The second step is to screen material candidates by the derived criteria defined in Eq. (7) and find out qualified redox materials. As described in Section 1, these criteria were derived by comprehensively considering non-stoic-hi-o-me-tric reaction mechanism, theoretical efficiency and practical operating conditions. It has to be pointed out that materials with (Δsolid, Δsolid) near the boundary of the favorable region (Fig. 1) should also be screened as qualified redox materials considering the accuracy of DFT calculations. In addition, Eq. (6) varies with target solar-to-chemical and thermal-to-chemical efficiencies as well as achievable solar-to-thermal efficiency. For example, Δsolidis ≤ 600 kJ?(0.5 mol O2)–1in Eq. (6) with the target solar-to-chemical efficiency reseted from 20% to 15%. Resultantly, the solid square scatter is inside the favorable region.

The third step is to perform reactor testing using qua-lified redox material. Thermodynamics of redox mate-rial candidates represents an initial screening criterion[23,32], which was demonstrated in this work. Reaction kinetics of redox material candidates, which is characterized in reactor testing, is the important subsequent criterion[33-34], although reaction kinetics is out of the scope of this work.

4 Conclusions

In summary, this work presented a rationale for therm-o-dynamic and first-principles assessments of redox mat-erials for solar-driven CO2splitting using two-step ther-m-o-chemical cycles. The combination of solid-state change of entropy (Δsolid) and enthalpy of formation (Δsolid) was used as the descriptor. Comprehensive criteria based on it were derived to obtain the (Δsolid, Δsolid) map. It was found that a triangular region in this map identified qualified material candidates featuring large positive Δsolidand small enough Δsolid. Furthermore, a DFT+based first-principles approach was developed to fast and rea-sonably predict Δsolidand Δsolidfor redox materials with-out available thermochemical data. This rationale was exemplified for pure and samaria-doped ceria.

The authors would like to acknowledge Dr. Steffen Grieshammer for helpful discussions on DFT calculations and Prof. Sheng Chen for VASP access.

Supporting materials related to this article can be found at https://doi.org/10.15541/jim20210164.

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太陽(yáng)能驅(qū)動(dòng)的兩步熱化學(xué)循環(huán)二氧化碳裂解反應(yīng)活性材料的熱力學(xué)與第一性原理評(píng)價(jià)

馮清影, 劉東, 張瑩, 馮浩, 李強(qiáng)

(南京理工大學(xué) 能源與動(dòng)力工程學(xué)院, 南京 210094)

太陽(yáng)能驅(qū)動(dòng)兩步熱化學(xué)循環(huán)裂解二氧化碳可制備碳中性燃料, 為替代化石燃料、緩解全球變暖提供了技術(shù)途徑。新型活性材料的開(kāi)發(fā)對(duì)該技術(shù)非常重要。已有研究通常采用能量描述符(材料生成焓或氧空位生成能)評(píng)價(jià)候選材料, 忽略了材料熵的重要性。本研究采用活性材料的熵和生成焓的組合作為描述符, 提出評(píng)價(jià)準(zhǔn)則, 開(kāi)展材料可行性的熱力學(xué)分析。結(jié)果表明, 活性材料應(yīng)兼具較大的正的熵變與較小的生成焓變。在此基礎(chǔ)上, 本研究以氧化鈰和釤摻雜的氧化鈰為例, 發(fā)展了基于第一性原理的活性材料熵和生成焓的計(jì)算方法, 為新型材料的篩選與開(kāi)發(fā)提供基礎(chǔ)。計(jì)算結(jié)果揭示了極化子振動(dòng)熵以及氧空位和極化子構(gòu)型熵對(duì)活性材料熵變的貢獻(xiàn)。

二氧化碳裂解; 兩步熱化學(xué)循環(huán); 第一性原理; 熵; 太陽(yáng)能制燃料

TK51

A

1000-324X(2022)02-0223-07

10.15541/jim20210164

2021-03-15;

2021-05-20;

2021-06-10

Basic Science Center Program for Ordered Energy Conversion of the National Natural Science Foundation of China (51888103); National Natural Science Foundation of China (52006103); Fundamental Research Funds of the Central Universities (30919011403, 30920021137)

FENG Qingying(1996–), female, PhD candidate. E-mail: fqy@njust.edu.cn

馮清影(1996–), 女, 博士研究生. E-mail: fqy@njust.edu.cn

ZHANG Ying, PhD. E-mail: ying.zhang@njust.edu.cn; LI Qiang, professor. E-mail: liqiang@njust.edu.cn

張瑩, 博士. E-mail: ying.zhang@njust.edu.cn; 李強(qiáng), 教授. E-mail: liqiang@njust.edu.cn