CexOyâ (x = 2â3) + D2O Reactions: Stoichiometric Cluster Formation

Article pubs.acs.org/JPCA

CexOy− (x = 2−3) + D2O Reactions: Stoichiometric Cluster Formation from Deuteroxide Decomposition and Anti-Arrhenius Behavior Jeremy A. Felton, Manisha Ray, Sarah E. Waller, Jared O. Kafader, and Caroline Chick Jarrold* Department of Chemistry, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States S Supporting Information *

ABSTRACT: Reactions between small cerium oxide cluster anions and deuterated water were monitored as a function of both water concentration and temperature in order to determine the temperature dependence of the rate constants. Sequential oxidation reactions of the CexOy− (x = 2, 3) suboxide cluster anions were found to exhibit anti-Arrhenius behavior, with activation energies ranging from 0 to −18 kJ mol−1. Direct oxidation of species up to y = x was observed, after which, −OD abstraction and D2O addition reactions were observed. However, the stoichiometric Ce2O4− and Ce3O6− cluster anions also emerge in reactions between D2O and the respective precursors, Ce2O3D− and Ce3O5D2−. Ce2O4− and Ce3O6− product intensities diminish relative to deuteroxide complex intensities with increasing temperature. The kinetics of these reactions are compared to the kinetics of the previously studied MoxOy− and WxOy− reactions with water, and the possible implications for the reaction mechanisms are discussed.

1. INTRODUCTION Bulk cerium oxides (CeO2 and Ce2O3) have attracted interest recently because of their ability to catalyze or co-catalyze a wide range of reactions, including the water−gas shift reaction, reduction and oxidation reactions, and methane re-formation reactions, among others.1−5 The particular oxidative activity of ceria can be attributed to its ability to store and conduct oxygen, and recent studies suggest that its oxidative reactivity is due to oxygen-centered radicals over the metal atoms.6,7 Cerium oxide, a common component in catalytic converters in automobiles, has also been considered for solid oxide fuel cells because it is both a good ionic conductor and a good support for active metal nanoparticles.8−10 The intense focus on ceria as a co-catalyst with noble or coinage metals in the water−gas shift reaction underscores the importance of low-dimensional, local interactions. We have previously undertaken a series of cluster reactivity studies in an effort to characterize local interactions between metals in various oxidation environments and small molecules such as water11−16 and carbon monoxide,17 the water−gas shift reactants. The current report describes the temperature dependence of reactions between cerium suboxide cluster anions (CexOy−; y < 2x) and water. Bonding on metal oxide surfaces has been described as having local, cluster-like character,18 which has spurred a number of computational and experimental studies implementing small cerium oxide clusters as model systems.7,19−22 Oxygen vacancies on metal oxide surfaces, in which electrons are localized, have been identified as potentially active sites.23 The focus of the current study is cerium sub-oxide cluster anion reactions with water, with the goal of adding to the understanding of the stoichiometry- and size-dependent reactivity of these clusters © 2014 American Chemical Society

and, more importantly, to the understanding of the reactivity and catalytic properties of bulk cerium oxide surface defects. Previous computational and experimental studies on MxOy− + H2O reactions (M = Mo, W) done in our group suggested that the entrance channels of many of the cluster−water addition reactions are barrierless at 0 K, though at finite temperatures, entropic barriers appear to become important.13,14,16 The reaction paths generally involve (1) formation of an electrostatic complex governed by local dipole−dipole interactions followed by (2) low-barrier formation of covalently bound intermediates featuring dihydroxide groups or hydride hydroxide groups, depending on the initial cluster−water complex formed: k1

k2

MxOy− + H 2O ⇌ [MxOy− ·H 2O] → Products k1′

(1)

These initial steps are shown schematically in Figure 1. For the most reduced clusters, the electrostatic complex undergoes fast hydride−hydroxide complex formation and subsequent H2 release, while for the more oxidized clusters, kinetically trapped dihydroxide complexes are sometimes observed.11,14,16 Reactions involving radicals, which are typically barrierless, often exhibit anti-Arrhenius temperature dependence.24,25 This effect can be rationalized with the Eyring equation for a secondorder reaction rate constant k(T), which any conventional physical chemistry textbook introduces when connecting transition state theory (TST, or activated complex theory, ACT) with the thermodynamics of the activated complex26−28 Received: August 5, 2014 Revised: October 11, 2014 Published: October 13, 2014 9960

