The Role of Surface Oxygen Vacancy Concentration on the

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C: Energy Conversion and Storage; Energy and Charge Transport

The Role of Surface Oxygen Vacancy Concentration on the Dissociation of Methane over Nonstoichiometric Ceria Kent John Warren, and Jonathan Richard Scheffe J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01352 • Publication Date (Web): 30 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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The Journal of Physical Chemistry

The Role of Surface Oxygen Vacancy Concentration on the Dissociation of Methane over Nonstoichiometric Ceria Kent J. Warrena and Jonathan R. Scheffea,* a

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, USA, 32611 *

Corresponding author. Phone: +1 352-392-0839; Email Address: [email protected]

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Chemical-looping reforming of methane over ceria-based materials is a promising route for the production of synthetic liquid fuel precursors, H2 and CO. In this work, a comprehensive kinetic model was established, based on thermogravimetric experiments, to describe the previouslyunresolved, surface-mediated mechanism of methane dissociation via ceria oxygen removal – the first heterogeneous, non-catalytic reaction within the aforementioned redox cycle. Prior studies have suggested that either a surface oxygen anion or vacancy is responsible for the activation of methane. However, here, these two theories are combined to unambiguously show that the prominence of each pathway is dependent on the availability of surface oxygen. Thus, at sufficiently high oxygen nonstoichiometries or for low surface area samples, as examined in this work, the vacancy-mediated dissociation of methane is predominant. This assertion was elucidated by mathematically describing a series of rate-determining steps based on surface interactions of known reactive intermediates and fitting the postulated reaction mechanism to temperaturedependent measurements obtained with multistage isothermal thermogravimetry. Corresponding Arrhenius parameters were extracted with excellent agreement between the model predictions and experimentally measured rates. Further validation of the hypothesized reaction mechanism is supported by (1) close similarity between activation energies obtained through model fits and separate isoconversional techniques and (2) expected trends observed with acceptor-doped ceria that has a higher concentration of extrinsic oxygen vacancies at the onset of the reaction. The quantitative kinetic insight obtained from the model presented herein allows for the evaluation and optimization of ceria-based materials in larger-scale, chemical-looping processes.


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1. Introduction Chemical-looping reforming (CLR) of methane is a promising Gas-to-Liquids (GTL) technology that leverages the redox behavior of metal oxides to facilitate syngas (a mixture of H2 and CO) production.1-3 Contrary to conventional reforming and partial oxidation processes where methane and an oxidant (H2O/CO2 and O2, respectively) are delivered concurrently, CLR cyclically operates between two steps: (1) endothermic release of lattice oxygen from a metal oxide to facilitate the non-catalytic partial oxidation of methane and (2) exothermic oxidation of the reduced metal oxide via H2O and/or CO2 dissociation. The primary output of step 1 is syngas with a 2:1 H2/CO ratio, and depending on the employed oxidant, step 2 can produce either H2 and/or CO. Importantly, if carbon is deposited during methane delivery, it is ultimately combusted to form additional CO during the subsequent oxidation step. In the absence of coking, the ideal chemical-looping scheme over a generic metal oxide (MxOy) is represented by the following net reactions: Reduction:

Mx Oy-δox + δCH4  Mx Oy-δred + 2δH2 + δCO

(1)

Oxidation:

Mx Oy-δred +  H2O +  CO2  Mx Oy-δox +  H2 +  CO

(2)

Overall:

δCH4 +  H 2O +  CO2   2δ    H 2 +  δ    CO

(3)

where δ is the oxygen nonstoichiometry, and α and β are oxidant magnitudes, whose sum equals the change in δ between reduction and oxidation (i.e., δred and δox, respectively). Although the products of each step are individually valuable (e.g., eqn. 1 is well-suited for methanol production4), the separate streams may also be combined and coupled with established catalytic pathways, like Fischer-Tropsch synthesis (FTS), to produce liquid fuels, such as diesel. Furthermore, integration of a renewable heat source (e.g., solar energy) can supplant natural and waste gas combustion, the current industrial standard, as the thermal energy required to generate syngas from the high-temperature conversion of methane, thereby reducing carbon emissions.5 When coupled with FTS, sustainably-driven CLR offers a unique strategy for scalable production of fungible fuels from methane. Notable advantages of CLR, as compared to traditional catalytic reforming, include lack of catalyst degradation due to fouling, thus enabling the dry reforming of methane if CO2 is selected as the oxidant (see eqn. 3). Furthermore, the flexibility in delivered oxidant provides versatility in the output syngas ratio: an important asset for fuels produced via FTS (e.g., the ideal feed H2/CO ratio for diesel is approximately 2.15:1 and 1.7:1 for cobalt and iron-based catalysts, respectively6). To yield similar syngas ratios in conventional reforming and partial oxidation processes requires the addition of energy-intensive equipment, such as polymerbased membranes or water-gas shift converters, at the expense of lower process efficiency.7



Ceria-based, oxygen-exchange materials have emerged as a promising class of redox intermediates to facilitate methane partial oxidation and subsequent H2O/CO2 splitting.8-17 Important characteristics of ceria include rapid redox kinetics18, 19 and favorable oxidation thermodynamics13; namely, ceria oxidation (eqn. 2) is feasible at sufficiently high temperatures near where oxygen evolution from reduction occurs (eqn. 1), thus enabling isothermal or nearisothermal operation. Although the dynamics of vacancy-mediated, oxygen-ion incorporation during the oxidation of ceria by H2O20, 21 and CO219, 22 is relatively well understood, the added complexities introduced by methane activation into the surface redox pathway of ceria remain unresolved. Kinetic information regarding syngas production via methane-driven reduction of ceria was first investigated by Otsuka et al., where a reaction mechanism and potential rate limiting step were postulated.9 Notably, by subjecting a packed bed of ceria to a series of methane pulses, the authors found that complete oxidation products, H2O and CO2, are only observed near reaction initiation, and thus concluded that an oxygen vacancy and reduced ceria cation were responsible for the selective production of syngas. Other studies have employed dissimilar isoconversional techniques to extract discrete values of activation energy with considerably different magnitudes.8, 23, 24

