Density-Functional Tight-Binding Study of Carbonaceous Species Diffusion on the (100)-γ-Al2O3 Surface

  • Aditya W. Sakti
    Aditya W. Sakti
    Element Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyotodaigaku-Katsura, Kyoto 615-8520, Japan
    Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo 169-8555, Japan
  • Chien-Pin Chou
    Chien-Pin Chou
    Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo 169-8555, Japan
  • , and 
  • Hiromi Nakai*
    Hiromi Nakai
    Element Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyotodaigaku-Katsura, Kyoto 615-8520, Japan
    Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo 169-8555, Japan
    Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan
    *E-mail: [email protected]. Phone: +81 3-5286-3452. Fax: +81 3-3205-2504.
    More by Hiromi Nakai
Cite this: ACS Omega 2020, 5, 12, 6862–6871
Publication Date (Web):March 18, 2020
https://doi.org/10.1021/acsomega.0c00203
Copyright © 2020 American Chemical Society
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Abstract

Carbonaceous or oxy-carbon species are intermediates formed during CxHy combustion on a Ptn/Al2O3 catalyst, which contain carbon, hydrogen, and oxygen atoms. The accumulation of the carbonaceous species, arguably, leads to catalytic deactivation; therefore, their removal is of importance. As the diffusion process is occasionally the rate-determining step in the growth of carbonaceous species, the present study aims to reveal the diffusion mechanisms. The free energy barriers of acetate, formate, and methoxy diffusion on the (100)-γ-Al2O3 surface were evaluated through extensive metadynamics simulations at the density-functional tight-binding level. The present work deduces that each adopted carbonaceous species exhibits different diffusion mechanisms and supports experimental evidence that the acetate species exhibits the slowest diffusivity among the adopted carbonaceous species.

1. Introduction

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The three-way catalyst (TWC) technology is among the innovative catalyst technologies for eliminating the generated hazardous exhaust gases, that is, carbon monoxide (CO), nitrogen oxides (NOx), and unburnt hydrocarbons (CxHy) from vehicles. (1−3) The catalysts are composed of, and not limited to, noble metals (Pt, Pd, or Rh) and metal oxides. The commonly used metal oxides that support TWC are alumina (Al2O3), (4−7) zirconia (ZrO2), (8−12) and ceria (CeO2). (13−17) Experimental (18−20) and theoretical (21−24) studies were performed extensively for exploring the catalytic activity and elucidating the reaction mechanism. (22,23) During the removal process, CO and CxHy are oxidized into CO2, whereas NOx is reduced to N2. (25) In such reactions, the CxHy oxidation leads to the formation of intermediates reported in ref (26), namely, oxygenated carbonaceous (oxy-carbon) species. The oxy-carbon intermediates are mainly accumulated on the Al2O3 surface. (26) The role of the oxy-carbon species is questionable. However, it has been presumed that the oxy-carbons only act as inert spectators during the oxidation reaction. (26) An experimental study was performed to investigate oxy-carbon growth on a metal oxide surface. (26)
The growth of the oxy-carbon species was observed by diffuse reflectance infrared Fourier-transform spectroscopy coupled with Fourier-transform infrared spectroscopy. (26) The same technique has been used extensively for investigating oxidation over various catalysts, namely, Pd/CeO2/Al2O3, (27) Pt/Al2O3, (28−30) Pt/WOx/Al2O3, (28) MgCr2O4, (31,32) Co3O4, (32) CuO, (32) and Pt/CeO2–ZrO2. (33) The oxy-carbon species observed on the support materials include acetate (CH3COO), (28,31,32) formate (HCOO), (27,28,31,32) alkoxy (RO), (32) carbonate (CO32–), (27−29,33) bicarbonate (HCO3), (33) acetone, (31,32) and unidentified species. (30) The unidentified species was detected when the experiment was conducted in the presence of the SO2 gas. Temperature-programmed oxidation (TPO) successfully elucidated the composition, location, reactivity, and the role of the oxy-carbon species in hydrocarbon oxidation. (34) The catalytic activity of the supported nanoparticles was also influenced by the kinetics of the TPO process, where the activity increased as the diffusion barrier decreased. (34)
Based on the previous experimental study in ref (26), the reactions represented in eqs 18 are plausible elementary reactions for the formation of the oxy-carbon species, where * denotes the active site of the surface. No observation was made to elaborate where the reactions were occurring. Assuming that all the processes occur on the metal nanocluster surface, the oxy-carbon species would spill over on the γ-Al2O3 surface.(1)(2)(3)(4)(5)(6)(7)(8)
The previous experimental study showed that it is more difficult to oxidize acetate species than the alkoxy and ketone derivatives. (26,34) It was further confirmed that the diffusion of oxy-carbon species plays an important role in the removal process, as diffusion is the rate-determining step of oxy-carbon oxidation. (34) Motivated by the aforementioned experimental facts, in the present theoretical study, the diffusion process of oxy-carbon species was elucidated via molecular dynamics simulations at the density-functional tight-binding (DFTB) level. (35−38) Molecular details on the diffusion mechanism and the surface driving force γ-Al2O3 were investigated.