dx.doi.org/10.1021/jp507900d | J. Phys. Chem. A 2014, 118, 9960−9969

The Journal of Physical Chemistry A

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behind BV1 was maintained at 80 psig. No O2 was added to the carrier gas to produce the cerium oxide clusters; the oxide layer on the cerium powder was sufficient to produce the suboxide cluster series presented below. A second beam valve (BV2) was used to inject the reactant gas mixture (also with 80 psig stagnation pressure) into the reaction channel downstream from ablation. The reactant gas mixture was prepared with D2O (99.9 atom %, Sigma-Aldrich Co., St. Louis, MO) maintained at 30 °C (the ambient temperature of the laboratory) and seeded into a total pressure of 400 psi of helium in a mixing tank separate from the carrier gas issued from BV1, to produce a 0.15% mixture based on the vapor pressure of D2O at 30 °C. D2O was used instead of water to overcome the limited resolution of the instrument at the mass-to-charge ranges being investigated, though significant H/D exchange was evident in the mass spectra. The number density of D2O, ND2O, in the reaction channel was controlled by varying the pulse duration of BV2. The effectiveness of this method was checked by comparing with similar experiments done by diluting the D2O mixture in the reservoir but keeping the BV2 duration constant. Concentration control by beam valve duration variation is the preferred method because it can be done in a shorter period of time, avoiding significant variations in source conditions encountered when making dilutions and allowing sufficient time for the gas to mix. The reaction channel temperature was controlled through the use of three 0.81 cm diameter button heaters (HeatWave Laboratories, P/N 101136) spaced equally around the circumference of the copper reaction channel, powered by a HeatWave Laboratories temperature controller (P/N 101303) with feedback from two K-type thermocouples positioned at different points on the channel. Whether the reaction mixture achieves thermal equilibrium with the channel is not known. However, we were able to verify that the temperature of the reactant clusters was influenced by the channel temperature by measuring anion photoelectron spectra of small cluster anions and observing the variation in vibrational and electronic hot band transitions (spectra of the cluster anions are the topic of a separate article). Reactivity studies were run at 30, 50, 70, and 100 °C. At temperatures above 100 °C, a sharp increase in metal-oxo carbide products was observed, presumably from reactions with diffusion pump oil.

Figure 1. Schematic free-energy path for a hypothetical CexOy− + H2O reaction. Relative minima for the electrostatic complex barrier to product formation are based on previous studies on MxOy− + H2O reactions (M = Mo, W).

k(T ) =

‡ ‡ kBT −ΔG‡(T )/ kBT kT e = B e−(ΔH (T )/ kBT ) + (ΔS (T )/ kB) hc° hc°

(2) ‡

ΔG (T) is the free energy of activation, a positive value in conventional reactions, generally leading to an increase in k(T) with T (c° is the standard concentration, and h and kB are the Plank and Boltzmann constants, respectively). If ΔH‡ is zero, the entropy of activation term can result in anti-Arrhenius behavior. The entropy of activation, ΔS‡(T) is a negative quantity because the complex has lower entropy than the two separated reactants and varies with temperature relative to a standard temperature (T0) via29 ⎛T ⎞ ΔS‡(T ) = ΔS‡(T0) + ln⎜ ⎟ΔCp‡ ⎝ T0 ⎠

(3)

where ΔC‡p is Cp of the complex minus Cp of the reactants. ΔC‡p can be less than zero, resulting in a more negative ΔS‡(T) with increasing T and, consequently, a decrease in k.29 Additional barriers along the reaction path (e.g., ΔG2‡ in Figure 1) can also affect the measured negative activation barrier in ways that will be explored below. The temperature dependence of rate constants has been measured for several CexOy− + H2O reactions and is consistent with anti-Arrhenius behavior from barrierless or multistep reactions. The activation energies range from approximately −20 kJ mol−1 to zero. However, the observed product distributions suggest that a much more complicated series of reactions take place from CexOy− + water interactions than those in our previous MxOy− + water studies. In particular, we observe production of stoichiometric Ce2O4− and Ce3O6− from reactions between deuteroxide precursor ions and water.

3. RESULTS AND ANALYSIS 3.A. Reaction Products. Figure 2 shows a typical initial distribution of CexOy− (x = 1−4) clusters generated in the cluster source (black trace) along with a typical reaction mixture distribution measured after introducing water into the reaction channel (blue trace). Table 1 lists the ions observed initially, with typical relative intensities, and after cluster−water reactions (product intensities depend on the number density of water in the reaction channel). While reactions were evident in all four cluster series (x = 1−4), we limited our analysis to the x = 2 and 3 series for practical reasons. The initial x = 1 series mass distribution exhibited a relatively high abundance of hydroxides (e.g., CeO2H2−), and the mass resolution of the apparatus at masses greater than the x = 3 series were inadequate to definitively assign many of the D2O addition or −OD abstraction products. Mass spectra of initial Ce4Oy− and Ce5Oy− cluster distributions with the subsequently measured

2. EXPERIMENTAL METHODS Cerium and cerium oxide cluster anions were produced, swept through a high-pressure, fast-flow reaction channel, and mass analyzed as a function of temperature and water concentration using a time-of-flight mass spectrometer described previously.11,30,31 Cluster anions were generated in an ablation source using the second harmonic output of a Nd:YAG laser (5 mJ/pulse) focused onto a target prepared from pressed cerium powder (Sigma-Aldrich Co., St. Louis, MO). The resulting plasma coalesced and cooled and was swept through the 2.5 cm long, 0.3 cm diameter reaction channel in a pulse of ultra-highpurity helium issued from a solenoid-type molecular beam valve (BV1), synchronized with the laser. The stagnation pressure 9961



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reaction mixture distributions are included in the Supporting Information (SI 1).

