Role of Transient Co-Subcarbonyls in Ostwald ... - ACS Publications

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Role of Transient Co-Subcarbonyls in Ostwald Ripening Sintering of Cobalt Supported on γ‑Alumina Surfaces Werner Janse van Rensburg,†,§ Pieter van Helden,*,† Denzil J. Moodley,† Michael Claeys,‡ Melissa A. Petersen,†,‡ and Eric van Steen*,‡ †

Sasol, Group Technology, 1 Klasie Havenga Road, Sasolburg 1947, South Africa Center for Catalysis Research, Department of Chemical Engineering, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa

‡

S Supporting Information *

ABSTRACT: The stability and mobility of atomic cobalt and of cobalt subcarbonyl species on γ-Al2O3 surfaces have been investigated using density functional theory (DFT) with a view to elucidate possible mobile species on these surfaces, which can act as agents in the Ostwald ripening process. The two most stable alumina surfaces γ-Al2O3(100) and γ-Al2O3(110) were probed at different levels of hydration. The stability of cobalt subcarbonyl species on γ-Al2O3(100) at high partial pressure of CO (10 bar) increases with increasing number of CO ligands attached to the central cobalt atom up to Co(CO)3 but exhibits a more complex behavior on γ-Al2O3(110). The effect of the hydration level on the stability of cobalt subcarbonyls was investigated. The interpretation of the DFT results in a thermodynamic model shows that at equilibrium the main cobalt subcarbonyl species present on the alumina surface at ca. 500K in the presence of CO are Co(CO)3 and Co(CO)4, with Co(CO)3 being the dominant species on dry γ-Al2O3(100) and wet γ-Al2O3(110). The fractional coverage of these species on a wetted alumina surface is lower than that on a dry alumina surface. The mobility of surface species was probed by exploring the potential energy surface of the adsorbed species on γ-Al2O3(100) and γ-Al2O3(110) at different hydration levels (ΘOH = 8.5 and 17.7 OH/nm2, respectively). Cobalt subcarbonyl species have a high mobility with activation barriers as low as 0.5 eV. It is argued that these species may contribute to the sintering process.

1. INTRODUCTION Heterogeneous catalysts are the workhorses of the chemical industry enabling a wide variety of chemical transformations. In the ideal case, heterogeneous catalysts are unaltered by the chemical process; however, in reality, the activity of these materials decreases with time online due to a variety of different processes,1,2 some of which originate from operating the catalyst under industrial conditions (such as poisoning), but most of them are inherently linked to the catalytic transformation (such as coking and sintering).3 The typical heterogeneous catalyst is composed of nanosized crystallites of the catalytically active phase to maximize the utilization of the catalytically active material. However, these crystallites will sinter in a thermodynamically inevitable process. Hence, kinetic barriers are needed to minimize this process. This can, for instance, be achieved by anchoring nanocrystallites on a support, which will increase not only their mechanical stability but also their thermal stability (i.e., their resistance against sintering).4 Sintering has historically been regarded as a high-temperature process,1,2 in which particles grow due to particle migration and coalescence or cluster migration.5 Particle © XXXX American Chemical Society

mobility is known to be affected by not only reaction temperature6,7 but also particle diameter.8 Harris8 argued that platinum particles with a diameter 550 K, while the complete dehydration of the (110) surface is predicted to require temperatures in excess of 1100 K. The calculated surface energy of the (110) surface at T = 500 K and PH2O = 4 bar is 0.780 J/nm2 compared with 0.937 J/m2 for the (100) surface under the same conditions, effectively mirroring the experimentally observed relative surface exposure trend.45,46 On the basis of these analyses, a selection of four representative surface models was made for the current study, as illustrated in Figure 2. This includes hydrated (100) at ΘOH = 8.5 OH/nm2 (termed as “Wet” (100)), hydrated (110) at ΘOH = 17.7 OH/nm2 (termed as “Wet” (110)), and two additional (100) surface models at lower levels of hydration: dehydrated (100) at ΘOH = 0.0 OH/nm2 (termed “Dry” (100)) and intermediate hydrated (100) at ΘOH = 2.1 OH/nm2 (termed “Int” (100)). For the (100) surface models 2 × 1 surface unit cell representations were used, corresponding to dimensions of a = 11.160 Å and b = 8.403 Å, while for the (110) surface a 1 × 1 surface unit cell of dimensions a = 8.403 Å and b = 8.071 Å was used. The (100) surfaces were modeled as four-layer slabs, corresponding to a thickness of ∼6.7 Å, of which the atoms situated in the bottom 2.3 Å (i.e., bottom two layers) of the slab were kept fixed to the corresponding bulk positions. The (110) surface was modeled as an eight layer slab of ∼10.2 Å thickness by keeping the bottom 5.0 Å (i.e., bottom four layers) of the slab fixed to corresponding bulk positions. A 14 Å vacuum spacing between surface slabs was used for all slab calculations. The determination of the lowest energy structures for adsorbed Co(CO)x and Co2(CO)x species on the γ-Al2O3(100) and (110) surfaces required the exploration of both the adsorption sites in the respective unit cells and the mode of coordination of the adsorbed species. Under these calculations, the adsorbed complex, adsorbed water and the top layers of the alumina surface (see Figure 2), were relaxed. A number of representative starting geometries were considered for each of the 20 optimized geometries reported here (i.e., for four Co(CO)x species on three γ-Al2O3-(110) surfaces and one γAl2O3-(110) surface as well as optimization of four different dimeric Co2(CO)x species on a single γ-Al2O3-(100) surface). The actual number of starting geometries in each case differed depending on the complexity and variety of potential adsorption sites and modes, with, for example 27 starting geometries being probed for the adsorption of CoCO on “Wet” (100), 28 different starting geometries for Co(CO)2 on “Dry” (100), and even as many as 57 starting structures for the dimeric Co2(CO)4 on “Wet” (100). In some cases a lower