2. Computational Details

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All DFTB calculations were performed using an in-house code DC-DFTBMD program, (39,40) whereas the reference calculations were performed at the density-functional theory (DFT) level using the Vienna ab Initio Simulation Package (VASP). (41,42) The DFTB calculation was performed using the third-order variant (DFTB3) with the modified parameter set made using the automatized DFTB parameterization toolkit, (43) hereafter called the Al2O3 parameter. As a reference, the calculations were also performed at the DFT level using the generalized-gradient approximation functional, Perdew–Burke–Ernzerhof, revised for solids (PBEsol). (44) To describe the dispersion interaction between the oxy-carbon and the γ-Al2O3 surface, the DFT-D3 dispersion correction with Becke–Johnson damping was employed in both DFTB and DFT calculations. (45) The initial structure of the bulk γ-Al2O3 was reconstructed based on the information obtained from refs (46) and (47). The chosen initial structure is a nonspinel type that has been extensively studied in some previous works. (24,48−53)
First, the initial geometry of the bulk Al2O3 was optimized at the DFT and DFTB levels. The lattice parameters and the optimized geometries were considered for generating the slab structures. The (100)-γ-Al2O3 slabs were generated by cutting the atoms along the (100) plane. Two slab models with different sizes that consist of 160 and 960 atoms, respectively, are shown in Figure 1. To overcome the computational cost for a large system, the divide-and-conquer (DC) option in the DCDFTBMD program was enabled. (39,40,54,55) The subsystems were created automatically using the cubic grid with dimensions of 3 × 3 × 3 Å3. A buffer radius of 6 Å was used to adjust the accuracy to the same level as the conventional DFTB method.

Figure 1

Figure 1. Representative (a) small and (b) large-size slab models adopted in the present work.

During the geometry optimization, three-bottom layers of the slab were fixed, while other atoms were relaxed. The oxy-carbon intermediates, namely, methoxy (CH3O), bicarbonate (HCO3), formate (HCOO), acetate (CH3COO), and propionate (CH3CH2COO) were attached on the slab surface. In each prepared structure, oxygen atoms of the oxy-carbon are bound to aluminum atoms, such that they form an octahedral geometry centered at the aluminum atom. The adsorption energies between the oxy-carbon and (100)-γ-Al2O3 slab were calculated at the DFT and DFTB levels with the following formula(9)
Eads, Eslab, and Ecarb represent the total energies of the adsorbed system, slab, and oxy-carbon species, respectively.
The adsorption energies calculated at the DFTB level were compared to the reference calculations at the DFT level. After confirming the parameter accuracy in describing the binding energy, the optimized adsorbed structures were used for MD simulations. At first, the equilibrations were performed under the canonical (NVT) ensemble at the DFTB3-D3(BJ) level for 20 ps with a time step of 1.0 fs to integrate the equation of motion. The equilibrated structures with the details summarized in Table 1 were adopted for further production runs via the metadynamics sampling scheme. (56−59) The surface coverages listed in Table 1 are calculated based on eq 10.(10)
Table 1. Slab Size, Adsorbate, Surface Coverage, Number of Adsorbed Oxy-Carbon Species, and Total Number of Atoms of the Adopted Systems
slab sizeadsorbatesurface coverage [%]Noxy-carbonNatoms
smallCH3COO5.001167
smallHCOO5.001164
smallCH3O2.501165
largeCH3COO0.831967
largeCH3COO1.672974
largeCH3COO9.17111037
Under the metadynamics scheme, the Al–O coordination number, as formulated in eq 11, was chosen as the collective variable.(11)rij and r0 denote the Al–O distance and cutoff radius, respectively. The value r0 = 1.9 Å was specified to smoothly define Al–O bond breaking and formation during the metadynamics simulations. The Gaussian bias potential with a height of 1.88 kcal/mol and a width of 0.1 (dimensionless, as the coordination number was chosen as the collective variable) was added every 40 fs. The simulations were performed until the estimated free energy barriers converged. The free energy barriers converged after performing 9 metadynamics trajectories with a simulation length of 60 ps. The free energy surfaces were reconstructed by estimating the unbiased probability density function via the weighted histogram analysis method. (60)

