Rhodium Oxide Cluster Ions Studied by Thermal Desorption

Article pubs.acs.org/JPCA

Rhodium Oxide Cluster Ions Studied by Thermal Desorption Spectrometry Fumitaka Mafuné,* Masato Takenouchi, Ken Miyajima, and Satoshi Kudoh Department of Basic Science, School of Arts and Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153-8902, Japan S Supporting Information *

ABSTRACT: Gas-phase rhodium oxide clusters, RhnOm+, were investigated by measuring the rate constants of oxidation and thermal desorption spectrometry. RhnOm+ was suggested to be categorized into different states as m/n ≤ 1, 1 < m/n ≤ 1.5, and 1.5 < m/n in terms of energy and kinetics. For m/n ≤ 1, the O atoms readily adsorbed on the cluster with a large binding energy until RhO was formed. Under the O2-rich environment, oxidation proceeded until Rh2O3 was formed with a moderate binding energy. In addition, O2 molecules attached weakly to the cluster, and Rh2O3 formed RhnOm+ (1.5 < m/n). The energetics and geometries of Rh6Om+ (m = 6−12) were obtained using density functional theory calculations and were found to be consistent with the experimental results.

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INTRODUCTION Rh is an important element that is used as a catalyst to remove harmful gases including NO and thus has been applied in a number of ways, such as three-way catalytic converters in automobiles.1 Because the standard enthalpy of formation of NO is positive, the reduction of NO to form N2 and O2 is energetically favorable. Nevertheless, the energy barrier for the reaction is so high that the reduction hardly proceeds in the gas phase. Hence, NO is commonly reduced at a high temperature in the presence of a catalyst. The adsorption chemistry and mechanism of NO reduction on a Rh surface have been intensively investigated by many researchers.2−11 In the presence of CO, the Rh surface is initially covered with mainly N atoms (N(a)), which are generated by the reaction of NO and CO to give N(a) and CO2. A NO molecule then reacts with N(a) to form N2O, and the N2−O bond is cleaved on the surface to release N2.7−10 This reaction is known to be temperature-dependent. Below 350 K, the chemisorbed NO monomers do not react with N(a), whereas the NO dimers formed in the second layer react with N(a) to give N2O(g) and NO(a). Above 350 K, the reaction path changes, with N(a) reacting with NO(a) to give N2(g) and O(a).11 In the catalytic reaction cycle of NO and CO on Rh surfaces, CO molecules react with O(a) on the Rh surface and produce CO2.12 If CO is deficient, O atoms are believed to accumulate on the surface, deteriorating reactivity for the NO reduction. In other words, O poisons the catalyst. When the surface is exposed to O2 gas, O2 tends to adsorb on the surface and behave similarly to the O atoms from NO. Hence, in interactions between the Rh surface and the O atoms, how strongly the O atoms are bound to the surface will influence the mechanism of NO reduction on the Rh surface. © XXXX American Chemical Society

In general, on a metal surface, the adsorption of gaseous molecules proceeds sequentially through three steps, with the physisorbed state first leading to molecular chemisorption and then to dissociation.2 The Rh(111) surface includes a stable end-on-adsorbed molecular O2. However, because the energy barrier toward the O2 decomposition is rather low, the adsorbed O2 decomposes rapidly.13 A minor extent of O coverage of the surface enhances the ability to decompose molecular O2. However, at higher O coverage (θ = 0.25), the activation energy for decomposition increases nearly exponentially, most likely because of the electron-withdrawing effect of the O atoms. At even higher coverage (θ = 0.875), the decomposition reaction becomes endothermic. Thus, O coverage stagnates at moderate O coverage.13 Thus, clearly the nature of adsorption varies with the coverage. To understand the reaction of O at an atomic level, the use of a gas-phase cluster for this reaction is advantageous because the ratio of Rh and O atoms is well-defined.14−18 For gas-phase Rh cluster, Harding et al. calculated the geometrical structures of Rh6Om+ (m = 1−4).19 For the monoxide and dioxide clusters, the O atoms occupy μ2 sites, whereas for the trioxide and tetroxide clusters, μ3 sites are favored. In particular, Rh6O4+ takes the symmetric O4h structure as the lowest-energy isomer, in which O atoms occupy nonadjacent μ3 sites. When four atoms are involved, O adsorbs on Rh6+ not as a molecule but as atoms. This is consistent with the extended bulk surface, which exhibits a low-energy barrier for the decomposition of O2.19 Received: September 30, 2015 Revised: December 22, 2015