Further mechanistic information regarding equation 1 can be elucidated from studies concerned with the complete oxidation of methane over ceria. Notable works include independent investigations25, 26 that examined methane activation on different surfaces of stoichiometric ceria using density functional theory, corrected for on-site Coulombic interactions (DFT+U). Importantly, these simulations revealed that the lowest energy pathway for methane activation proceeds through dissociative adsorption of a hydrogen atom and formation of a methyl radical in the gas-phase, otherwise known as a rebound mechanism; thereafter, the radical species is predicted to chemisorb onto an available surface oxygen anion. This pathway for methane dehydrogenation on the oxidized ceria surface is also supported by later DFT computations.27, 28 Although limited to the stoichiometric (111) surface of ceria, Knapp and Ziegler published the complete reaction coordinate diagram for oxidation of methane into H2O and CO2.26 From the aforementioned literature, it is evident that methane-driven reduction of ceria involves interactions between both surface oxygen anions and vacancies. This suggests that the prevalence of either pathway likely depends on the availability of surface oxygen, such that oxide surface area and oxygen nonstoichiometry may play an important role. We have qualitatively observed this in a prior study,15 where reaction kinetics were described via a compositionallydependent, apparent activation energy that increases from 20 to 80 kJ mol-1 as δ increases from 0.15 to 0.40. Building off of this work, we aim to further use thermogravimetry to quantify the prevalence of each methane activation pathway (i.e., oxygen-anion- or vacancy-mediated) as a function of oxygen nonstoichiometry and temperature. A comprehensive analytical model, based on the aforementioned reaction mechanisms, is proposed and fit to experimental data at elevated temperatures (i.e., 750 °C to 1050 °C) to obtain kinetic parameters and mechanistic insight. To further examine the less-established, vacancy-mediated dissociation of methane, 10 mol % gadolinium-doped ceria powder was also subjected to experimental and theoretical analysis. 2. Experimental Methods


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Powdered ceria (Alfa Aesar, 11328) and 10 mol % gadolinium-doped ceria or 10GDC (Sigma Aldrich, 734519-10G) samples, previously calcined at 1200 °C for 10 hours in air, were subjected to a randomized sequence of isothermal mass relaxation experiments using a horizontally-oriented thermogravimetric analyzer (HT TGA/DSC 2, Mettler Toledo). The horizontal configuration of the hermetically-sealed sample chamber ensures intimate contact between the reactive gases that flow over the solid sample, while minimizing turbulence induced by thermal buoyancy. The specific surface areas of commercial and calcined samples were measured via BET analysis (ChemBET 3000, Quantachrome). Changes in sample mass (Δms) were controlled by tuning the local oxygen partial pressure (pO2) via input gas delivery from a mass flow controller (GC200, Mettler Toledo). Each reduction and oxidation regime was initiated with a mixture of CH4/Ar and O2, respectively, and followed by an Ar purge; concomitant products were detected by downstream mass spectrometry (QMS 100 series, Stanford Research Systems). As motivated by a prior thermodynamic analysis,13 redox reactions were performed at methane partial pressures (pCH4) between 0.02 and 0.04 atm, an ambient system pressure of 1 atm, and programmed reference temperatures (Tref) between 750 and 1050 °C. The corresponding sample temperature (Ts) was recorded with an R-type thermocouple imbedded directly into the sample holder within the furnace. A more detailed description of the experimental setup and procedure is provided in a prior work. Importantly, initial ceria and 10GDC masses (ms,i) of 15 mg were arranged as a monolayer of particles on a platinum dish crucible (Alfa Aesar, 46686) to (1) ensure that heat and mass transfer to the sample were uniform and (2) deter conflicting carbon deposition on the crucible surface; fresh samples were employed prior to each experiment. Furthermore, the duration of oxidation in O2 was extended to completely remove surface adsorbates, such as carbonates and hydroxyls, and thus eliminate their impact on subsequent reduction intervals. 15

3. Kinetic Theory Unlike the catalyzed activation of methane over metal additives or clusters,29-31 potentially active sites to facilitate methane oxidation over undoped ceria include surface and near-surface oxygen anions, doubly ionized oxygen vacancies, and cerium cations (i.e., OOx, VO••, and CeCex, respectively). Low adsorption energies between an intact methane molecule and clean ceria surface indicate weak interaction.32 Thus, for stoichiometric ceria, methane activation has been reported to initiate via dissociative adsorption of an abstracted hydrogen atom (H) on an exposed oxygen anion, as suggested by independent DFT+U simulations.25, 26 The remaining gas-phase methyl radical then rebounds towards the surface, binds to an adjacent oxygen anion, and further dissociates by sequentially transferring hydrogen atoms across cerium cations to nearby oxygen sites.26 Each homolytic C-H bond cleavage is accompanied by the formation of a stabilized, surface hydroxyl (OHO•) intermediate,33 shortening of the C-O bond, and reduction of a neighboring cerium cation (CeCe′) via electron donation from an abstracted hydrogen atom.25-28 The relevant steps in methane dissociation over stoichiometric ceria are described below using Kröger-Vink notation, where CHx* corresponds to a chemisorbed methane fragment on a surface oxygen anion.34  x CH4 (g)  CeCe  OOx  CH*3 +  OH O + CeCe

(4)



 x CH*3  CeCe  OOx  CH*2 +  OH O + CeCe

 CH*2  CeCx e  OOx  CH* +  OH O + CeCe  x CH*  CeCe  OOx  C* +  OH O + CeCe

The final hydrogen abstraction from chemisorbed methylidine (CH*) prompts spontaneous desorption of carbon monoxide, which may subsequently bind with an available oxygen anion to form carbon dioxide.26 x C*  2CeCe  OOx  VO + 2CeCe + CO(g)

(5)

Adsorbed hydroxyl ions may lead to the formation of either steam or gaseous hydrogen, as recently observed in-operando by analyzing hydrogen-oxidation and water-splitting over ceria under a surface-reaction-limited regime.20 Thermodynamics and high availability of surface oxygen (e.g., near reaction initiation or downstream as in a packed-bed configuration) will dictate the formation of partial or complete oxidation products (i.e., H2 and CO versus H2O and CO2) from methane.13 As supported by equilibrium thermodynamic predictions13 and qualitatively confirmed by downstream mass spectrometry (see Figure S1 of the supplementary material), H2O and CO2 production is negligible under the conditions examined in this study. Furthermore, lack of complete combustion products is expected, as ceria samples with lower surface area (and thus less available near-surface oxygen) have demonstrated greater selectivity to syngas.35 The H2 formation reaction is shown below.  x 2  OH O + 2CeCe  2OOx  2CeCe + H2 (g)

(6)

Each doubly ionized surface oxygen vacancy is coupled to two reduced cerium cations and created by oxic product evolution (see eqn. 5). Simultaneous replenishment of the ceria surface proceeds through bulk-to-surface oxygen diffusion, consistent with a Mars-van Krevelen type mechanism.3, 36 However, as reduction continues, less-available lattice oxygen constrains the first pathway, and thus methane dissociation may transition to a vacancy-mediated mechanism. Evidence for a second pathway is corroborated by prior experimental observations under pulsed methane delivery that suggest an oxygen vacancy is responsible for the selective production of syngas from methane-driven reduction of ceria.9 Furthermore, DFT calculations indicate that adsorption energies for CHx fragments are lowest with respect to a surface oxygen vacancy.32 Analogous to H2O20, 21 and CO222 splitting over reduced ceria, each C-H bond cleavage in methane dissociation over an oxygen vacancy is assumed heterolytic. As a result, following the framework established in the first pathway, we hypothesize that methane activation now proceeds via dissociative adsorption of an abstracted hydron (H+) on an exposed oxygen anion. Subsequent CHx fragments form defect species incorporated on surface oxygen vacancies by transferring other


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hydrons to nearby oxygen anions and creating hydroxyl groups. The relevant steps in methane dissociation over reduced ceria are described below using Kröger-Vink notation.