number of starting structures were thought to be required to probe the potential energy surface, viz. only 12 starting geometries were considered for the adsorption of Co(CO)3 on “Dry” (100) and 15 starting structures for the adsorption of Co(CO)3 on “Wet” (100). It is believed that the potential energy surfaces (PESs) were appropriately probed in all cases given the balance between computational demand and accuracy of results that was required in the current study. The potential energy surfaces (PESs) for the adsorption of Co(CO)x on the various species were further explored for the diffusion studies described, where 48 and 36 structures were, respectively, considered for each of the considered subcarbonyl species on evenly spaced grids on the γ-Al2O3-(100) and (110) surfaces. In all cases, the energy profiles determined for the diffusion studies confirmed the lowest energy adsorption structures. 2.4. Energies. In the current paper two sets of energies are reported. The adsorption energy of cobalt subcarbonyl (Eads) at 0 K (excluding zero-point energy corrections) is defined as follows for monomeric, Co(CO)x (x = 0−4) species Eads = ECo(CO)x‐Surf − ECo(CO)x − ESurf

(Monomer)

(1)

and dimeric, Co2(CO)y (y = 0, 2, 4, 6, 8) species, respectively Eads = [ECo2(CO)y‐Surf − 2ECo(CO)1/2y − ESurf ]/2

(Dimer) (2)

where ECo(CO)x‑Surf is the total energy of adsorbed Co(CO)x on an alumina surface with particular hydration level at 0 K, ECo(CO)x is the total energy of gas-phase Co(CO)x at 0 K, ESurf is the total energy of the clean alumina surface with a particular hydration level at 0 K, ECo2(CO)y‑Surf is the total energy of adsorbed Co2(CO)y (y = 0, 2, 4, 6, 8) on an alumina surface with a particular hydration level at 0 K, and ECo(CO)1/2y is the total energy of gas-phase Co(CO)1/2y at 0 K. (Strictly speaking, the change in energy upon adsorption and formation of the dimeric cobalt subcarbonyl represents an adsorption of a monomeric cobalt subcarbonyl species followed by its dimerization.) The Gibbs free energies of formation (ΔGf) of monomeric, Co(CO)x (x = 0−4), and dimeric, Co2(CO)y (y = 0, 2, 4, 6, 8), Co-subcarbonyls on the γ-alumina surfaces are similarly defined as ΔGf = GCo(CO)x‐Surf − GCo(bulk) − x·GCO(g) − GSurf

(Monomer)

(3) ΔGf = [GCo2(CO)y‐Surf − 2·GCo(bulk) − y·GCO(g) − GSurf ]/2

(Dimer)

(4)

where GCo(CO)x‑Surf is the Gibbs free energy of adsorbed Co(CO)x (x = 0−4) on an alumina surface with particular hydration level, GCo(bulk) is the Gibbs free energy of a single Co atom in bulk face-centered cubic (fcc) Co metal, GCO(g) is the Gibbs free energy of CO in the gas phase, GSurf is the Gibbs free energy of the subcarbonyl-free alumina surface with a particular hydration level, and GCo2(CO)y‑Surf is the Gibbs free energy of adsorbed Co2(CO)y (y = 0, 2, 4, 6, 8) on an alumina surface with a particular hydration level. (Further details are given in the Supporting Information.)