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DOI: 10.1021/acs.jpca.5b09531 J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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COMPUTATIONAL METHODS To estimate the binding energies of O2 on Rh6Om+, density functional theory (DFT) calculations were performed using the Gaussian09 program.25 The LANL2DZ effective core potential and basis set were used to describe the Rh atoms,26 while the 631G(d) basis set was used to describe the O atoms.27,28 Becke’s three-parameter hybrid density functional29 with the Lee− Yang−Parr correlation functional (B3LYP) was used for all calculations.30 For Rh6O2+ and Rh6O4+, structures with dissociatively adsorbed oxygen reported by Harding and coworkers were adopted as initial structures and reoptimized.19 For Rh6Om+ (m = 6, 8, 10, and 12), initial geometries, which were set essentially randomly, were optimized for all possible spin states. In addition, for Rh6O10+ and Rh6O12+, structures with 10 or 12 randomly placed O atoms to the octahedral Rh6+ structure reported by Torres and co-workers,31 and those with two or four O atoms randomly attached to the preoptimized Rh6O8+, respectively, were adopted as initial structures. For Rh6O12+, those with two O atoms or an O2 molecule randomly attached to the preoptimized Rh6O10+ were also employed. We adopted the optimized structures having the lowest energies as the most stable isomers for each cluster. The natural bond orbital (NBO) analyses32 were also performed to calculate the natural charge.

The following question thus arises: How do additional O atoms react with the Rh clusters? In the present study, we examine the reaction of O2 on Rhn+. This process involves the formation of rhodium oxide clusters, RhnOm+, in thermal equilibrium at 300 K. In addition, RhnOm+ was introduced to an extension tube with an elevated temperature of 300−1000 K, and we then investigated whether RhnOm+ released O2 by thermal desorption at higher temperatures.

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EXPERIMENTAL METHODS The reactivity and thermal stability of gas-phase rhodium oxide cluster ions RhnOm+ were investigated using mass spectrometry in combination with thermal desorption spectrometry, as shown in Figure 1.20−23 The RhnOm+ clusters were prepared

Figure 1. Schematic diagram of the experimental apparatus used in the present study.

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RESULTS AND DISCUSSION Formation of RhnOm+ Clusters. Figure 2 shows mass spectra of RhnOm+ prepared in the cluster source at different

using pulse laser ablation and a cluster source: A Rh-metal rod (99.95%) was vaporized using a focused second harmonic of a Nd:YAG pulsed laser at a typical pulse energy of 50 mJ with a repetition rate of 10 Hz. The cluster ions were formed in a gas flow of He containing O2 from a pulsed valve at a stagnation pressure of 0.8 MPa. The concentration of O2 in the He in the valve was finely tuned between 0−1% using mass flow and pressure controllers. In addition, the partial pressure of O2 inside the cluster source chamber was monitored using a residual gas analyzer. Nevertheless, it is quite difficult to directly measure a number density of O2 molecules in the beam. Hence, we also estimated the O2 number density by measuring the reaction rates of Nbn+ + O2 under experimental conditions for which the rate constants are known.24 The RhnOm+ clusters prepared were introduced into an extension tube (120 mm in length and 4 mm in inner diameter) before expansion in a vacuum chamber. The extension tube was heated to 300−1000 K using a resistive heater, and the temperature was monitored using thermocouples. The residence time of the cluster ions and the density of the He gas in the extension tube were estimated to be ∼100 μs and ∼1 × 1018 molecules cm−3, respectively. The thermal equilibrium of the clusters was therefore achieved through collisions with the He carrier gas before expansion into the vacuum. Temperature-dependent changes in the cluster ions were monitored using mass spectrometry. The cluster ions were accelerated by the pulsed electric field to gain a kinetic energy of 3.5 keV for mass analysis with a timeof-flight spectrometer. After passing through the 1 m field-free flight tube, the ions were detected using a Hamamatsu doublemicrochannel plate detector, and the signals were amplified with a preamplifier and digitized using an oscilloscope. The mass resolution (m/Δm) was sufficiently high (>1000 at m = 1000) to distinguish Rh and O atoms in the mass spectra.