CH4 (g)  VO  OOx   CH3 O +  OH O 



(7)

 CH3 O  OOx   CH2 O +  OH O 



x

 CH2 O  OOx   CH O +  OH O 

x

 CH O  OOx  CO +  OH O 

Interaction between the remaining carbon defect (CO′′) and an adjacent oxygen anion, described below in equation 8, facilitates carbon monoxide desorption, oxygen vacancy creation, and concomitant reduction of six neighboring ceria cations.37 Desorption of hydrogen proceeds as previously described in equation 6. x CO  6CeCe  OOx  2VO + 6CeCe + CO(g)

(8)

As lattice oxygen continues to deplete, OHO• and CO′′ cease to desorb as gaseous products, thus inhibiting further methane activation and inducing reaction termination. The essential features of each pathway for syngas generation via methane activation over ceria are schematically represented in Figure S2. Importantly, each sequence is not stringent, as, for example, hydrogen may associate and desorb immediately after the formation of two hydroxyl ions from C-H bond cleavage. In this work, we mathematically define the overall mechanism as a compilation of four pertinent “elementary” reactions (listed below), each assumed irreversible in the forward direction and written according to the law of mass action. CH4 dissociation over OOx (see eqn. 4): x r1.1  k1.1 ( pCH4 / ptot )[CeCe ][OOx ]

(9)

CH4 dissociation over VO•• (see eqn. 7):

r1.2  k1.2 ( pCH4 / ptot )[VO ][OOx ]

(10)

H2 desorption (see eqn. 6):  r2  k2 [ OH O ]2 [CeCe ]2

(11)

CO desorption (see eqn. 8):



x 6 r3.2  k3.2 [CO ][CeCe ] [O Ox ]

(12)

Square brackets denote reactant concentration per surface mole of ceria, and rate constants (k) are assumed to follow the Arrhenius expression. Thus, each k contains a unique pre-exponential factor (A) and activation energy (Ea); k = Aexp(-Ea/RTs), where R is the ideal gas constant. In accordance with the high bond dissociation enthalpy of methane,38 all reactions involving CHx fragments are assumed quasi-equilibrated, such that methane dissociation over a surface oxygen anion or vacancy is solely described by the first C-H bond cleavage. Note that there is evidence for the inhibition of methane conversion due to hydrogen oxidation,15 but this (i.e., the reverse of eqn. 6) was ignored here. Finally, CO desorption is only governed by equation 8, since the alternate pathway for oxidation of chemisorbed carbon was predicted to be spontaneous by Knapp and Ziegler.26 Otsuka et al. have postulated that hydrogen association and desorption may be the ratedetermining step (RDS) after noticing a significant delay in the H2 signal (measured via downstream residual gas analysis), as compared to a 2:1 pulse of H2/CO in the absence of ceria.9 Importantly, this hypothesis was only adopted after first excluding C-H bond cleavage and bulk oxygen diffusion as potential RDS, indicated by the following observations: (1) measurement of a low kinetic isotope effect (KIE) for the initial conversion of methane versus deuterated methane and (2) negligible impact on the measured rate following inclusion of metal-additives known to enhance bulk-oxygen diffusion.9 However, after further inspection of their experimental results, it is evident that the conversion of CH4 and CD4 deviates as the reaction continues, thus increasing the KIE and suggesting that C-H bond cleavage may be rate-determining at later times. Moreover, the delay in the H2 signal could be readily explained by the added frictional losses from intraparticle dispersion, an artefact of their pack-bed apparatus. As a result, we hypothesize that methane-driven reduction of low surface area (LSA) ceria is primarily vacancy-mediated and limited by CO desorption for low nonstoichiometries, and as surface oxygen diminishes, methane activation dictates further reaction progression. Therefore, we define the predicted rate (ṙp) as the linear combination of these reactions, shown below.

rp  r3.2  r1.2

(13)

Considering methane-driven reduction of ceria, repeatable and reversible shifts between CeO2 and Ce2O3 (i.e., δ = 0.50) have been experimentally demonstrated;15 however, the influence of defect clusters, (CeCe′VO••CeCe′)x,39 on the surface-mediated dissociation of methane remains unresolved and was not considered here. 4. Model Formulation and Numerical Methods Kinetics of heterogeneous, solid-state reactions are commonly described using the master plot analysis,40 which employs theoretical, physico-chemical conversion functions that are preassociated to typical rate-limiting mechanisms. However, the irrelevance between the statistical choice and the physical meaning of the corresponding model can lead to ambiguous mechanistic interpretation. An alternative methodology to model heterogeneous, catalytic reactions is the Langmuir-Hinshelwood approach.34, 41 However, this technique is formulated on the assumption


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that the solid surface within a heterogeneous system is energetically uniform and is thus only well suited for predicting the kinetics of catalytic-type or pseudo-equilibrated reactions, such as the dry reforming of methane.42 To account for the surface and bulk redox behavior of ceria during chemical-looping, a surface analysis,41 defined below, was applied to temporally describe abundant reactive intermediates and thus provide quantitative kinetic insight. The pseudo-steadystate hypothesis41 was leveraged to exclude consideration of VO•• in equation 14, consistent with the observation that surface vacancies are completely saturated with hydroxyl ions during ceria oxidation by H2O.20 Other assumptions include the following: (1) the ceria surface area (SCeO2) is temporally independent and (2) the considered reactive intermediates (i.e., OHO• and CO′′) are confined to the surface layer. As a result, bulk-to-surface diffusion (J̇) of each reactant was neglected, so that the molar amounts (N) were solely described by their generation or consumption during reaction progression. The generation/consumption of both species is defined as the product of the surface molar density ( ̅ρCeO2) and respective rate (ṙk) of formation or depletion according to equations 9 – 12;41 the contribution from each “elementary” reaction is described by the stoichiometric coefficient (ν).43

d  Nj  dt  SCeO2

  = J j,bulk + CeO2  jrk k 

(14)

 j   OH O , CO

k  1.1, 1.2, 2, and 3.2 The governing analysis is coupled to the following surface conservation equations. O-site balance:  [VO ]  [OOx ]  [ OH O ]  [CO ]  2

(15)

Ce-site balance: x [CeCe ]  [Ce Ce ] 1

(16)

Electroneutrality condition:  2[VO ]  [ OH O ]  [CeCe ]  2[CO ]

(17)

After reaction initiation, bulk-to-surface transport of small polarons and oxygen anions, both driven by an electrochemical potential gradient, enable further reduction/oxidation of ceria. Under oxidizing conditions (i.e., at lower temperatures and higher oxygen activities), the concomitant spatial distribution of defects is more significant; recent in-operando measurements by Chueh et al. revealed a notable difference in the equilibrium surface and bulk Ce3+ concentration for 20 mol % Sm-doped ceria.44 These observations were later supported by kinetic



assessments of ceria oxidation via H2O21, 45 and CO222 splitting, which considered the impact of bulk oxygen diffusion in a comparable analysis as presented herein. However, for the highly reducing environment examined in this work, extrapolation of the reported trends by Chueh et al.44 (see Figure S3) indicates that the ratio of surface to bulk Ce3+ concentration at equilibrium approaches unity. Therefore, although surface oxygen vacancies (and thus bulk oxygen diffusion) could be described by equation 14 in this work, additional computational intensity was avoided by leveraging the following empirical relationship to connect the surface and bulk reaction chemistry.