Figure 2. Typical mass spectra of the initial distribution of cluster anions produced by laser ablation of a cerium target (black trace) and the distribution after clusters are exposed to D2O in a reaction channel (blue trace).

Table 1. Summary of Clusters Observed Initially and after Water Exposurea CexOy x=1

predominant clusters, initial, with typical relative intensities within an x-series Ce− (0.3) CeO− (0.3) CeO2H2− (0.3) other oxo-hydroxides (0.1)

x=2

Ce2O− (0.85) Ce2O2− (0.15)

x=3

Ce3− (0.15) Ce3O− (0.5) Ce3O2− (0.25) Ce3O3− (0.1)

x=4

Ce4− (0.1) Ce4O− (0.5) Ce4O2− (0.25) Ce4O3− (0.05)

complexes observed after water reactions Ce− significantly decreased CeO− CeO2D2− CeO3 CeO4D2−; CeO4D4− (predominant) CeO5D2−; CeO5D3− Ce2O− significantly decreased Ce2O2−; CeO2D− Ce2O3D− Ce2O4− (small); Ce2O4D3− Ce2O5− (small); Ce2O5D2−3−; Ce2O5D5−6− Ce3− significantly decreased Ce3O− significantly decreased Ce3O2− decreased Ce3O3− (predominant) Ce3O4D− Ce3O5D2− Ce3O6− (small); Ce3O6D3−5− Ce4− depleted Ce4O− significantly decreasesd Ce4O2− decreased Ce4O3− intensity approximately constant Ce4O4− Ce4O5− present, not abundant

Figure 3. Series of mass spectra of Ce2OyDz− species recorded with increasing cluster−D2O collisions in the reaction channel, collected at T = (a) 30 and (b) 100 °C. The numeric value associated with each trace is the number of collisions based on approximations described in the text.

Figures 3 and 4 show representative sets of mass spectra that were collected for Ce2Oy− and Ce3Oy−, respectively, at both (a) 30 and (b) 100 °C with an increasing number of cluster−D2O collisions. Similar figures showing mass spectra acquired at 50 and 70 °C are included in the Supporting Information (SI 2 and SI 3). The number of cluster−D2O collisions was approximated with simple collision theory, using ND2O (from the vapor pressure of D2O in the BV2 gas supply and the fractional contribution of the gas from BV2 to the overall pressure in the reaction channel), a hard-sphere collisional cross section of 4 × 10−19 m2, and a residence time of clusters in the reaction channel, estimated at 10−50 μs, based on the variation in the timing of subsequent pulsed electronic components in the mass spectrometer with the length of the reaction channel. We note here that the number of collisions is based on several approximations and should be treated as an order-of-magnitude estimate. However, they serve as a consistent point of comparison between the current study

a

Relative intensities of clusters in the initial distribution can vary with source conditions and should be taken as approximate values under typical conditions. 9962



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internal energy gained in cluster reactions results in thermionic emission. Table 2 includes the explicit size-specific reactions observed in this study. With increasing collision number, Ce2O2− intensity decreases while ions with higher mass increase in intensity, suggesting that Ce2O2− also reacts with D2O. However, direct oxidation of Ce2O2− to produce Ce2O3− is not observed. No Ce2O3− is observed in the mass spectrum, and the Ce2O3D− peak intensity increases with the number of collisions, suggesting that Ce2O2− reacts via k

CexOy− + D2 O → CexOy + 1D− + D•

(5)

With production of Ce2O3D−, the subsequent reactions branch between water addition, −OD abstraction, and, unexpectedly, bare oxide formation. The predominant reaction appears to primarily involve water addition to Ce2O3D− via k

CexOy D− + D2 O → CexOy + 1D3−

(6)