3. RESULTS 3.1. Co-Subcarbonyl Species on γ-Al2O3 Surfaces. In the current study the interaction of neutral monomeric and D

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Figure 3. Most stable, DFT-optimized structures for Co(CO)x (x = 0−4) formation on “Dry” γ-alumina (100) and “Wet” γ-alumina (100), that is, at ΘOH = 0.0 and 8.5 OH/nm2, respectively, along with calculated adsorption energies, Eads, at 0 K.

energies of formation of cobalt subcarbonyl, ΔGf, are determined and reported. 3.1.1. Co(CO)x (x = 0−4) on γ-Al2O3(100). A systematic DFT analysis of adsorption positions and adsorption modes for neutral monomeric Co-subcarbonyl interaction with “Dry” (100), “Int”(100), and “Wet”(100) γ-Al2O3 surfaces, corresponding to respective hydration levels of ΘOH = 0.0, 2.1, and 8.5 OH/nm2 probing different adsorption positions on the surface and orientations of the cobalt subcarbonyl species, resulted in the identification of the lowest energy structures in each case. It was found that the preferred adsorption positions for Co(CO)x (x = 0−4) on the “Int” (100) surface did not involve a direct interaction with the OH functionality on the surface effectively yielding structures that are equivalent in terms of adsorption positions and adsorption modes compared with the “Dry” (100) surface. The only exception is Co(CO)4, where the structure is equivalent to adsorption on “Wet” (100). (See the Supporting Information for further details.) Therefore, only the optimized structures for Co(CO)x (x = 0−4) adsorbed on the “Dry” and “Wet” (100) surfaces are illustrated in Figure 3. The most preferred adsorption position for atomic cobalt on the “Dry” (100) surface is to adopt a three-fold coordination mode involving two surface O atoms and one surface Al, effectively resulting in the cobalt atom being contracted into the surface. The preferred adsorption site of atomic cobalt on γ-

dimeric Co-subcarbonyl species, including Co and Co2, with the respective alumina surface models is considered. The precedence of neutral monomeric Co-subcarbonyls in the form Co(CO)x (x = 1−4) is well established, evident from the reported53−57 production of Co(CO)4 from both the pyrolysis of Co2(CO)8 and the photolysis of Co(CO)3(NO). The formation of Co(CO)x (x = 1−4) from thermal reactions of atomic cobalt with CO molecules has been characterized by matrix IR and ESR spectroscopy57,58 and also previously studied with DFT.38−40 The experimental59−61 and theoretical40,41 characterization of Co2(CO)8 is known, but DFT studies of Co2(CO)y (y = 1−7) are limited to Co2(CO)7 to the best of our knowledge.40 A DFT study of Co(CO)x (x = 1−4) and Co2(CO)y (y = 2, 4, 6, 8) interacting with γ-Al2O3 surfaces has, to the best of our knowledge, not been previously reported, although some DFT studies focusing on the interaction of atomic cobalt and cobalt clusters on model γ-Al2O3 surfaces are known.62−65 Furthermore, a DFT study of the interaction of Co(CO)3 and Co(CO)4 with cluster SiO2 surface models has been reported.66 In the remainder of this section the DFToptimized geometries for Co(CO)x (x = 0−4) interacting with “Dry” (100), “Int”(100), “Wet”(100), and “Wet”(110) γ-Al2O3 surface models, as well as Co2(CO)y (y = 0, 2, 4, 6, 8) interacting with the “Wet”(100) γ-alumina surface, will be presented. From these structures the corresponding free E

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Figure 4. Most stable DFT-optimized structures for Co(CO)x (x = 0−4) formation on “Wet” γ-Alumina (110), that is, at ΘOH = 17.7 OH/nm2, along with calculated adsorption energies, Eads, at 0 K.

interaction on “Wet” and “Dry” (100) γ-alumina surfaces is different. Further below, it is explored whether this is reflected in the relative formation free energies and the diffusion characteristics of the subcarbonyls on the two surfaces. 3.1.2. Co(CO)x (x = 0−4) on γ-Al2O3(110). Figure 4 illustrates the most favorable DFT-optimized geometries for the interaction of Co(CO)x (x = 0−4) with the “Wet” (110) γAlumina surface (ΘOH = 17.7 OH/nm2). The relatively high hydration level on this surface results in six surface H2O molecules per (110) surface unit cell, effectively representing a uniform hydration of the surface in which surface O and Al from γ-Al2O3 are not readily available for direct interaction with adsorbate species. This contrasts with the “Wet” (100) surface (ΘOH = 8.5 OH/nm2; four surface H2O molecules per unit cell) in which significant exposure of surface O and Al atoms of γAlumina is found, effectively representing well-defined “dehydrated” regions on the surface. Consequently, the interaction of all Co(CO)x (x = 0−3) species with “Wet” (110) is found to involve intimate interaction with surface hydroxyl groups. The most favorable adsorption of atomic cobalt is found to result in a four-coordinated complex on the surface, involving coordination to oxygen in the alumina surface, oxygen in two surface hydroxyls, and a hydrogen atom. The adsorption site for atomic cobalt on “Wet” γ-Al2O3(110) is similar to the adsorption site reported for atomic Pt on hydrated γ-Al2O3(110),67 with differences possibly attributable to differences in the degree of hydration. The coordination modes of Co(CO)x (x = 1−3) are all similar, involving monodentate coordination of cobalt to oxygen of a surface hydroxyl. A relatively weak adsorption of Co(CO)4 presumably via long-range H interactions with oxygen in a carbonyl ligand is obtained, similar to the adsorption of Co(CO)4 on “Wet” (100). A comparison of the calculated adsorption energies (Eads) for each Co(CO)x (x = 0−4) on the “Wet” (110) and “Wet” (100) surfaces shows no clear preference for Co-subcarbonyl adsorption for either of the two hydrated surfaces. Adsorption of, in particular, Co and Co(CO)3, but also Co(CO)2, is stronger on the “Wet” (110) surface with the adsorption energy on the “Wet” surface being more negative by ca. 0.4 to 0.5 eV. On the contrary, the adsorption of Co(CO) and Co(CO)4 is