Figure 2. (a) Mass spectrum of Rhn+ (n = 6−8) produced by the laser ablation of an Rh rod in He (0.8 MPa). (b−d) Mass spectra of Rh6Om+ (m = 0−10) produced by laser ablation of a Rh rod in the presence of O2 diluted by He (0.8 MPa) at 300 K. The concentrations of O2 in He in the pulsed valve were 0.01%, 0.1%, and 1% in panels (b), (c), and (d), respectively.

concentrations of O2 in He (0−1%). Rh cluster ions Rhn+ (n = 6, 7, and 8) have been observed to appear when no O2 gas is loaded. In this study, Rhn+ clusters with n = 4−11 were observed, but only selected ions are shown in the figure. Plots (b−d) show the mass spectra when O2 gas was added to the bath gas: The ion peaks corresponding to Rh6Om+ (m = 0−10) can be clearly seen. From these plots, the number of O atoms uptaken by Rh6+ was found to increase as the O2 concentration increased. For example, the intact Rh6+ completely disappeared in intensity at 0.01%, and O-adducts Rh6O4−6+ were formed instead. At 0.1%, Rh6O7−10+ are formed, and the cluster size distribution shifted toward O-rich Rh6O9,10+ at 1.0%. To examine the O2 concentration dependence of the ion intensities in depth, the concentration of O2 in the pulsed valve was varied finely in the range of 0−1.0% using mass flow B


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Figure 3. Ion intensities of Rh6Om+ and Rh8Om+ as a function of O2 concentration in the pulsed valve: (a) and (c) linear and (b) and (d) semilogarithmic plots for Rh6Om+ and Rh8Om+, respectively.

controllers. Figure 3 shows the ion intensities of Rh6Om+ (m = 0−10) and Rh8Om+ (m = 0−15) as a function of the O2 concentration. The semilogarithmic plot (b) shows that for Rh6Om+ (m ≤ 6), the clusters were likely to be formed in a stepwise manner at O2 concentrations below 0.1%: O2

O2

O2

Rh 6+ → Rh 6O2+ → Rh 6O4 + → Rh 6O6+

constants for O2 adsorption onto Rh8O8+ and Rh8O9+ (Rh8O8+ + O2 → Rh8O10+ and Rh8O9+ + O2 → Rh8O11+, respectively) are lower than those for Rh8Om+ (m ≥ 10), suggesting that the energy barriers for the formation of Rh8O10+ and Rh8O11+ are high. In reality, the oxidation of Rh8Om+ comprises two reaction steps: adsorption of O2 on the cluster and incorporation of oxygen atoms into the framework of the cluster. Apparently, the second step is considered to involve the reaction barrier (see Scheme 1). If the oxidation reaction proceeds under the

(1)

as evidenced by the alternating intensities. For Rh6Om+ (m ≥ 8), the clusters began to increase as the O2 concentration above 0.02%. Note that clusters comprising an odd number of O atoms also appeared and were dominant for larger m; the formation of these clusters cannot be explained by the simple inclusion of O2 molecules, as shown in eq 1. Instead, O2 molecules introduced from the pulsed valve likely adsorbed on the surface of the Rh rod, forming RhnO1+ upon laser ablation. The adsorption on the rod became more significant as the O2 concentration in the carrier gas increased, supporting this inference. Alternatively, one O atom could be released from Rh6Om+2+ when O2 reacts with RhnOm+. Such an abstraction mechanism, in which one O atom is bound to the surface while the other is released into vacuum, was observed on the surface of Al(111).33 However, this mechanism is energetically unfavorable. According to the DFT calculation, for example, the adsorption energy of O on Rh6O4+ (3.3 eV) is lower than the bond dissociation energy of O2 (5.1 eV). Other possibilities, including the fragmentation of RhO from Rh7Om+1+, could be explored. However, no clear evidence of a decrease in Rh7Om+1+ was observed as Rh6Om+ increased. A similar O2 concentration dependence was observed for other clusters (see Figure S1). For example, Figure 3c and d shows the intensities of Rh8Om+ (m = 0−15) as a function of O2 concentration. For Rh8Om+ (m ≤ 8), the clusters were formed gradually below 0.1%, whereas for Rh8Om+ (m ≥ 9), the clusters begin to increase as the O2 concentration was increased above 0.02% without the formation of abundant Rh8O10,11+. Such concentration dependence should be observed if the rate