Ce2O4−

However, is also produced in small quantities, more abundantly at lower temperatures than at higher temperatures, as can be seen in the representative mass spectra shown in Figure 3a and b. Figure 5a shows three overlaid mass spectra in the Ce2O− to Ce2O7Dz− mass range obtained at 30 °C, showing the initial cluster distribution, and the distributions measured after 60 and 160 cluster−D2O collisions. Dashed vertical lines guide the eye to bare 140Ce2Oy− oxide masses. The appearance of Ce2O4− with increasing D2O collisions is somewhat baffling if Ce2O3D− is the precursor ion. One possibility is that a dihyroxide (or a hydride−hydroxide) is formed, followed by decomposition via ka

CexOy D− + D2 O → CexOy + 1D2− + D• kb

→ CexOy + 1− + D2 (+ D•) Figure 4. Series of mass spectra of Ce3OyDz− species recorded with increasing cluster−D2O collisions density in the reaction channel, collected at T = (a) 30 and (b) 100 °C. The numeric value associated with each trace is the number of collisions based on approximations described in the text.

(7b)

Evidence of Ce2O5− production is also seen in Figures 3a and 5a, though Ce2O5D2−3− and Ce2O5D5−6− are more abundant. These ion masses are indicated in Figure 5a. The Ce3Oy− series of clusters has a similarly complicated sequence of oxidation and water addition reactions, reflected in Figure 4a and b. The initial cluster distribution ranges from the metallic cluster, Ce3−, up to Ce3O3−. Sequential oxidation with D2 production via eq 4 appears to occur for y = 0 up to 3, after which deuteroxide addition via eqs 5 and 7a results in sequential Ce3O4D− and Ce3O5D2− formation, respectively. Again, Table 1 summarizes the products observed. As in the Ce2Oy− series, mass spectral peaks of species with y > x are broadened both by a range of z values in Ce3Oy>3Dz− and by the presence of H. However, we again observe production of the bare, stoichiometric Ce3O6− cluster, apparently from decomposition of hydroxide (or hydride− hydroxide) complexes, more abundantly at lower temperatures than at higher temperatures. Figure 5b shows three mass spectra obtained at T = 30 °C, showing the initial cluster distribution and distributions observed with 90 and 180 cluster−water collisions, with the bare oxide masses indicated by dashed vertical lines. While the peaks associated with y > 3 species are broad and spread to masses greater than bare oxide masses, the group of masses associated with Ce3O6Dz− has a clearly different profile from neighboring peaks in that there is a sharp onset of ion signal at the mass expected for the bare oxide. On the basis of this peak width and profile, it appears

and past studies, and the relative changes in collision number are accurate to within 15%. Evident in the mass spectra are contributions from two principle isotopes of cerium, 140Ce and 142Ce, which have a relative abundance of approximately 8:1, resulting in a 4:1 ratio for the 140Ce2Oy− to 140Ce142CeOy− intensities, and 8:3 for the 140 Ce3Oy− to 140Ce2142CeOy− intensities. Both the Ce2Oy− and the Ce3Oy− series exhibit the typical pattern for sequential oxidation for the lowest oxides, with −OD or D2O addition becoming more prevalent for the higher oxides. As seen in Figure 3a and b, the initial cluster distribution in the Ce2Oy− series is dominated by Ce2O− and Ce2O2−. No Ce2− is observed; Ce2 may have a negative EA (the ground state of neutral Ce2 is predicted to be closed-shell32,33); Ce−, Ce3−, and Ce4− are all observed. Upon introduction of water, the Ce2O− intensity diminishes as the Ce2O2− intensity increases, consistent with direct oxidation of the form k

CexOy− + D2 O → CexOy + 1− + D2

(7a)

(4)

We note here that there is no attenuation in overall ion signal with the addition of water; therefore, there is no evidence that 9963



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Table 2. Calculated Reaction Rate Constants and Activation Energies for Selected Oxidation and Water-Addition Reactions reaction k1

Ce2O− + D2 O → Ce2O2− + D2

pseudo-1° rate constant (collision−1) 30 °C

activation barrier (kJ mol−1)