[CeCe ]  [CeCe ]b  2[VO ]b  2

(18)

Equivalency of the equilibrium surface and bulk Ce3+ concentration is assumed valid throughout the reaction duration, in agreement with prior observations that exclude bulk-to-surface transport as a potential RDS.9, 15 Further, by applying the bulk electroneutrality condition (i.e., [CeCe′]b = 2[VO••]b), the surface Ce3+ concentration was equated to δ under the assumption that the molar quantity of surface vacancies is negligible with respect to the bulk. Here, the subscript “b” denotes reactant concentration per mole of ceria in the bulk, contrary to the prior definition of squarebracketed terms. When the kinetic model is applied to 10GDC, only the pertinent surface conservation equations, shown below, require modification. The O-site balance remains as defined in equation 15. Ce-site balance: x [GdCe ]  [CeCe ]  [CeCe ] 1

(19)

Electroneutrality condition:  2[VO ]  [ OH O ]  [GdCe ]  [CeCe ]  2[CO ]

(20)

Although the bulk electroneutrality condition (i.e., [GdCe′]b + [CeCe′]b = 2[VO••]b) also considers the contribution of Gd3+ cations, the final equation to connect the surface and bulk reaction chemistry (eqn. 18) remains unchanged. Here, [VO••]b accounts for the measured δ and the concentration of bulk vacancies introduced by gadolinium doping (i.e., one VO•• for every two Gd3+ cations). Unlike conventional catalytic reactions (e.g., steam reforming of methane), the evolution of syngas during methane-driven reduction of ceria is governed by non-equilibrated surface and/or bulk-mediated phenomena. Therefore, in order to properly assess the local sample environment and inherently transient kinetic signature of the redox material, the partial pressures of reactant and product gases at the sample surface were approximated according to the following differential mole balance41 represented by equation 21.


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dN j dt

= Gj + Fj,in  Fj,out

(21)

Derived from applying a control volume to the TGA sample chamber, N, Ġ, and Ḟ respectively refer to the number of moles, molar rate of generation/consumption, and molar entrance/exit rate (denoted by subscripts in and out, respectively) by flow of species j: Ar, CH4, H2, or CO. Assumptions include a well-mixed sample chamber and negligible H2O and CO2 production, and thus the molar flow rates of gaseous constituents (e.g., ḞCO,out) were determined via mass conservation. In accordance with equation 1, the local rates of syngas generation and methane consumption are proportional to the rate of oxygen removal (dδ/dt) from the ceria lattice. For example, the generation rate of CO in molesCO min-1 is shown below in equation 22. GCO =

dδ ms,i 1 molCO dt M CeO2 1 molO

(22)

Here, the sample-averaged oxygen nonstoichiometry (δ), defined below, is the product between the relative change in the initial sample mass (ms,i) and molar mass ratio of ceria (MCeO2) to oxygen (MO).

 (t ) 

ms (t )  M CeO2    ms,i  M O 

(23)

A three point numerical differentiation routine41 was applied to equation 23 to determine the rate of oxygen release. With the aforementioned assumptions, the governing surface analysis (eqn. 14) is algebraically simplified to the following set of equations. d  [ OH O ] = 4  r1.1 + r1.2   2r2 dt

(24)

d  [CO ] = r1.2  r3.2 dt

(25)

Temporal profiles of pCH4, δ, dδ/dt, and Ts, obtained via thermogravimetry or the solution to equation 21, enable determination of the pre-exponential factors (Ak) and activation energies (Eak) associated with each reaction rate constant. After choosing an initial guess for these eight unknowns, the entire redox process (described in eqns. 14 – 18 for ceria) can be then solved through numerical integration. The number of fitted parameters was required to avoid sacrificing important mechanistic information. In this work, the sum of squared errors (SSE), defined below, was leveraged to compare the predicted (see eqn. 13) and measured rates (i.e., dδ/dt), normalized by their respective maxima (denoted by ṙp,n and ṙm,n, respectively). For completeness, other



combinations of “elementary” steps were examined to describe ṙp; however, the resultant fits were poor compared to those described by equation 13.

f =

  w  r

p,n

pCH4 Tref

 rm,n 

2

(26)

t

To extract the unknown kinetic parameters, measurements at seven reference temperatures (i.e., Tref = 750:50:1050 °C) and three methane atmospheres (i.e., pCH4 = 0.02:0.01:0.04 atm) were simultaneously fitted. Each reaction rate was multiplied by a weighting factor ratio (0 < w ≤ 1) based on 95% of the equilibrium time as compared to that of the shortest reaction. The objective function (f), or total error, was then minimized by randomly varying the initial guess for each kinetic parameter over a wide range (i.e., A from 1 – 1e10 min-1 and Ea from 0 – 300 kJ mol-1) using fmincon-SQP, a gradient-based optimization algorithm inherent to MATLAB. This routine was repeated for 30 iterations, and for each simulation, the fitted parameters associated to the minimum f were categorized. The magnitudes of each objective function minimum were nearly equivalent, thus ensuring global convergence of the constrained nonlinear multivariable system. The results presented herein are reported as arithmetic mean values with 95% confidence intervals. 5. Results and Discussion A typical experimental result, obtained with our refined method of multistage isothermal thermogravimetry,15 is shown in Figure 1. As expected in a kinetically-controlled operating regime, reaction rates strongly increased with increasing temperature, and consequently the time required to reach equilibrium decreased. In agreement with equilibrium thermodynamic predictions,13 the Δms (i.e., oxygen removal) also increased with increasing temperature.

Figure 1. Collocated mass-relaxation profiles for methane-driven reduction of ceria obtained by multistage isothermal thermogravimetry. Experimental conditions include: ms,i = 15.5 mg, pCH4 = 0.04 atm, and tox = 10 min.