Al2 O3(100) bears strong resemblance to the reported adsorption site of atomic Pt67 and atomic Pd68 on this surface. This preferred three-fold adsorption position for cobalt is retained for Co(CO)1 and Co(CO)2. However, it is evident from the geometries of Co(CO)1 and Co(CO)2 that atomic cobalt is slightly extracted from the alumina surface compared with adsorbed atomic cobalt, pointing toward stabilization of the central cobalt atom by CO ligands. This stabilization of cobalt is also reflected in the systematic decrease in the magnitude of the adsorption energy (Eads) for all Co(CO)x (x = 0−4) upon increasing the number of CO-ligands on the central cobalt atom. This results in adsorbed Co(CO)3 being two-fold bridged over surface Al−O, while Co(CO)4 is only weakly adsorbed with no apparent direct covalent bonds of the central cobalt atom to the atoms of the “Dry” (100) γ-alumina surface. Interaction of Co(CO)x (x = 0−4) with the “Wet” (100) surface shows preferred three-fold atomic cobalt adsorption on to surface alumina atoms, similar to the corresponding structure on “Dry” (100). However, the adsorption of Co(CO) results in the transfer of one surface H2O for exclusive coordination to cobalt in the most favored structure while still retaining the three-fold coordination of the cobalt atom to the alumina surface. For Co(CO)2 no formal covalent coordination of Co to surface alumina atoms is found; instead, coordination proceeds via interaction of cobalt with the oxygen of a surface hydroxyl. Similarly, monodentate Co(CO)3 coordination proceeds by bonding of the central cobalt atom to the oxygen in surface hydroxyl. The most favorable coordination of Co(CO)4 seems to involve weak hydrogen-bonding interaction between oxygen in the carbonyl ligands and surface hydroxyl groups. The strength of adsorption of Co(CO)x (x = 0−4) on the “Wet” (100) surface becomes weaker with increasing number of CO ligands, as was observed on “Dry” (100). However, the bonding on “Wet” (100) surface for Co(CO)x (x = 0−3) is consistently weaker by ca. ∼ 0.52 ± 0.05 eV compared with the bonding on “Dry” (100) surface. In contrast, the adsorption of Co(CO)4 is more favorable on “Wet” (100), where the opportunity for H bonding becomes the determining stabilizing factor when direct coordination via the Co-subcarbonyl Co atom does not occur. It is clear from an overall comparison of the geometries in Figure 3 that the nature of Co-subcarbonyl F

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Figure 5. Most stable DFT-optimized structures for Co2(CO)y (y = 0, 2, 4, 6, 8) formation on “Wet” γ-Alumina (100), that is, at ΘOH = 8.5 OH/ nm2, along with calculated adsorption energies, Eads, at 0 K in eV/Co.

Figure 6. DFT-calculated formation free energies (ΔGf) in eV for Co(CO)x (x = 0−4) in the gas phase and adsorbed on “Dry” (100), “Int” (100), “Wet” (100), and “Wet” (110) γ-Alumina surfaces at T = 503.15 K and (a) PCO = 1 bar and (b) PCO = 10 bar (horizontal dashed lines labeled with Nc depict the energy of a single Co atom (in eV) contained in different coordination numbers in a fcc Co lattice structure, which can be considered as alternative reference states; colored dashed lines are a guide to the eye).