3. Results and Discussion

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3.1. Structural Property of Bulk γ-Al2O3

The cell parameters of the optimized bulk structure are listed in Table 2. All DFT functionals fairly reproduce the experimental cell volumes. The PBEPBE functional shows the largest deviation of 6.94% with a volume of 49.61 Å3, while the experimental cell volume is 46.39 Å3. Other functionals, such as PBEsol, M11-L, MN12-L, and PW91, exhibit smaller volume deviations of −3.54, −1.60, 1.42, and 2.18%, respectively. The DFTB variants also show smaller volume deviations, namely, –0.13 and −1.74%, for the DFTB3 and DFTB3-D3(BJ) methods, respectively. Despite the volume deviation, the dispersion correction is important for describing weak interactions between oxy-carbon moieties.
Table 2. Comparison of Cell Parameters, Optimized at Different DFT Functionals, and the DFTB Method
methodPBEsolPBEPBEaM11-LaMN12-LaPW91bDFTB3DFTB3-D3(BJ)
a [Å]5.4665.6485.4915.5595.5875.5705.533
b [Å]8.2458.5288.2858.3648.4138.4278.378
c [Å]7.9568.2418.0298.0978.0687.8977.865
β [deg]90.7691.0091.2491.2890.5989.4690.66
volume [Å3/Al2O3]44.7549.6145.6547.0547.4046.3345.58
volume deviation [%]c–3.546.94–1.601.422.18–0.13–1.75
a

Calculated results from ref (61).

b

VASP calculations, using the plane wave basis from ref (47).

c

The deviations were calculated relative to the experimental volume of 46.39 Å3/Al2O3 (ref (62).)

3.2. Adsorption of Oxy-Carbon Species on the (100) Surface of γ-Al2O3

The oxy-carbon species or carbonaceous species was deposited on the (100)-γ-Al2O3 surface, which was formed after the spillover process. The optimized geometries of the oxy-carbon species adsorbed on the (100)-γ-Al2O3 surface, namely, methoxy (#1–#2), ethoxy (#3–#5), formate (#6–#9), acetate (#10–#13), propionate (#14–#17), and bicarbonate (#18–#20) are shown in Figure 2.

Figure 2

Figure 2. Adsorbed methoxy (#1–#2), ethoxy (#3–#5), formate (#6–#9), acetate (#10–#13), propionate (#14–#17), and bicarbonate (#18–#20) species on (100)-γ-Al2O3 obtained from geometry optimizations at the DFTB3-D3(BJ) level.

The calculated adsorption energies (ΔEads) for the acetate, formate, and methoxy species on (100)-γ-Al2O3 are shown in Table 3. The DFTB method predicts shorter O–Al bond lengths with a mean average deviation (MAD) of 0.06 Å, relative to the bond lengths obtained at the PBEsol level. Despite such short bond distances, the calculated ΔEads at the DFTB level are smaller than those calculated at the DFT level. The adsorption energies are also well reproduced with a MAD of 0.09 eV (2.08 kcal/mol). Such a deviation is under the level of accuracy of the DFTB method as reported in previous works. (63−67) Inclusion of the dispersion correction to both DFT and DFTB calculations also leads to the same MAD as shown in Table 4.
Table 3. Calculated Adsorption Energies and O–Al Bond Distances for Acetate, Formate, and Methoxy on the (100)-γ-Al2O3 Surfacea without Dispersion Correction
  rO–Al [Å]Eads[eV]
entryoxy-carbonPBEsolDFTB3bPBEsolDFTB3b
#1methoxy1.841.79 (−0.05)–1.36–1.40 (−0.04)
#2methoxy1.891.81 (−0.08)–0.96–0.94 (+0.02)
#3ethoxy1.841.77 (−0.07)–1.22–1.38 (−0.16)
#4ethoxy1.901.82 (−0.08)–0.94–0.91 (+0.04)
#5ethoxy1.901.82 (−0.08)–1.09–1.17 (−0.08)
#6formate1.911.81 (−0.10)–0.98–0.90 (+0.09)
#7formate1.891.86 (−0.04)–1.23–1.07 (+0.16)
#8formate1.901.86 (−0.04)–0.98–0.79 (+0.19)
#9formate1.931.85 (−0.08)–0.84–0.74 (+0.10)
#10acetate1.901.81 (−0.09)–0.96–0.98 (−0.02)
#11acetate1.881.86 (−0.02)–1.21–1.15 (+0.07)
#12acetate1.881.86 (−0.02)–0.95–0.87 (+0.09)
#13acetate1.921.85 (−0.07)–0.80–0.81 (−0.01)
#14propionate1.901.81 (−0.09)–0.99–0.91 (+0.08)
#15propionate1.881.85 (−0.03)–1.24–1.08 (+0.16)
#16propionate1.881.85 (−0.03)–0.99–0.80 (+0.19)
#17propionate1.921.84 (−0.08)–0.83–0.75 (+0.08)
#18bicarbonate1.901.81 (−0.09)–1.01–1.18 (−0.17)
#19bicarbonate1.881.86 (−0.02)–1.26–1.34 (−0.08)
#20bicarbonate1.891.86 (−0.03)–1.01–1.07 (−0.06)
 MAD 0.06 0.09
a