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Figure 2 displays an exemplary temporal distribution of reactant and product partial pressures near the sample, determined through integration of equation 21, and the corresponding rate of oxygen removal. Within a few seconds, the desired methane atmosphere (in this case, pCH4 = 0.03 atm) equilibrated in the sample chamber as a consequence of small chamber volume (44.6 ml) relative to the total volumetric flow rate (Qtot = 340 ml min-1). Subsequent reaction initiation is characterized by a rapid increase in the rate followed by a gradual decay, prompting a subtle decrease in the sample temperature due to reaction endothermicity (see top subplot). Notably, the gradual decrease in the rate is interrupted by a slight shift in concavity before completion of the reaction. Syngas generation follows a similar profile (H2/CO = 2:1), thus lowering the local partial pressure of methane during reaction progression; experimentally, this variation in local pCH4 due to product gas evolution became more apparent with increasing sample mass.15 The inflection in the rate at long times differs from typical kinetic behavior of comparable heterogeneous reactions, such as the oxidation of ceria by H2O,46 where a sharp peak followed by an exponential decay is generally observed, and a single step is thought to be rate-determining (i.e., the small polaron transfer from a reduced ceria cation to a surface hydroxyl group20). Therefore, the bimodal-type behavior observed at higher nonstoichiometries, likely introduced by the added complexities of methane dissociation over ceria, may be indicative of a shift in RDS. Collectively, pCH4, δ, dδ/dt, and Ts serve as the experimental inputs into the kinetic model presented herein.

Figure 2. An exemplary, temporal distribution of the local, gas-phase reactant and product partial pressures (solid, colored lines) derived from the measured reaction rate (dashed, black line) at a program temperature of 1050 °C (top subplot). Experimental conditions include: ms,i = 15.5 mg, pCH4 = 0.03 atm, and tox = 10 min. A comparison between the methane-driven reduction rate of ceria and 10GDC under identical experimental conditions is displayed in Figure 3; the measured BET surface areas of



commercial and calcined samples are provided in Table 1. Interestingly, when compared to the kinetic profile of ceria at Tref = 1050 °C, 10GDC follows a similar trend but exhibits a more notable inflection after the initial peak. Furthermore, although 10GDC samples of larger surface area than ceria were employed, the peak rate of 10GDC reduction is lower. These observations are consistent for all evaluated temperatures, although less prominent at Tref = 750 °C, and are hypothesized to be directly related to the extrinsic oxygen vacancies introduced by doping (e.g., Ce0.9Gd0.1O1.95). Additionally, the observed similarity in kinetic profiles provides qualitative evidence to support the assertion that methane dissociation over LSA ceria is predominantly vacancy-mediated.

Figure 3. Measured kinetic profiles of the reduction of ceria and 10 mol % Gd-doped ceria facilitated via methane partial oxidation at program temperatures of 1050 °C and 750 °C. Experimental conditions include: ms,i = 15.5 mg, pCH4 = 0.03 atm, and tox = 10 min. Table 1. Specific surface areas of ceria and 10 mol % Gd-doped ceria samples. Specific surface area (m2 g-1) Sample CeO2

Ce0.9Gd0.1O1.95

commercial

7.02

11.46

calcined

0.83

4.25

For all temperatures at pCH4 = 0.03 atm, the experimentally measured rates of ceria reduction and model predictions are displayed in Figure 4; the measured oxygen nonstoichiometry is shown on the right ordinate. The entirety of the simultaneous modeling effort (normalized with respect to δ for ease of comparison) can be seen in Figure S4. Under the examined conditions,


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excellent agreement is observed, as the linear combination of “elementary” reactions used to describe the predicted rate accurately captures both the initial peak and subsequent inflection that is more prominent at higher temperatures. The concomitant kinetic parameters obtained from the minimization routine are summarized in Table 2. Activation energies associated with the postulated rate-determining steps (i.e., Ea1.2 = 77 ± 3 kJ mol-1 and Ea3.2 = 32 ± 3 kJ mol-1) agree well with our prior work,15 which leveraged isoconversional methods to extract a compositionallydependent (or apparent) activation energy from thermogravimetric measurements (i.e., 20 kJ mol1 < Ea,app < 80 kJ mol-1 for 0.05 ≤ δ ≤ 0.40). Other activation energies (i.e., Ea1.1 = 203 ± 8 kJ mol1 and Ea2 = 218 ± 6 kJ mol-1) are also in near agreement with comparable values reported in literature. For example, from DFT+U simulations, Knapp and Ziegler26 reported a kinetic barrier of 36 kcal mol-1 (or 151 kJ mol-1) for the dissociative adsorption of a methyl radical and hydrogen on the stoichiometric ceria (111) surface (corresponds to Ea1.1). Conversely, for the association and desorption of H2 from adsorbed hydroxyls (Ea2), Zhao et al.21 predicted an activation energy of 190 ± 50 kJ mol-1 from modeling the kinetics of hydrogen-oxidation and water-splitting over oxidized and reduced ceria, respectively.

Figure 4. Comparison between the model predictions (solid lines) and measured reaction rate (colored symbols), dδ/dt, of the reduction of ceria facilitated via methane partial oxidation at pCH4 = 0.03 atm and different Tref. The corresponding measured oxygen nonstoichiometry (dashed lines) refers to the right ordinate.



Table 2. Fitted kinetic parameters for the methane-driven reduction of ceria and 10 mol % Gddoped ceria. Fitted Parameters

CeO2

Ce0.9Gd0.1O1.95

A1.1 (min-1)

1.83e6 ± 7.93e5

6.49e6 ± 1.40e6

Ea1.1 (kJ mol-1)

203 ± 8

216 ± 7

A1.2 (min-1)

5.44e6 ± 9.66e5

4.25e6 ± 1.49e6

Ea1.2 (kJ mol-1)

77 ± 3

76 ± 4

A2 (min-1)

1.94e6 ± 9.20e5

4.68e6 ± 1.23e6

Ea2 (kJ mol-1)

218 ± 6

219 ± 5

A3.2 (min-1)

8.50e5 ± 3.32e5

2.05e6 ± 8.45e5

Ea3.2 (kJ mol-1)

32 ± 3

33 ± 4

Upon solving equations 14 – 18, insight into the temporal profile of each surface intermediate is obtained; exemplary distributions are displayed in Figure 5 for ceria subjected to pCH4 = 0.03 atm. For all temperatures (Figures 5A through 5C), as the reaction progresses, the surface concentrations of CeCe′, OHO•, and CO′′ increase, thus decreasing the magnitudes of [OOx] and [CeCex] as expected. As temperature increases, the overall change in the concentration of each intermediate increases, a consequence of greater reduction extents (see Figure 1). Furthermore, the final magnitudes of [OHO•] and [CO′′] are more significant at higher temperatures where the bimodal-type kinetic profiles are more obvious. Alternatively, the surface concentration of VO•• (Figure 5D) generally decreases with increasing Tref. Here, the bimodal distributions of [VO••] reflect the temperature-dependence of the kinetic trends observed in Figure 4. At higher temperatures, the second peak represents the onset of methane dissociation over a surface oxygen vacancy as the RDS because, as surface oxygen dissipates, accumulation of CO′′ (Figures 5A and 5B) occludes potential sites for the continued dissociation of methane. Conversely, at Tref = 750 °C (Figure 5C), the lower concentration of CO′′ near reaction completion suggests that, under these conditions, CO′′ reacts as quickly as it is formed, and thus lower temperature reactions may be primarily governed by the oxidation of carbon imbedded on an oxygen site (eqn. 12). For all temperatures, reaction termination is accompanied by the surface saturation of OHO• and/or CO′′, in agreement with prior observations that insufficient regeneration of reduced ceria impacted the subsequent reaction within our multistage experimental procedure.15 Observed noise in the calculations is an artefact of measurement uncertainty (± 1 μg) that is comparatively more apparent as the reaction rate diminishes.