Scheme 1

adiabatic condition, the cluster could overcome the reaction barrier readily, as the excess energy generated upon adsorption of the O2 molecule is conserved. In contrast, in the present experimental setup, the reaction proceeds in the presence of He gas. As the collision frequency of He gas to the cluster is 2 × 108 s−1, the excess energy is likely to be dissipated by the collision of He gas in a thermal equilibrium with the reaction cell. Hence, the cluster needs to overcome the reaction barrier. Here, we estimated the absolute rate constants for the oxidation reaction RhnOm+ + O2 → RhnOm+2+ from the concentration dependence of O2. Figure 4 shows the rate constants with respect to the atomic ratio, m/n. All the Rh C


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changes in the intensities indicate that O2 molecules were sequentially released from the cluster by heating as Rh 6Om+ → Rh 6Om − 2+ + O2 → Rh 6Om − 4 + + 2O2 → ··· (2)

The intensity changes observed with Rh8Om+ are essentially the same as those observed with Rh6Om+. The unidentified Rh8O10,11+ in Figure 3c and d were actually observed in the temperature range of 600−900 K, suggesting that these species are thermodynamically stable in the gas phase. Thus, Rh8O10,11+ did not appear in the course of sequential O2 reaction because the formation was kinetically controlled. From the thermal desorption plots, we estimated a threshold energy, Em, of O2 release (2) for each RhnOm+ cluster based on the Arrhenius equation

Figure 4. Rate constants of O2-adsorption reactions (RhnOm+ + O2 → RhnOm+2+) plotted with respect to m/n.

clusters exhibit similar trends regardless of the number of Rh atoms n: The rate constants range from 1 × 10−10 to 1 × 10−11 cm3 s−1 for small m/n and suddenly decrease as m/n approaches 1. In addition, the values of the rate constant become scattered as m/n is increased further. Thermal Desorption Spectrometry. To elucidate the stability of the clusters, the thermal responses of the Rh6Om+ and Rh8Om+ clusters were investigated. Figure 5 shows thermal

⎛ E ⎞ km(T ) = A mexp⎜ − m ⎟ ⎝ kBT ⎠

(3)

where km, Am, Em, kB, and T are the rate constant, the preexponential factor of the Arrhenius equation, the threshold energy of unimolecular O2 release (Rh6Om+ → Rh6Om−2+ + O2), the Boltzmann constant, and the temperature, respectively. In the sequential O2 release reactions, the intensity of Rh6Om+ was determined according to the balance between the increase resulting from O2 release from Rh6Om+2+ and the decrease resulting from O2 release in the formation of Rh6Om−2+ within the predetermined probing time, which was the same as the residence time of the clusters in the extension tube (100 μs). Because each rate constant km increased differently as the temperature increased depending on Em, the intensities of the clusters changed with the temperature, as shown in Figure 5 (see Appendix for a detailed explanation). The threshold energies were estimated numerically using a homemade program. The estimated threshold energy of O2 release from Rh6Om+ (m = 7−11) is ∼0.2−1.4 eV, as shown in Figure 6. The

Figure 5. Thermal desorption plots for RhnOm+ (n = 6 and 8): Rh6Om+ (m ≥ 8) and Rh8Om+ (m ≥ 12) were prepared at 300 K in the cluster source and then introduced into the extension tube, which was heated at 300−1000 K.

Figure 6. Threshold energy of O2 release from Rh6Om+ (m = 7−11) estimated from thermal desorption spectrometry. Threshold energy for each m obtained by experiment (●) and calculation (△). Experimental uncertainty ≈ 0.3 eV.

desorption plots for RhnOm+ (n = 6 and 8): Rh6Om+ (m ≥ 8) and Rh8Om+ (m ≥ 12) prepared at 300 K in the cluster source were introduced into the extension tube, which was heated to 300−1000 K. The intensities of the clusters remaining after passing through the tube were measured by mass spectrometry. Rh6Om+ (m ≥ 10) was found to rapidly dissociate below 600 K, thereby increasing the amounts of Rh6O8+ and Rh6O9+. Then, Rh6O9+ decayed at 800 K, forming Rh6O7+. In addition, Rh6O8+ decayed at 800 K, increasing Rh6O6+. These concomitant

uncertainty in the threshold energy is ∼0.3 eV for each m. The energies of Rh6Om+ (m = 7, 8, and 9) are higher than those of other species, suggesting that the O atoms are strongly bound to the cluster. In contrast, the energies of Rh6Om+ (m = 10 and 11) are below 0.5 eV. Figure 6 also shows the dissociation energies, the difference between the formation energies of Rh6Om+ and Rh6Om−2+ plus O2, which were obtained by the DFT calculations for different m. The values agree well with the D