0.017 ± 0.005

−11 ± 4

50 °C 70 °C 100 °C 30 °C

0.010 0.0088 0.0071 0.023

± ± ± ±

0.002 0.0010 0.0005 0.010

−18 ± 5

50 °C 70 °C 100 °C 30 °C

0.016 0.011 0.007 0.027

± ± ± ±

0.008 0.002 0.002 0.002

−10 ± 5

50 °C 70 °C 100 °C 30 °C

0.019 0.020 0.012 0.014

± ± ± ±

0.006 0.003 0.002 0.003

−3 ± 5

50 °C 70 °C 100 °C 30 °C

0.008 0.008 0.011 0.018

± ± ± ±

0.004 0.003 0.003 0.006

−4 ± 5

k7

50 °C 70 °C 100 °C 30 °C

0.013 0.011 0.013 0.015

± ± ± ±

0.003 0.004 0.003 0.005

−9 ± 5

k8

50 °C 70 °C 100 °C 30 °C

0.017 0.007 0.009 0.006

± ± ± ±

0.010 0.003 0.003 0.002

∼0

50 °C 70 °C 100 °C

0.009 ± 0.005 0.007 ± 0.002 0.007 ± 0.003

k2

Ce2O2− + D2 O → Ce2O3D− + D

k3

Ce2O3D− + D2 O → Ce2O4 D3−

k5

Ce3− + D2 O → Ce3O− + D2

k6

Ce3O− + D2 O → Ce3O2− + D2

Ce3O2− + D2 O → Ce3O3− + D2

Ce3O3− + D2 O → Ce3O4 D− + D

that Ce3O5D2− + D2O forms complexes that are unstable relative to Ce3O6− + 2D2 and Ce3O6D2− + D2 formation, along with the comparably more abundant product, Ce3O6D4−. This is clearly a system worth exploring with a detailed computational study similar to those done previously in our group. On the basis of the mass spectra, and as summarized in Table 1, it is apparent that direct oxidation accompanied by D2 production is favored up to x = y, at which point −OD abstraction appears to be favored, followed by additional −OD abstraction or water addition. As will be discussed below, this sequence of reactions is significantly different from results of previous studies in our group on MoxOy− + H2O/D2O and WxOy− + H2O/D2O reactions.11,12 3.B. Rate Constants and Activation Energies. While the sequence of Ce2Oy− + D2O and Ce3Oy− + D2O reactions for higher values of y is complicated and involves multiple product channels, we can determine the relative rate constants for the initial steps in the sequence of reactions at different temperatures in order to determine the activation barriers. Rate laws for what we assume to be bimolecular reactions can be treated with pseudo-first-order kinetics because the water number density in the reaction channel is 102−103 times greater than the cluster number density.34 Ce2O− is the most reduced cluster in the x = 2 series, and the reaction with water is expected to follow the rate law

dNCe2O− dt

= −k1″·NCe2O−·ND2O = −k1′·NCe2O−

(8)

Dividing the rate law by the collision frequency, z = dc/dt, which is a constant under these conditions, converts the second-order rate constant to a pseudo-first-order rate constant expressed in collision−1 (c−1) instead of time−1

(

dNCe2O− dt

z

) = −k ·N 1

Ce2O−

(9)

The experiment involves varying the number density of D2O in the reactor rather than the time the cluster spends in the reactor; therefore, the rate constants reported below can therefore be taken as reaction efficiencies. With this treatment, pseudo-first-order reaction rate constants were determined for the most reduced clusters, Ce2O− and Ce3−, based on plots of the natural log of the ion signal versus the number of collisions, c ln

NCe2O− NCe2O−,initial

= −k1·c

(10)

Rate constant determination for subsequent oxidations and water-addition reactions depends on the rate constant associated with the more reduced cluster in the series. For 9964



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Figure 5. Series of mass spectra obtained at T = 30 °C in the (a) Ce2Oy− cluster range and the (b) Ce3Oy− cluster range, showing the evolution of deuteroxide and water addition products with increasing exposure to D2O. The masses of bare oxides are indicated with vertical dashed lines, showing that CexO2x− clusters evolve, though no CexO2x−1− clusters are observed.

example, Ce2O2− is produced via the Ce2O− + D2O reaction and consumed via the Ce2O2− + D2O reaction per dNCe2O2− dc

= k1·NCe2O− − k 2·NCe2O2−

(11) Figure 6. Representative plots illustrating how pseudo-first-order rate constants (in units of collision−1) are determined graphically from the cluster anion intensity versus cluster−water collisions. (a) Relative intensities of the Ce3OyDz− ions as a function of collisions at T = 70 °C. (b) The rate constant for the Ce3− + D2O reaction is determined from the negative slope of the plot of ln(ICe3/I0) versus collisions; (c) the application of eq 11 to the Ce3O− + D2O reaction rate constant determination.

We can use the following plot with the previously determined value of k1 to determine k2 k1·NCe2O2− −

dNCe2O2− dc

= k 2·NCe2O2−

(12)

However, when the CexOy+1− cluster concentration is fairly constant, plots of (dNCexOy+1−/dc] − ka · NCexOy− as a function of NCexOy+1− resemble scatter plots. In these cases, we identify the maximum of the NCexOy+1− curve (i.e., (dNCexOy+1−/dc) = 0), and approximate kb from ka ·