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Figure 5. Exemplary distributions of surface concentrations (units: molj molCeO2-1) during the reduction of ceria facilitated via methane partial oxidation at pCH4 = 0.03 atm and (A) Tref = 1050 °C, (B) Tref = 900 °C, and (C) Tref = 750 °C; the surface concentration of oxygen vacancies are plotted on a semilog (right) ordinate in subplot (D) for all examined Tref. For methane-driven reduction of 10GDC, exemplary comparisons between the experimentally measured rates and model predictions are displayed in Figure 6 (top panels), where δ is shown on the right ordinate. The entirety of the simultaneous modeling effort can be seen in Figure S5. Excellent agreement is again observed under the examined conditions, as the differences introduced by gadolinium doping are accurately described by the model alterations. The concomitant kinetic parameters obtained from the minimization routine are also summarized in Table 2. When compared to the results of the analysis applied to methane-driven reduction of ceria, the extracted activation energies, particularly those associated with the postulated RDS, are in agreement. Conversely, the extracted pre-exponential factors, a representation of the number of surface sites in a heterogeneous system, are either on par or greater than the counterparts reported for ceria; recall that 10GDC samples of greater initial surface area were examined (see Table 1).



The corresponding concentrations of surface intermediates are displayed in the bottom panels of Figure 6. While the trends observed for methane-driven reduction of 10GDC and ceria (see Figure 5) are similar, the respective magnitudes are different due to the presence of extrinsic vacancies; for example, prior to the reaction, [OOx] and [CeCex] are 1.95 and 0.9, respectively. As the reaction proceeds, the inherent VO•• are immediately consumed, and a sharp increase in the concentration of OHO• is observed (thus decreasing [OOx] accordingly). Further reaction progression is accompanied by a more notable increase in the concentrations of OHO• and CO′′ than that observed for ceria samples near reaction completion.

Figure 6. (Top) Comparison between the model predictions (solid lines) and measured reaction rate (colored symbols), dδ/dt, of the reduction of 10 mol % Gd-doped ceria facilitated via methane partial oxidation at different Tref. The measured oxygen nonstoichiometry (dashed lines) is plotted with respect to the right ordinate. (Bottom) Corresponding distributions of surface concentrations (units: molj mol10GDC -1). Each subplot was examined at pCH4 = 0.03 atm. The temperature-dependence of methane-driven reduction of ceria and 10GDC is also observed in Figures 7A and 7B, respectively. Here, Arrhenius-type plots, showing the natural logarithm of the rate versus inverse temperature, were generated at constant composition (shown for δ = 0.15) and organized according to sample type and examined pCH4; multiple experiments were performed at each condition to ensure repeatability. For a given temperature, the oxygen removal rate of each sample decreased with decreasing pCH4. Using an adaptation of Friedman’s differential isoconversional approach,47 kinetic information (i.e., Ea,app) was extracted by


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evaluating the slope of each linear trend line over a wide δ range, as discussed more thoroughly in our prior work.15 For both samples, the compositionally-dependent Ea,app is displayed in Figure 7C and is not significantly impacted by changes in pCH4, as expected. However, at large reduction extents, Ea,app increases from approximately 20 to 90 kJ mol-1. Importantly, at low reduction extents (δ < 0.15), the comparable barriers are indicative of a similar kinetic, not diffusive, limitation, as the rate of methane-driven reduction is much greater for ceria than 10GDC under these conditions. In accordance with observations from Figure 5, the observed increase in Ea,app further supports the hypothesized reaction mechanism: methane-driven reduction over LSA ceria or 10GDC is primarily vacancy-mediated and governed by CO desorption at low nonstoichiometries (Ea3.2 ≈ 30 kJ mol-1), and as surface oxygen diminishes, methane activation dictates further reaction progression (Ea1.2 ≈ 80 kJ mol-1). For 10GDC, the presence of inherent vacancies accelerates the transition between RDS. As a result, the first peak (as can be seen in Figure 3) associated with the oxidation of carbon imbedded on an oxygen vacancy is comparably less significant, and thus the increase in the extracted Ea,app occurs sooner (at δ > 0.10 and δ > 0.15 for 10GDC and ceria, respectively). Notably, the model-fitted activation energies that correspond to the projected set of RDS (see Table 2) fall within the ranges reported in Figure 7C.



Figure 7. Oxygen removal rate of (A) ceria and (B) 10 mol % Gd-doped ceria plotted as a function of inverse temperature for different pCH4 at ms,i = 15.5 mg and tox = 10 min. For a given pCH4, the measured rates and corresponding trend line are denoted by discrete symbols and a solid line, respectively. (C) Compositionally-dependent or apparent activation energy for the aforementioned samples and experimental conditions; solid and dashed trend lines were included to differentiate the results from each sample. 6. Conclusion Prior literature has postulated that methane dissociation over ceria may be mediated by either a surface oxygen anion or vacancy. Here, we conclusively demonstrate that methane activation involves interactions between both pathways; however, for low surface area ceria and 10 mol % gadolinium-doped ceria, the reaction mechanism proceeds almost exclusively via surface oxygen vacancies and is governed by a combination of the following rate-determining steps: (1) carbon monoxide desorption and (2) methane activation.