stronger on the “Wet” (100) surface. This emphasizes the need to consider both surfaces in the current study. 3.1.3. Co2(CO)y (y = 0, 2, 4, 6, 8) on γ-Alumina (100). The interaction of neutral dimeric Co-subcarbonyl species with the “Wet” (100) γ-Alumina surface was studied and compared based on the energy of the adsorption of the corresponding neutral monomeric Co-subcarbonyl species and its subsequent dimerization. The selection of the dimers was made such that each dimer represents a dimeric form of the monomeric Cosubcarbonyl species, Co(CO)x (x = 0−4), that were considered in the previous sections. Figure 5 illustrates the most favorable DFT-optimized geometries for Co2(CO)y (y = 0, 2, 4, 6, 8) interacting with “Wet” (100), along with the corresponding

adsorption energies (Eads) of each of the dimers. It is evident that diverse coordination and orientation modes are preferred by the different Co2(CO)y (y = 0, 2, 4, 6, 8) species. In particular, the adsorption of Co2 results in the preferential, perpendicular coordination mode, in which only one of the cobalt atoms interacts in a three-fold coordination mode similar to the result for single atomic Co shown (see Figure 3), while the other cobalt atom is not directly interacting with the alumina surface. Alternative adsorption geometries for Co2 involving the interaction of both cobalt atoms to the alumina surface were found to be higher in energy. The Co2 adsorption energy of Eads = −2.36 eV/Co represents a dimerization energy of −0.18 eV/Co when compared with Co adsorption on “Wet” G

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Figure 7. DFT-calculated formation free energies (ΔGf) in eV/Co for Co2(CO)x (x = 0, 2, 4, 6, 8) in the gas phase and adsorbed on the “Wet” (100) γ-Alumina surface at T = 503.15 K and (a) PCO = 1 bar and (b) PCO = 10 bar (horizontal dashed lines labeled with Nc depict the energy of a single Co atom (in eV) contained in different coordination numbers in a fcc Co lattice structure, which can be considered as an alternative reference state; colored dashed lines are a guide to the eye).

“Wet” (110) γ-Al2 O3 surfaces under relevant reaction conditions for cobalt-based Fischer−Tropsch synthesis (temperature, partial pressure of carbon monoxide and water) were determined to study the potential formation of cobalt subcarbonyl on γ-Al2O3 surface. Figure 6 presents the calculated ΔGf values for monomeric Co(CO)x (x = 0−4), in both the gas and adsorbed states. The Gibbs free energy of formation is referenced to bulk fcc-cobalt, that is, the energy of a single cobalt atom contained in the bulk of the fcc Co lattice. (fcc Co phase is used because FCC particles should be more stable than HCP particles below 110 nm.)69 This corresponds to a cobalt atom with a coordination number (Nc) of 12, which represents the most stable form of metallic cobalt. However, liberation of less stable atomic Co, with lower coordination numbers, during Ostwald ripening sintering is more likely and will therefore alter the reference state for calculated ΔGf values. These alternative reference states are included as horizontal lines in Figure 6 as a function of atomic fcc Co coordination numbers (Nc), viz. Nc = 9 (Co in the surface layer of fcc Co(111)), Nc = 8 (Co in the surface layer of Co(100)), Nc = 7 (edge Co atom of Co(211)), and Nc = 3 (Co as adatom Co(111)).70−72 The calculated ΔGf energies for all adsorbed Co(CO)x (x = 0−4) species on the four different γ-Al2O3 surfaces are shown in Figure 6. All Gibbs free-energy (ΔGf) values for the formation of the mononuclear cobalt subcarbonyl species are significantly endergonic if the partial pressure of CO is 1 bar (ΔGf for the most favored formation of Co(CO)4 is 1.6 eV) when referenced against most stable atomic Co in bulk fcc metal (Nc = 12). Only at higher energy atomic Co, for example, when the coordination number of cobalt is 7 (Nc = 7), is it found that the formation of Co-subcarbonyls, such as Co(CO)3 and Co(CO)4, starts to become thermodynamically more favored. The increase in the partial pressure of CO from 1 to 10 bar (Figure 6b) results in a systematic decrease in the Gibbs free energy of formation by ca. 0.1 eV per CO ligand. The free energies of adsorption of the respective gas-phase cobalt subcarbonyls may readily be determined from Figure 6 as the difference between the Gibbs free energy of formation of

(100) in Figure 3, emphasizing the stabilizing effect of Co−Co bond formation. The most favorable adsorption mode for Co2(CO)2 involves the interaction of a single cobalt atom with surface oxygen, while the other cobalt is three-fold coordinated to a hydroxyl O and surface Al and O atoms. It is noticeable that no bridging CO groups are present for adsorbed Co2(CO)2, in contrast with the most stable corresponding gas-phase geometry (Figure 1). The resulting horizontal coordination mode of Co2(CO)2 is contrasted by the preferred perpendicular coordination mode of Co2(CO)4 in which one cobalt coordinates to a single surface O, while the other cobalt atom is bonded to two carbonyl ligands and bridged to cobalt by two additional carbonyl-groups. No interaction of Co2(CO)4 with surface hydroxyls is observed, and once again, significant differences in the preferred structures of Co2(CO)4 are found upon comparing the adsorbed and gas-phase species (Figure 1). A bidentate coordination mode of Co2(CO)6 is preferred involving Co−OSurf and Co−OOH interactions, while the adsorbed structure retains the geometry of the most preferred gas-phase Co2(CO)6 structure (Figure 1). The coordination mode of Co2(CO)8 is found to involve H-bonding-like interactions between oxygen in the carbonyl groups and surface hydroxyl groups. The adsorption energy for Co2(CO)8 on “Wet” (100) is significantly higher (Eads = −0.82 eV/Co) than for the corresponding Co(CO)4 (Eads = −0.23 eV). This may be readily explained by the optimal horizontal orientation of Co2(CO)8 parallel to the H2O molecules on the surface, effectively facilitating optimal H-bonding interactions, accounting for the relatively favorable dimerization energy for adsorbed Co(CO)4 of −0.59 eV/Co. In general, dimerization of monomeric Co-subcarbonyls to the corresponding dimeric species is favored on the “Wet” (100) γ-Alumina surface, as reflected in the calculated dimerization energies of surface Co(CO), Co(CO)2, and Co(CO)3 of −0.28, −1.02, and −0.81 eV/Co, respectively. 3.1.4. Free Energy of Formation of Co-Subcarbonyl. The Gibbs free energies of formation (ΔGf) for the adsorbed Cosubcarbonyls on “Dry” (100), “Int” (100), “Wet” (100), and H