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The Journal of Physical Chemistry A threshold energy obtained in the present study. If transition states that form higher activation barriers than the O2 dissociation limit exist in the reaction pathway, the threshold energy should be given by the energy barrier. The good agreement between the results indicates that transition states are not significantly higher in energy than the O2 dissociation limit. The energy balance is summarized in Scheme 1. Note that existence of the reaction barrier for the incorporation of the oxygen atoms is suggested by the O2 concentration dependence. Figure 7 shows the threshold energies for all RhnOm+ (n = 5− 10) estimated using thermal desorption spectrometry. When

Figure 8. Geometrical structures of Rh6Om+ (m = 6, 8, 10, and 12) obtained by DFT calculations.

Rh6O6+ and Rh6O8+ binds to two or three O atoms, respectively, supporting this inference. In contrast, O-rich Rh6O10+ possesses an O atom bound to their terminal μ1 sites. In addition, one O2 molecule was weakly bound to the cluster in Rh6O12+. Thus, Rh6+ is able to include approximately eight O atoms in the rhodium oxide framework as bridge O atoms, whereas the excess O atoms are bound to the clusters as the terminal O atom and the O2 molecule. The DFT calculation results are consistent with the thermal desorption spectrometry, suggesting that Rh clusters are oxidized until m/n = 1.5 is formed and that the excess O atoms are able to attach weakly to the cluster as O2, resulting in RhnOm+ (m/n > 1.5). Average values of natural charge of Rh and O atoms obtained by NBO analysis are shown in Table 1 for Rh6Om+ (m = 2, 4, 6,

Figure 7. Threshold energy of O2 release from RhnOm+ (n = 5−10) estimated from thermal desorption spectrometry and plotted with respect to m/n.

plotted with respect to the atomic ratio m/n, the threshold energies were found to exhibit similar trends, regardless of the number of Rh atoms n: For m/n = 1, the threshold energies were higher than for other values and exceeded 2 eV. The energies of RhnOm+ (1 < m/n ≤ 1.5) were distributed between 1−2 eV and were reduced to ≤0.5 eV for RhnOm+ (1.5< m/n). The low threshold energy for RhnOm+ (1.5< m/n) suggests that O atoms were weakly bound. Thus, Rh clusters were oxidized until RhnOm+ (m/n = 1.5) were formed with a composition of Rh2O3. Structure of Rh6Om+. The rate constants of oxidation and the threshold energies of desorption suggest that rhodium oxide clusters can be categorized into three states: m/n ≤ 1, 1 < m/n ≤ 1.5, and 1.5 < m/n. For m/n ≤ 1, the O atoms readily are involved in the cluster with a large binding energy. In contrast, for 1.5 < m/n, the O atoms adsorb weakly on the cluster and exhibit limited reaction probabilities. The clusters with 1 < m/n ≤ 1.5 exhibit moderate oxidation and desorption between those of the other two categories. To elucidate the natures of the different states, the geometrical structures of Rh 6 O m + (m = 6−12) were investigated based on the calculations by Harding et al. for Rh6Om+ (m = 2 and 4) and on the DFT calculation in the present study for Rh6Om+ (m = 6−12; see Figure 8). The O atoms in Rh6O6+ and Rh6O8+ dominantly occupy bridge μ2 sites, and one O atom locates a hollow μ3 site in Rh6O6+ and Rh6O8+. By virtue of the μ2 oxide bridges, the Rh−Rh distance in Rh6O6+ increases by 7.4% and 5.2% with respect to pure Rh6+ and solid Rh, respectively. As the structural isomer of Rh6O8+ with slightly higher formation energy (0.6 eV) also involves one O atom in the μ3 site, the μ3 site is considered to be characteristic to Rh6O6+ and Rh6O8+. It is highly likely that RhnOm+ (m/n = 1) corresponds to RhO, which comprises a Rh(+II) atom and an O(−II) atom. Evidently, each Rh atom in