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A comprehensive kinetic model was formulated on the basis of analyzing abundant reactive intermediates as they interact with the ceria surface during reaction progression and applied to temperature-dependent rate data obtained with a refined method of multistage isothermal thermogravimetry. Excellent agreement between the experimentally determined rates and corresponding predictions is observed under a wide range of temperatures for methane partial pressures between 0.02 and 0.04 atm. Fitted activation energies that correspond to the hypothesized combination of rate-determining steps agree well with the compositionallydependent, apparent activation energy extracted through isoconversional techniques from a prior work.15 For example, activation energies of carbon monoxide desorption (rate-limiting at low δ and low T) and methane activation (rate-limiting at high δ when T > 750 °C) over a reduced ceria surface are 32 ± 3 and 77 ± 3 kJ mol-1, respectively. The postulated reaction mechanism and selection of rate-determining steps was further validated by applying the aforementioned model to rate data obtained with 10 mol % gadolinium-doped ceria. When compared to ceria, extrinsic vacancies expedited the shift in rate-determining step to lower nonstoichiometries, as evidenced by notable differences in the kinetic profiles and isoconversional results; however, similar activation energies associated to each rate-determining step were extracted from the model. The interpretation of these observations indicates that methane activation over a reduced ceria surface is likely rate-determining when the accumulation of carbon obstructs sites for further reduction. Conversely, oxidation of carbon imbedded on an oxygen site, which requires the reduction of six adjacent cations to prompt oxygen vacancy creation and carbon monoxide desorption, is likely rate-determining at low oxygen nonstoichiometries and temperatures. Supporting Information Acknowledgements This work was supported by the Qatar National Research Fund (grant number: NPRP8-370-2-154, Funder ID. 10.13039/100008982). The authors would like to thank Dr. Helena Hagelin-Weaver and Bochuan Song for their assistance in obtaining all BET measurements and also acknowledge Dr. Peter Loutzenhiser for his helpful suggestions regarding weighting parameters within our minimization routine. Nomenclature A = pre-exponential factor, min-1 Ea = activation energy, kJ mol-1 f = objective function for minimization Ḟ = entrance/exit rate, mol min-1 Ġ = generation/consumption rate, mol min-1 J̇ = diffusive flux, mol m-2 min-1



k = rate constant, min-1 m = mass, mg M = molar mass, g mol-1 N = number of moles, mol Q = volumetric flowrate, ml min-1 p = partial pressure, atm ṙ = rate, min-1 R = ideal gas constant, 8.314 J mol-1 K-1 S = surface area, m2 t = time, min T = temperature, °C w = weighting factor Greek α, β = oxidant magnitudes δ = degree of nonstoichiometry Δ = change ̅ρ = surface molar density, mol m-2 ν = stoichiometric coefficient Subscripts/Superscripts app = apparent b = bulk i = initial j = species index


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k = numeric index m = measured n = normalized ox = oxidation p = predicted red = reduction ref = reference s = sample tot = total Abbreviations 10GDC = 10 mol % gadolinium-doped ceria BET = Brunauer-Emmett-Teller CLR = chemical looping reforming DSC = differential scanning calorimetry DFT = density functional theory FTS = Fischer-Tropsch synthesis GTL = gas-to-liquids KIE = kinetic isotope effect LSA = low surface area QMS = quadrupole mass spectrometer RDS = rate-determining step(s) SQP = sequential quadratic programming SSE = sum of squared errors



TGA = thermogravimetric analyzer XPS = X-ray photoelectron spectroscopy References 1. Protasova, L.; Snijkers, F., Recent developments in oxygen carrier materials for hydrogen production via chemical looping processes. Fuel 2016, 181, 75-93. 2. Voitic, G.; Hacker, V., Recent advancements in chemical looping water splitting for the production of hydrogen. RSC Advances 2016, 6, (100), 98267-98296. 3. Krenzke, P. T.; Fosheim, J. R.; Davidson, J. H., Solar fuels via chemical-looping reforming. Solar Energy 2017. 4. Lange, J.-P. J. C. T., Methanol synthesis: a short review of technology improvements. 2001, 64, (1-2), 3-8. 5. Agrafiotis, C.; von Storch, H.; Roeb, M.; Sattler, C., Solar thermal reforming of methane feedstocks for hydrogen and syngas production—a review. Renewable and Sustainable Energy Reviews 2014, 29, 656-682. 6. Dry, M. E. J. J. o. C. T.; Biotechnology: International Research in Process, E.; Technology, C., High quality diesel via the Fischer–Tropsch process–a review. 2002, 77, (1), 4350. 7. Wilhelm, D.; Simbeck, D.; Karp, A.; Dickenson, R., Syngas production for gas-to-liquids applications: technologies, issues and outlook. J Fuel processing technology 2001, 71, (1-3), 139-148. 8. Otsuka, K.; Sunada, E.; Ushiyama, T.; Yamanaka, I., The production of synthesis gas by the redox of cerium oxide. Studies in Surface Science and Catalysis 1997, 107, 531-536. 9. Otsuka, K.; Wang, Y.; Sunada, E.; Yamanaka, I., Direct partial oxidation of methane to synthesis gas by cerium oxide. Journal of Catalysis 1998, 175, (2), 152-160. 10. Krenzke, P. T.; Davidson, J. H., Thermodynamic analysis of syngas production via the solar thermochemical cerium oxide redox cycle with methane-driven reduction. Energy & Fuels 2014, 28, (6), 4088-4095. 11. Gao, X.; Vidal, A.; Bayon, A.; Bader, R.; Hinkley, J.; Lipiński, W.; Tricoli, A., Efficient ceria nanostructures for enhanced solar fuel production via high-temperature thermochemical redox cycles. Journal of Materials Chemistry A 2016. 12. Krenzke, P. T.; Fosheim, J. R.; Zheng, J.; Davidson, J. H., Synthesis gas production via the solar partial oxidation of methane-ceria redox cycle: Conversion, selectivity, and efficiency. International Journal of Hydrogen Energy 2016. 13. Warren, K. J.; Reim, J.; Randhir, K.; Greek, B.; Carrillo, R.; Hahn, D. W.; Scheffe, J. R., Theoretical and Experimental Investigation of Solar Methane Reforming through the Nonstoichiometric Ceria Redox Cycle. Energy Technology 2017. 14. Welte, M.; Warren, K.; Scheffe, J. R.; Steinfeld, A., Combined ceria reduction and methane reforming in a solar-driven particle-transport reactor. Industrial & engineering chemistry research 2017, 56, (37), 10300-10308. 15. Warren, K. J.; Scheffe, J. R., Kinetic insights into the reduction of ceria facilitated via the partial oxidation of methane. Materials Today Energy 2018, 9, 39-48. 16. Fosheim, J. R.; Hathaway, B. J.; Davidson, J. H., High efficiency solar chemical-looping methane reforming with ceria in a fixed-bed reactor. Energy 2018.