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Figure 8. Minimum energy pathways depicted on nine (2 × 1) surface unit cells and the lowest estimates for diffusion activation energies (Ea‑Diff) for inter-unit-cell diffusions on DFT-calculated potential energy surface (PES) diagrams for Co(CO)x (x = 0−3) adsorption and diffusion on “Dry” (100) γ-Alumina (Al: pink; O: red; (v) and (h): vertical and horizontal inter-unit-cell diffusion pathways for Co).

For example, the formation of Co(CO)3 on the “Dry” (100), “Int” (100), and “Wet” (110) surfaces is thermodynamically favored for N c ≤ 7. At increased CO pressure the thermodynamic stabilization of all Co-subcarbonyl gas and adsorbate species is observed, most notably for Co(CO)3 and Co(CO)4. Lastly, the comparative formation free energies (ΔGf) for dimeric Co-subcarbonyls, Co2(CO)y (y = 0, 2, 4, 6, 8), on the “Wet” (100) surface, in both the gas and adsorbed states, are summarized in Figure 7. This may conveniently be compared with the corresponding Co(CO)x (x = 0−4) formation free energies on “Wet” (100), as summarized in Figure 6. In line with the 0 K Eads data that are presented in Figures 3 and 5, it can be seen that the Gibbs free energies of dimerization, defined as the difference between ΔGf’s for the dimers (Figure 7) and the corresponding monomers (Figure 6), are consistently favorable across the whole spectrum of cobalt subcarbonyl species considered. In particular, the dimerization free energy for the formation of CO2(CO)4 in the adsorbed state is strongly favored by −0.8 eV/Co at PCO = 1 and 10 bar. A weaker preference for the dimeric Co2(CO)6 state is found with a dimerization free energy of −0.3 eV/Co at 1 and 10 bar PCO. In contrast, no thermodynamic preference for Co(CO)4 over Co2(CO)8 is found in both the gas and adsorbed states on the “Wet” (100) surface. As also observed for the corresponding monomer (Figure 6), desorption of Co2(CO)6 and Co2(CO)8 from “Wet” (100) is thermodynamically favorable. In general, it may be concluded from all Cosubcarbonyl formation free energies presented in Figures 6 and

the gas-phase cobalt subcarbonyl species and the Gibbs free energy of formation of these species on the alumina surfaces. For Co and Co(CO), the free energies of adsorption are exergonic on all four γ-Al2O3 surfaces, and it is thus likely that these Co-subcarbonyls will remain adsorbed to the γ-Al2O3 surfaces if formed during an Ostwald-ripening-type sintering mechanistic sequence. Adsorption is also predicted to be exergonic for Co(CO)2 and Co(CO)3, with the exception of adsorption of these species on the “Wet” (100) surface. In contrast, desorption of Co(CO)4, if formed, is thermodynamically favored from all four γ-Al2O3 surfaces. To assess the role of different degrees of hydration of the γAl2O3 surface, the Gibbs free energy of formation of cobalt subcarbonyl (ΔGf) on the “Dry”, “Int”, and “Wet” (100) surfaces may be considered in Figure 6. From these three sets of results, it is evident that the most favored formation free energies are calculated for the “Dry” (100) surface. A further comparison of the values for the Gibbs free energy of formation obtained for the fully hydrated “Wet” (100) and (110) surfaces shows no clear preference for formation of adsorbed Co(CO)x (x = 1−4) species, with Co(CO)2 and Co(CO)3 favored on “Wet” (110), while Co(CO) is not favored. No preference for either surface is observed for Co(CO)4. However, a clear preference for atomic Co formation on “Wet” (110) is found that may be attributed to more effective “solvation” of the cobalt atom on “Wet” (110). At PCO = 1 bar it is evident from Figure 6a that the thermodynamic formation of specific adsorbed Co(CO)x (x = 1−4) species is dependent on the metallic Co reference state. I