Table 1. Average Values of Natural Charges of Rh and O Atoms in Rh6Om+ Clusters (m = 2, 4, ..., 12) Obtained by Natural Bond Order Analysis Rh6O2+ Rh6O4+ Rh6O6+ Rh6O8+ Rh6O10+ Rh6O12+

Rh atom

O atom

0.33 0.59 0.67 0.87 1.00 0.98

−0.50 −0.63 −0.51 −0.53 −0.50 −0.41

8, 10, and 12). The natural charge of the O atom is almost the same, ranging from −0.50 to −0.53 for Rh6Om+ with the exception that the charges are −0.63 and −0.41 for Rh6O4+ and Rh6O12+, respectively: Exceptionally high negative value of Rh6O4+ is considered due to the highly symmetrical and stable structure.19 In contrast, the natural charges of the Rh atom increase with an increase in m (2 ≤ m ≤ 10), suggesting that the Rh atoms become more positively charged with m. For Rh6O12+, the average value of the natural charge of the Rh atoms is similar to that of Rh6O10+, because two O atoms out of 12 atoms form an O2 molecule attaching weakly to Rh6O10+: The natural charges of the oxygen atoms are −0.016 and +0.15. In the presence of O2, Rh clusters tend to be oxidized, forming RhO. The oxide clusters are further oxidized to Rh2O3 in O2-rich environments. However, the transition from RhO to Rh2O3 accompanies structural changes, as exemplified in the geometries of Rh6O6+ and Rh6O8+; thus, the formation of Rh2O3 has a high energy barrier. The decrease in the rate constants at m/n = 1 in Figure 4 is considered to correspond to this energy barrier. E


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⎛ E ⎞ k = A × exp⎜ − ⎟ ⎝ kBT ⎠

CONCLUSIONS The reactivity and thermal stability of gas-phase rhodium oxide cluster ions RhnOm+ were investigated using mass spectrometry combined with thermal desorption spectrometry. In the presence of O2, gas-phase Rh clusters Rhn+ were found to be oxidized into RhnOm+ by uptaking O2 molecules in a stepwise manner, as in eq 1. The rate constants of the oxidization reactions clearly decreased at m/n = 1, regardless of the size n. The thermal desorption spectrometry revealed a threshold energy for O2 desorption from RhnOm+, indicating that the energy changed with m/n regardless of n: For m/n = 1, the threshold energies were higher than for other values and exceeded 2 eV. The energies of RhnOm+ (1 < m/n ≤ 1.5) were 1−2 eV and were reduced to ≤0.5 eV for RhnOm+ (1.5 < m/n). Thus, the rate constant and threshold energy for desorption were found to be related to m/n, that is, to the cluster composition. To understand the geometrical structure of the oxide clusters, the formation energy and connectivity of Rh6Om+ (m = 6−12) were investigated using DFT calculations. The O atoms in Rh6O6+ and Rh6O8+ dominantly occupied bridge μ2 sites, whereas O-rich Rh6O10+ possessed an O atom bound to their terminal μ1 sites. In addition, one O2 molecule was weakly bound to the cluster in Rh6O12+. Thus, Rh6+ is able to include approximately eight O atoms in the rhodium oxide framework as bridging O atoms, whereas the excess O atoms are bound to the clusters as terminal O and weakly bound O2. In addition, each Rh atom in Rh6O6+ and Rh6O8+ binds to two or three O atoms, respectively, suggesting that Rh6O6+ consists of RhO, which comprises a Rh(+II) atom and an O(−II) atom. In contrast, Rh6O8+ is closer to Rh6O9+, namely, Rh2O3 as a stoichiometry, which is considered to comprise Rh(+III) atoms and O(−II) atoms. The natural charges of the clusters obtained by the NBO analysis are consistent with the inference. In summary, for m/n ≤ 1, the O atoms readily adsorbed on the cluster with large binding energies until RhO was formed. Under O2-rich environments, oxidation proceeded until Rh2O3 was formed with a moderate binding energy. In addition, O2 molecules attached weakly to the clusters of Rh2O3 forming RhnOm+ (1.5 < m/n).

where A is the pre-exponential factor, E is the threshold energy for the reaction, and kB is the Boltzmann constant. Hence, the intensity of X after heating, [X], is given by ⎛ ⎛ E ⎞⎞ [X] = [X]0 exp⎜⎜ −Atr exp⎜ − ⎟⎟⎟ ⎝ kBT ⎠⎠ ⎝