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17. Chuayboon, S.; Abanades, S.; Rodat, S., Syngas production via solar-driven chemical looping methane reforming from redox cycling of ceria porous foam in a volumetric solar reactor. Chemical Engineering Journal 2019, 356, 756-770. 18. Ackermann, S.; Scheffe, J. R.; Steinfeld, A., Diffusion of oxygen in ceria at elevated temperatures and its application to H2O/CO2 splitting thermochemical redox cycles. The Journal of Physical Chemistry C 2014, 118, (10), 5216-5225. 19. Ackermann, S.; Sauvin, L.; Castiglioni, R.; Rupp, J. L.; Scheffe, J. R.; Steinfeld, A., Kinetics of CO2 reduction over nonstoichiometric ceria. The Journal of Physical Chemistry C 2015, 119, (29), 16452-16461. 20. Feng, Z. A.; El Gabaly, F.; Ye, X.; Shen, Z.-X.; Chueh, W. C., Fast vacancy-mediated oxygen ion incorporation across the ceria–gas electrochemical interface. Nature Communications 2014, 5, 4374. 21. Zhao, Z.; Uddi, M.; Tsvetkov, N.; Yildiz, B.; Ghoniem, A. F., Redox Kinetics Study of Fuel Reduced Ceria for Chemical-Looping Water Splitting. The Journal of Physical Chemistry C 2016, 120, (30), 16271-16289. 22. Zhao, Z.; Uddi, M.; Tsvetkov, N.; Yildiz, B.; Ghoniem, A. F., Enhanced intermediatetemperature CO 2 splitting using nonstoichiometric ceria and ceria–zirconia. Physical Chemistry Chemical Physics 2017, 19, (37), 25774-25785. 23. Ramırez-Cabrera, E.; Atkinson, A.; Chadwick, D., Reactivity of ceria, Gd-and Nb-doped ceria to methane. Applied Catalysis B: Environmental 2002, 36, (3), 193-206. 24. Nair, M. M.; Abanades, S., Tailoring Hybrid Non-stoichiometric Ceria Redox Cycle for Combined Solar Methane Reforming and Thermochemical Conversion of H2O/CO2. Energy & Fuels 2016. 25. Mayernick, A. D.; Janik, M. J., Methane activation and oxygen vacancy formation over CeO2 and Zr, Pd substituted CeO2 surfaces. The Journal of Physical Chemistry C 2008, 112, (38), 14955-14964. 26. Knapp, D.; Ziegler, T., Methane dissociation on the Ceria (111) surface. The Journal of Physical Chemistry C 2008, 112, (44), 17311-17318. 27. Krcha, M. D.; Mayernick, A. D.; Janik, M. J., Periodic trends of oxygen vacancy formation and C–H bond activation over transition metal-doped CeO2 (1 1 1) surfaces. Journal of catalysis 2012, 293, 103-115. 28. Salcedo, A.; Iglesias, I.; Mariño, F.; Irigoyen, B., Promoted methane activation on doped ceria via occupation of Pr (4f) states. Applied Surface Science 2018, 458, 397-404. 29. Lustemberg, P. G.; Palomino, R. M.; Gutierrez, R. A.; Grinter, D. C.; Vorokhta, M.; Liu, Z.; Ramírez, P. J.; Matolín, V.; Ganduglia-Pirovano, M. V. n.; Senanayake, S. D., Direct conversion of methane to methanol on Ni-ceria surfaces: metal–support interactions and waterenabled catalytic conversion by site blocking. Journal of the American Chemical Society 2018, 140, (24), 7681-7687. 30. Xie, P.; Pu, T.; Nie, A.; Hwang, S.; Purdy, S. C.; Yu, W.; Su, D.; Miller, J. T.; Wang, C., Nanoceria-supported single-atom platinum catalysts for direct methane conversion. ACS Catalysis 2018, 8, (5), 4044-4048. 31. Zhang, F.; Yao, S.; Liu, Z.; Gutiérrez, R. A.; Vovchok, D.; Cen, J.; Xu, W.; Ramírez, P. J.; Kim, T.; Senanayake, S. D., Reaction of Methane with MO x/CeO2 (M= Fe, Ni, and Cu) Catalysts: In Situ Studies with Time-Resolved X-ray Diffraction. The Journal of Physical Chemistry C 2018, 122, (50), 28739-28747.



32. Fronzi, M.; Piccinin, S.; Delley, B.; Traversa, E.; Stampfl, C., CH x adsorption (x= 1–4) and thermodynamic stability on the CeO 2 (111) surface: a first-principles investigation. RSC Advances 2014, 4, (24), 12245-12251. 33. Trovarelli, A., Catalytic properties of ceria and CeO2-containing materials. Catalysis Reviews 1996, 38, (4), 439-520. 34. Davis, M. E.; Davis, R. J., Fundamentals of Chemical Reaction Engineering. 1st ed.; McGraw Hill: New York, NY, 2003. 35. Pantu, P.; Kim, K.; Gavalas, G. R., Methane partial oxidation on Pt/CeO 2–ZrO 2 in the absence of gaseous oxygen. Applied Catalysis A: General 2000, 193, (1), 203-214. 36. Mullins, D. R., The surface chemistry of cerium oxide. Surface Science Reports 2015, 70, (1), 42-85. 37. Zhao, Z. Redox kinetics study for chemical-looping combustion, water and CO₂ splitting using nickel and cerium-based oxygen carrier. Massachusetts Institute of Technology, 2016. 38. Horn, R.; Schlögl, R., Methane activation by heterogeneous catalysis. Catalysis Letters 2015, 145, (1), 23-39. 39. Otake, T.; Yugami, H.; Yashiro, K.; Nigara, Y.; Kawada, T.; Mizusaki, J., Nonstoichiometry of Ce1− XYXO2− 0.5 X− δ (X= 0.1, 0.2). Solid State Ionics 2003, 161, (1-2), 181-186. 40. Gotor, F. J.; Criado, J. M.; Malek, J.; Koga, N., Kinetic analysis of solid-state reactions: the universality of master plots for analyzing isothermal and nonisothermal experiments. The journal of physical chemistry A 2000, 104, (46), 10777-10782. 41. Fogler, S. H., Elements of Chemical Reaction Engineering. Third ed.; Prentice-Hall, Inc.: Upper Saddle River, New Jersey 07458, 1999. 42. Laosiripojana, N.; Assabumrungrat, S., Catalytic dry reforming of methane over high surface area ceria. Applied Catalysis B: Environmental 2005, 60, (1), 107-116. 43. Abbott, M. M.; Smith, J. M.; Van Ness, H. C., Introduction to Chemical Engineering Thermodynamics. McGraw-Hill: 2005. 44. Chueh, W. C.; McDaniel, A. H.; Grass, M. E.; Hao, Y.; Jabeen, N.; Liu, Z.; Haile, S. M.; McCarty, K. F.; Bluhm, H.; El Gabaly, F., Highly enhanced concentration and stability of reactive Ce3+ on doped CeO2 surface revealed in operando. Chemistry of Materials 2012, 24, (10), 1876-1882. 45. Carrillo, R. J.; Warren, K. J.; Scheffe, J., Experimental framework for evaluation of the thermodynamic and kinetic parameters of metal-oxides for solar thermochemical fuel production. Journal of Solar Energy Engineering. 46. Chueh, W. C.; Haile, S. M., A thermochemical study of ceria: exploiting an old material for new modes of energy conversion and CO2 mitigation. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 2010, 368, (1923), 3269-3294. 47. Friedman, H. L. In Kinetics of thermal degradation of char‐forming plastics from thermogravimetry. Application to a phenolic plastic, Journal of Polymer Science: Polymer Symposia, 1964; Wiley Online Library: 1964; pp 183-195.


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For Table of Contents Only



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The Role of Surface Oxygen Vacancy Concentration on the

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