NCexOy− NCexOy+1−

in the mass spectrum are proportional to the ion number densities. Figure 6b shows a plot of ln(NCe3−/NCe3−,initial) = −k5·c (analogous to eq 10), from which the rate constant for the oxidation of Ce3− is determined from the slope, and the rate constant for the sequential oxidation of Ce3O−, k6, is determined using a plot of the appropriate equation analogous to eq 11 in Figure 6c. Note from the plot in Figure 6a that the Ce3O2− ion intensity does not vary in the monotonic way that Ce3− and Ce3O− ion intensities decay with the number of water collisions, and therefore, the rate constant, k7, associated with oxidation of Ce3O2− is determined via eq 13. Table 2 summarizes the rate constants determined with this analysis for sequential reactions for the x = 2 (y = 1−3) and x =

= kb (13)

Ce3Oy−

An analogous analysis is applied to the series. The reactions for which pseudo-first-order rate constants were determined are listed explicitly in Table 2. To illustrate the application of these analyses, Figure 6a shows a representative plot of Ce3OyDz− peak intensities as a function of approximate collisions with D2O, obtained at 70 °C. For all analyses, we assume that the integrals of peaks measured 9965



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cally from y = 1 to 3 for all four temperatures. The Ce3Oy− series shows that the Ce3O− oxidation has the highest rate constant in the series of rate constants determined. To determine the activation energies, the natural logarithms of the rate constants were plotted as a function of 1/RT, which, given the Arrhenius equation, would yield a slope of −Ea, which was used to generate plots of

3 (y = 0−3) clusters. Beyond y = 3 for both x = 2 and 3, numerous products were observed, making rate constant determination prone to high uncertainty. Three separate series of mass spectra were taken at each temperature, and rate constants determined in each set of data were averaged together to give the reported rate constants. First-order rate constants can be converted subsequently to second-order rate constants by multiplying by the collisional volume swept per time, given z = σ⟨νrel⟩ND2O.11,12 From Table 2, it can be seen that the rate constants are sizedependent and, generally, but not uniformly, decrease as the temperature is increased. Figure 7 shows the rate constants associated with (a) the Ce2Oy− oxidation reactions and (b) the Ce3Oy− oxidation reactions, plotted for each temperature. The error bars conservatively bracket the three values contributing to the average. The Ce2Oy− rate constants increase monotoni-

⎛E ⎞ ln(k) = −⎜ a ⎟ + ln(A) ⎝ RT ⎠

(14)

Figure 8a shows Arrhenius plots for the rate constants associated with the oxidation of Ce2O− (k1), Ce2O2− (k2),

Figure 8. Plots of ln k versus (RT)−1 for (a) Ce2Oy− reaction rate constants and (b) Ce3Oy− reaction rate constants.

and Ce3O3D− (k3). Figure 8b shows the plots for the oxidation of Ce3− (k5), Ce3O− (k6), Ce3O2− (k7), and Ce3O3− (k8). The slopes for oxidation in the Ce2Oy− series show very definitively positive slopes, indicating a negative Ea value, while the slopes associated with the Ce3Oy− series are closer to zero. The activation energies determined from the slopes of the plots are summarized in Table 2. Plots showing the fitting parameters, including the value of the pre-exponential factor (A) are included in the Supporting Information (SI 4).

4. DISCUSSION While the negative activation energies determined for several CexOy− + D2O reactions were not unanticipated, interpretation of the negative values is not straightforward. On the basis of our previous studies, the reaction free-energy paths generally feature multiple barriers.13,14,16 For reactions in which molecular hydrogen is a final product, the barriers between intermediates along the path are below the internal energy gained upon initial complex formation. In a simple steady-state approximation picture, the effective rate constant for a mechanism with two elementary reactions, treating MxOy−· H2O as a transient intermediate (Figure 1, eq 1), is k1k 2 keff = k1′ + k 2 (15)

Figure 7. Rate constants for CexOy− + D2O reactions, plotted as a function of y for (a) Ce2Oy− and (b) Ce3Oy−. 9966