Figure A1. Intensities of clusters, X and Y, relative to the temperature by setting A = 1 × 1012 s−1 and E = 1.0 eV as typical values.

decreases with the temperature, [Y] increases by the same magnitude. The fitting of this model eq 8 to the experimentally observed intensity ratio would yield values of A and E. Second, for a two-step reaction (9)

X→Y→Z

the intensities of X and Y change with the reaction time as

APPENDIX In thermal desorption spectrometry, clusters are heated by collision with He atoms that are in good thermal equilibrium with the tube surface at elevated temperatures as they pass through the extension tube. 34 Hence, they begin to unimolecularly dissociate as they move within the tube. Let us first consider a single reaction step as

[X] = [X]0 exp(−kt )

(10)

⎛ k1 ⎞ [Y] = [X]0 ⎜ ⎟(exp(−k1t ) − exp(−k 2t )) ⎝ k 2 − k1 ⎠

(11)

The rate constants for the first and second steps, k1 and k2, depend differently on temperature because both the preexponential factor Ai (i = 1, 2) and the threshold energy Ei (i = 1, 2) determine the rate constants. Hence, the intensity of Y changes with T as ⎛ −E A1 × exp k T1 ⎜ B [Y ] = [X ]0 ⎜ ⎜ A 2 × exp −E2 − A1 × exp kBT ⎝

( )

( )

(5)

( ) −E1 kBT

⎞ ⎛ ⎛ ⎛ ⎛ − E ⎞⎞ ⎛ − E ⎞⎞⎞⎟ × ⎜⎜exp⎜⎜− A1tr × exp⎜ 1 ⎟⎟⎟ − exp⎜⎜− A 2tr × exp⎜ 2 ⎟⎟⎟⎟⎟⎟ ⎝ kBT ⎠⎠ ⎝ kBT ⎠⎠⎠⎟ ⎝ ⎝ ⎝ ⎠

The intensity of X decreases with the reaction time t as [X] = [X]0 exp(−kt )

(8)

Figure A1 depicts [X] and [Y] relative to the temperature by setting A = 1 × 1012 s−1 and E = 1.0 eV as typical values. As [X]

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X→Y

(7)

(6)

(12)

where square brackets designate the intensity of the indicated species, a subscripted 0 indicates the initial state, and k is the rate constant of the unimolecular reaction. For example, X and Y correspond to the Rh6O10+ and Rh6O8+, respectively, in the text body. In the present study, the reaction time tr was predetermined and was equal to the residence time of the ions in the tube (100 μs). In addition, the rate constant is a function of temperature T as

Figure A2 depicts the intensity changes of X, Y, and Z with the temperature by setting A1 = A2 = 1 × 1012 s−1, E1 = 0.7 eV, and E2 = 1.2 eV. The alternating intensities as the temperature increase indicate that X changes unimolecularly into Y and then into Z. The relationship between the reactant and the product in a stepwise reaction can be more clearly understood when the F


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Science, and Technology of Japan (MEXT) and by the Genesis Research Institute, Inc (cluster research).

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Figure A2. Intensity changes of clusters, X, Y, and Z, with the temperature by setting A1 = A2 = 1 × 1012 s−1, E1 = 0.7 eV, and E2 = 1.2 eV.

intensity changes are displayed differentially. Figure A3 shows the intensities of X, Y, and Z differentiated by T. A product

Figure A3. Intensities of X, Y, and Z differentiated by T by setting A1 = A2 = 1 × 1012 s−1, E1 = 0.7 eV, and E2 = 1.2 eV.

peak appears on the positive side at the identical temperature as the corresponding reactant peak on the negative side. Thus, the differential form allows the identification of the reactant and product pair, which is especially useful for easily interpreting complicated real reactions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b09531. Ion intensities of RhnOm+ (n = 4, 5, 7, 9, and 10) as a function of oxygen concentration in the pulsed valve; results of temperature desorption spectrometry for RhnOm+ (n = 4, 5, 7, 9, and 10); stable structures of Rh6Om+ optimized by the DFT calculation; tabulated spin multiplicities and atomic coordinates. (PDF)

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REFERENCES

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work is supported by Grants-in-Aid for Scientific Research (A) (No. 25248004) and Exploratory Research (No. 26620002) from the Ministry of Education, Culture, Sports, G


Article

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Rhodium Oxide Cluster Ions Studied by Thermal Desorption

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