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Figure 9. Minimum energy pathways overlaid on nine (2 × 1) surface unit cells and the lowest estimates for diffusion activation energies (Ea‑Diff) for inter-unit-cell diffusions on DFT-calculated PES diagrams for Co(CO)x (x = 0−3) adsorption and diffusion on “Wet” (100) γ-Alumina (Al: pink; O: red; OH2O, oxygen associated with adsorbed water molecules: blue; (v) and (h): vertical and horizontal inter-unit-cell diffusion pathways).

respective PESs in Figure 8 proceed with lower overall barriers upon increase in the coordination of the central cobalt atom with CO ligands. For atomic cobalt, it is found that the independent diffusion pathways in the two dimensions on the alumina surface exhibit similar energy barriers, with the pathway in one direction proceeding with an upper estimate of the activation energy (Ea‑Diff) of 1.95 eV, while the corresponding other pathway proceeds with an upper barrier estimate of 1.98 eV (Figure 8a). These relatively high barriers for atomic cobalt diffusion contrast the significantly lower overall energy barriers that were calculated for Co(CO)x (x = 1−3), showing consistent lowering of Ea‑Diff from 0.92 eV for Co(CO), to 0.80 eV for Co(CO)2, and 0.54 eV for Co(CO)3. This implies that increased rates for diffusion of these cobalt subcarbonyls on this surface are to be expected upon increasing the number of CO ligands attached to the central cobalt atom. It is noticeable that the identified minimum energy paths for diffusion of all four Co(CO)x (x = 0−3) species follow similar diffusion routes. Figure 9 illustrates the DFT-calculated results for Co(CO)x (x = 0−3) diffusion on the “Wet” (100) γ-Al2O3 surface in four separate displays. From the nature of H2O adsorption on the “Wet” (100) surface it is evident that the H2O molecules form a linear arrangement. Hence, there are two different diffusion pathways for cobalt subcarbonyl species on the “Wet” (100) surface, that is, along the “valley” between the rows of H2O molecules or “across” the row of adsorbed H2O molecules on the same surface. In Figure 9a it is shown that the overall diffusion barrier for atomic Co along the “valley” on the “Wet”

7 that the Gibbs free energies of formation for mono- and dimeric species as calculated from the DFT analyses are found in a relatively narrow similar range. 3.2. Diffusion of Cobalt Subcarbonyl Species on γAl2O3 Surfaces. In an effort to extend fundamental insight into the nature of cobalt subcarbonyl adsorbates on γ-Al2O3 surfaces, DFT investigations of diffusion characteristics of selected monomeric species, that is, Co(CO)x (x = 0−3), were performed. Three representative γ-Al2O3 surfaces were considered, viz. “Dry” (100), “Wet” (100), and “Wet” (110) (see Figure 2). Grid potential energy surface (PES) calculations were performed for each of four cobalt subcarbonyl species with the lowest energy on each of the three surface models, effectively resulting in 12 sets of diffusion data. Analysis of these data sets resulted in the identification of the lowest energy diffusion pathways for each species, along with associated maximum diffusion barriers in each case, associated with diffusion between most stable adsorption sites between adjacent surface unit cells. In the remainder of this section, the diffusion results for the (100) and (110) surfaces will be presented. 3.2.1. Diffusion of Co(CO)x (x = 0−3) on γ-Al2O3(100). Figure 8 illustrates the DFT-calculated diffusion pathway for Co(CO)x (x = 0−3) on “Dry” (100) γ-Al2O3 surface in four separate displays. In each case the lowest energy diffusion pathways starting from the lowest energy adsorption position in the surface unit cell and terminating at the equivalent position in an adjacent surface unit cell is indicated. It is evident that the interpolated minimum energy paths for diffusion in the J

DOI: 10.1021/acs.jpcc.7b01907 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 10. Minimum energy pathways depicted on nine (1 × 1) surface unit cells and the lowest estimates for diffusion activation energies (Ea‑Diff) for inter-unit-cell diffusions on DFT-calculated PES diagrams for Co(CO)x (x = 0−3) adsorption and diffusion on “Wet” (110) γ-Alumina (Al: pink; O: red; OH2O, oxygen associated with adsorbed water molecules: blue; (g) and (o): green and orange inter-unit-cell diffusion pathways).