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how they relate to features in the reaction free-energy path. We conclude that the range of negative barriers determined from the Arrhenius plots is in line with what is expected based on the energy and entropy of complex formation and subsequent covalently bound complex formation. The activation energies determined for the Ce3Oy− series are closer to zero, which, based on our analysis, may be expected with higher barriers to covalent bond formation or long-lived intermediates that undergo collisional cooling. Computational studies on CexOy− + H2O reaction free-energy paths are currently underway. 4.A. CexOy− + D2O Reaction Rate Constants Vary with y. The rate constants determined for most of the CexOy− + D2O reactions were found to be approximately an order of magnitude lower than those determined previously for tungsten oxide and molybdenum oxide cluster anion reactions with water using this experimental apparatus (at room temperature).11,12 However, MxOy− + H2O/D2O (M = Mo, W) rate constants decreased with increasing values of y for the x = 2 and 3 cluster series. That is, as the clusters approached bulk stoichiometry, the reaction rates decreased. That trend is in contrast to the trends determined from the current study, most notably for the Ce2Oy− series. For all four temperatures at which measurements were made, the rate constants for sequential oxidation increased with y (k1 < k2 < k3). Previous studies on MoxOy− and WxOy− clusters showed initial cluster distributions ranging from y = x to 3x, unlike the more reduced CexOy− initial cluster distribution, with y ≤ x. While we have not yet done a computational treatment of possible pathways for CexOy− + water reactions, previous studies suggest that the dipole−dipole interaction between an O−H bond of water and a local M−O bond is stronger than charge−dipole interactions in the electrostatic complex in the optimized structure,16 and the dipole−dipole alignment facilitates formation of the dihydroxide intermediate. The local M−O dipole increases as M becomes more oxidized, but the stronger dipole−dipole interactions are counteracted by increasing steric hindrance from additional O atoms. It is therefore possible that the increase in rate constant with y in the Ce2Oy− series (y = 1, 2) and Ce2O3D− is due to sequentially stronger local dipole−dipole interactions between water and the cluster, while O atoms are not sufficiently abundant to impose steric hindrance. The trend of increasing rate constant with oxidation is limited in the Ce3Oy− series. The rate constant for Ce3− oxidation (charge−dipole interactions stabilize a complex in which the O atom in D2O is pointed away from the Ce3− cluster) is lower than that for the oxidation of Ce3O−. However, the rate constant for Ce3O2− oxidation is comparable to that for Ce3− oxidation, and the rate constant for Ce3O3− oxidation is lower still. This is clearly evident in the series of mass spectra in Figure 5a, which shows the intensity of Ce3O3− increasing but never reaching the point where subsequent oxidation exceeds production via oxidation of Ce3O2−. In contrast, the intensities of Ce3O4D− and Ce3O5D2− appear to increase together, which could be explained by the existence of multiple Ce3O4D− structures, one of which immediately reacts to form Ce3O5D2− + D•. Computational studies on this cluster series would provide valuable insight into the structure versus reactivity relationship. 4.B. Stoichiometric Cluster Formation and Analogies to Bulk Ce Reactivity. As with all lanthanides, the +3 oxidation state of Ce ([Xe] 4f configuration) is stable. Bulk metallic cerium reacts with water to form Ce(OH)3 (2Ce +

into which Eyring expressions can be substituted, to get an explicit keff(T). While calculations on the CexOy− + H2O reaction free-energy paths, from which we would draw the energies and entropies associated with the elementary reactions, have not yet been undertaken, we can get an estimate of negative activation energies that would be consistent with the thermodynamics associated with electrostatic complex formation, followed by low-barrier, highly exothermic covalent bond formation. On the basis of numerous calculations on similar systems, we have found that the energy difference between the separated reactants, MxOy− + H2O, and the electrostatic complex, MxOy−·H2O is fairly consistently −60 kJ mol−1, which is large because of strong dipole−dipole interactions that enhance charge−dipole interactions. However, the free-energy well associated with the electrostatic complex is shallow because of the large negative entropy change, and entropy is further reduced at the saddle point between the electrostatic complex and the highly exothermic and irreversible dihydroxide (or other covalently bound structure) formation. Different cluster systems were calculated to have fairly wide-ranging barriers to covalently bound structure formation. An additional consideration is that the internal energy of the complex is not necessarily dissipated between complex−He collisions, which occur on the nanosecond time scale. At one limit, the temperature of the MxOy−·H2O complex is higher than the initial reactants by an amount given by the internal energy gained divided by the complex heat capacity (Tcomplex = Treactants + Eint,complex/Ccomplex, with a similar relationship for Tsaddle, assuming that heat capacities are constant over the temperature range). Assuming typical electrostatic complex energies and ΔS(T) values associated with the three elementary step reaction in eq 1 from a recently published study,16 assuming no energy dissipation, we calculated activation energies for a range of saddle point energies and found barriers of ∼−20 kJ mol−1 if the barriers associated with k1 and k2 were zero over the experimental temperature range. The explicit equations and thermodynamic quantities used to calculate keff(T) and plots of ln keff(T) [and ln k1(T), for comparison] versus (RT)−1 are included in the Supporting Information (SI 5 and SI 6). As expected, with low barriers to covalent bond formation from the MxOy−·H2O complex, keff(T) ≈ k1(T). Preequilibrium conditions were established between the separated reactants and the MxOy−·H2O complex (k′1 ≫ k2) when the barrier associated with k2 exceeded approximately one-third of the energy of MxOy−·H2O complex formation, which underscores the impact of the entropic drive. The negative barriers predicted for a range of barriers associated with k2 are included in the Supporting Information (SI 6). At the other limit, we assumed complete thermalization of the MxOy−·H2O complex (Tcomplex = Treactants) and plotted the resulting ln keff(T) for several different barriers assuming thermalization of the complexes (Supporting Information, SI 7). Plots of ln keff versus (RT)−1 resulted in curved lines over the experimental temperature range for low barriers associated with k2, with definitive anti-Arrhenius behavior only emerging when a significant barrier to covalent bond formation was invoked. While the entropies, heat capacities, and energies of species along the actual CexOy− + H2O reaction coordinate are not expected to be identical to values determined in our previous computational studies on transition metal oxides,13,14,16 the plots serve to show the range of negative barriers expected and 9967



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Ce2Oy− + D2O sequential oxidation reactions exhibited antiArrhenius temperature dependence, and the magnitude of the negative activation energies is consistent with exothermic but entropically unfavorable formation of electrostatic complexes, followed by low-barrier dissociative addition steps, similar to those calculated previously for transition-metal oxide cluster anion reactions with water.11,14 Activation energies determined for Ce3Oy− reactions with D2O were close to zero.

6H2O → 2Ce(OH)3 + 3H2). However, bulk cerium hydroxide decomposes in air to form CeO2. Bulk cerium hydrides also can form CeO2 in reactions with water.35,36 In our current study, deuteroxide formation is preceded by suboxide formation in reactions between metallic or highly reduced clusters with water, after which −OD groups add sequentially. However, the emergence of Ce2O4− and Ce3O6− from deuteroxide (or deuteride) precursors is evocative of the bulk properties, whether the −OD groups remain as deuteroxyls or rearrange to form deuteride groups. Of course, the reaction between bulk water and bulk metallic cerium is different from the gas-phase reactions because formation of molecular hydrogen does not immediately come into play in the gas-phase CexOx− + D2O → CexOx+1D− + D• reaction (−OD addition initiates when x = y). What the current results suggest, however, is that −OD abstraction from water without the molecular hydrogen formation is energetically viable, if not thermodynamically favored over oxide formation for certain clusters. The D−OD bond dissociation energy is 5.24 eV.37 While we were not able to find any literature values for the Ce− OH bond dissociation energy, the Ce−F bond dissociation energy is 6.45 eV; therefore, if the Ce−OH (and Ce−OD) bond energy is comparable, −OD abstraction is energetically viable. The average oxidation state of the Ce centers in CexOx− (x = y) clusters is 2 − (1/x), and addition of −OD to a Ce atom in CexOx− would result in the stable +3 oxidation state for that atom, with the anion’s excess electron localized on the more reduced centers.15 Interestingly, odd numbers of −H atoms attributed to hydroxyl groups formed by abstraction from water were observed in abundance in a previous study on cerium oxide cluster anions formed by ablation of CeO2.19 In that study, Aubriet et al. noted that, with the negative charge, the most abundant species featured Ce atoms with an average oxidation state of +4 for clusters with fewer than four Ce atoms. The clusters in our studies, in contrast, are produced by ablation of Ce metal, and average oxidation states of Ce atoms in the observed initial cluster distribution are ∼+1 or less. The point at which abstraction apparently becomes important is when at least one of the Ce centers can achieve a +3 oxidation state. By starting with different ablation targets, our combined studies underscore the stability of both the +3 and +4 oxidation states, a feature that figures heavily in the catalytic properties of cerium oxides.

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ASSOCIATED CONTENT

* Supporting Information S

Mass spectra of Ce4Oy− and Ce5Oy− series measured before and after introducing D2O into the reaction channel, series of mass spectra in the Ce2Oy− and Ce3Oy− cluster ranges measured over a range of D2O number densities in the reaction channel at 30, 50, 70, and 100 °C, linear fits and fitting parameters for ln k versus (RT)−1 plots, k1 through k3 and k5 through k8, and plots of ln keff versus (RT−1) using thermodynamic quantities from previous studies on similar systems. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 812-855-8300. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation CHE-1265991.

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REFERENCES

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5. CONCLUSIONS The temperature-dependent kinetics of the CexOy− (x = 2, 3; y < 2x) + D2O reactions have been measured and analyzed. CexOy− clusters have reaction rate constants that are approximately 1 order of magnitude lower than those of previously studied metal suboxide cluster anions.11,12 The sequences of CexOy− + D2O reactions were more complicated than those previously studied and included −OD abstraction and subsequent decomposition of D-containing clusters, resulting in CexO2x− stoichiometric cluster production. In addition, rate constants associated with the sequence of water reactions with the Ce2Oy− series increased at all temperatures with increasing y, in contrast with previous studies that found decreasing rate constants with increasing y. The increasing rate constants may be the result of increasing dipole−dipole interactions in the initial complexes formed between the cluster anions and water. 9968



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CexOyâ (x = 2â3) + D2O Reactions: Stoichiometric Cluster Formation

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