and that the degree of carbonylation results in only marginal differences in energy barriers associated with diffusion. The effect of hydration on diffusion of Co(CO)x (x = 0−3) species on the (100) γ-Alumina surface may be obtained from a comparison of the results summarized in Figures 8 and 9. For both the “Dry” and “Wet” (100) surfaces the diffusion of atomic Co is significantly less favorable than the corresponding Co-subcarbonyls. Atomic Co diffusion is calculated to be more facile on the “Wet” (100) surface compared with the “Dry” (100) surface by 0.30 eV. However, the role played by surface H2O can only be attributed as indirect because the atomic Co diffusion pathway on “Wet” (100) favors a route that does not involve direct interaction of the migrating Co with adsorbed H2O. This trend of relatively less favorable diffusion on the “Dry” (100) surface is continued for CoCO and Co(CO)2, evident from the calculated diffusion barriers that are higher by 0.40 and 0.27 eV, respectively, compared with its diffusion on “Wet” (100). Once again, this favoring of diffusion on the “Wet” surface cannot be attributed to more favored direct interaction of the migrating Co-subcarbonyls to adsorbed water, as the preferred diffusion pathways proceed via the

(100) surface (Ea‑Diff = 1.65 eV) is significantly more favorable compared with the alternative “crossing” of the row of adsorbed H2O molecules (Ea‑Diff = 1.94 eV). The formal diffusion and interaction of atomic Co with surface H2O groups on “Wet” (100) requires significant lifting of the cobalt atom from the surface and consequently a relatively high barrier for diffusion. The preference for diffusion along the “valley” of “Wet” (100), as opposed to “crossing” the linearly adsorbed H2O molecules, is also found for the Co(CO)x (x = 1−3) species. The differences in barriers of these competing pathways for each species are not consistent, with Co, CoCO, Co(CO)2, and Co(CO)3 diffusion barriers “across” the linear H2O molecules found to be higher in energy by 0.29, 0.11, 0.15, and ∼0.40 eV (the latter not indicated in Figure 9), respectively, compared with the corresponding pathway along the “valley”. No clear preference or trend associated with the number of CO groups coordinated to Co for the Co(CO)x (x = 1−3) species is found upon comparison of the lowest diffusion barriers in each case (Ea‑Diff between 0.52 and 0.64 eV). This suggests that carbonylation of Co is sufficient for diffusion to become facile K

DOI: 10.1021/acs.jpcc.7b01907 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C dehydrated regions of “Wet” (100). A similar preference for Co(CO)3 diffusion on the “Wet” (100) surface is not found from the calculations, with Co(CO)3 diffusion on “Dry” (100) found to be slightly more favorable by 0.10 eV. 3.2.2. Diffusion of Co(CO)x (x = 0−3) on γ-Alumina (110). To compare Co-subcarbonyl diffusion energies between the “Wet” (100) and “Wet” (110) γ-Alumina surfaces, the diffusion barriers for Co(CO)x (x = 0−3) diffusion on “Wet” (110) were calculated as presented in Figure 10. Because of the relatively high hydration level of “Wet” (110) of ΘOH = 17.7 OH/nm2, a comparatively complete coverage of the alumina surface by H2O is found. The lowest overall barrier for atomic Co diffusion on “Wet” (110) is Ea‑Diff = 2.25 eV, which is significantly higher than the corresponding barrier on “Wet” (100) of Ea‑Diff = 1.65 eV and may be partially related to the greater stability of atomic cobalt on the “Wet” (110) surface. In contrast, a similar inhibition of Co(CO)x (x = 1−3) diffusion is not found because the lowest overall barriers for diffusion of these Co-subcarbonyls fall in a low and narrow Ea‑Diff range of 0.50 to 0.54 eV. From this, it is thus evident that the calculated diffusion barriers for Co(CO)x (x = 1−3) diffusion on “Wet” (100) and “Wet” (110) are similar.

the chemical potential under standard condition of 1 bar (μ0i ) between the products and the reactants 0 0 Δrxn G° = μCo(CO) − μCo x

nanoparticle

0 − x·μCO

(6)

The chemical potential of a hemispherical cobalt nanoparticle of a size dCo in contact with alumina is given by 0 μCo

nanoparticle

0 = μCo,bulk −

3·MCo 6·MCo ·ECo−Al 2O3 + ·γ dCo·ρCo dCo·ρCo Co (7)

μ0Co,bulk

where is the chemical potential for bulk fcc cobalt, MCo is the molar mass of cobalt, and ρCo is the density of fcc-Co. The interaction energy between cobalt and alumina (ECo−Al2O3) is given by the adhesion energy of 1.14 J/m2,74 which is as a first estimate considered to be independent of the level of hydration. The surface energy of cobalt exposed to the gas

(

phase is given byγCo = 2.14· 1 + 2

75

1.45 dCo

+

0.55 2 dCo

) (with γ

Co

in J/

m and dCo in nm). Coverage of nanoparticles with reactants and products, for example, CO, would further stabilize the nanoparticles. In the absence of CO, the coverage of atomic cobalt on alumina will be negligibly small: The fractional coverage of cobalt atoms in equilibrium with 4 nm metallic cobalt crystallites on a pristine “Dry” (100) Al2O3 surface will be