Herein, the O atom refers to the one that belongs to the oxy-carbon species. The calculations were performed without dispersion correction.

b

Differences from the PBEsol method are shown in parentheses.

Table 4. Calculated Adsorption Energies and O–Al and the Acetate, Formate, and Methoxy Bond Distances on the (100)-γ-Al2O3 Surfacea with Dispersion Correction
  rO–Al [Å]Eads[eV]
entryoxy-carbonPBEsol-D3(BJ)DFTB3-D3(BJ)bPBEsol-D3(BJ)DFTB3-D3(BJ)b
#1methoxy1.841.80 (−0.05)–1.57–1.62 (−0.05)
#2methoxy1.901.83 (−0.07)–1.15–1.20 (−0.05)
#3ethoxy1.841.78 (−0.06)–1.52–1.69 (−0.17)
#4ethoxy1.891.82 (−0.07)–1.16–1.20 (−0.04)
#5ethoxy1.911.82 (−0.09)–1.08–1.03 (+0.06)
#6formate1.891.86 (−0.03)–1.32–1.20 (+0.12)
#7formate1.901.86 (−0.04)–1.08–0.93 (+0.14)
#8formate1.931.86 (−0.08)–0.93–0.85 (+0.08)
#9formate1.901.82 (−0.08)–1.33–1.28 (+0.05)
#10acetate1.881.85 (−0.03)–1.08–1.10 (−0.03)
#11acetate1.881.85 (−0.03)–1.08–1.00 (+0.08)
#12acetate1.921.85 (−0.07)–0.92–0.93 (−0.01)
#13acetate1.901.81 (−0.09)–1.13–1.05 (+0.08)
#14propionate1.881.85 (−0.03)–1.38–1.22 (+0.15)
#15propionate1.881.85 (−0.03)–1.13–0.95 (+0.18)
#16propionate1.911.85 (−0.07)–0.97–0.87 (+0.10)
#17propionate1.911.81 (−0.10)–1.12–1.30 (−0.18)
#18bicarbonate1.881.85 (−0.03)–1.36–1.46 (−0.10)
#19bicarbonate1.891.85 (−0.04)–1.12–1.20 (−0.08)
#20bicarbonate1.921.85 (−0.07)–0.96–1.12 (−0.16)
 MAD 0.06 0.09
a

Herein, the O atom refers to the one that belongs to the oxy-carbon species. All calculations were performed with the DFT-D3(BJ) dispersion correction.

b

Differences from the PBEsol method are shown in parentheses.

Based on Table 4, the calculated Eads values strongly depend on the location where the oxy-carbon is adsorbed on the surface. According to the estimated Eads values at the DFTB level, the tendency of the oxy-carbon adsorbed on the surface of (100)-γ-Al2O3 is ethoxy ≈ methoxy > bicarbonate > propionate ≈ formate > acetate. Such an order suggests that removing the acetate species from the surface is energetically easier than that of the formate and methoxy species. However, despite this the acetate species exhibits the smallest adsorption energy, it does not mean that it is easier to be removed from the surface. Because one acetate molecule is adsorbed to the surface via two O–Al bonds, a complete acetate removal requires dissociation of those bonds. Therefore, a more thorough analysis on the free energy of diffusion in the next subsection is of importance to further determine which oxy-carbon species is easier to be removed from the surface.

3.3. Diffusion of Acetate, Formate, and Methoxy Species on the (100) Surface of γ-Al2O3

Snapshots of acetate, formate, and methoxy diffusion are shown in Figure 3. Initially, the oxygen from the acetate, formate, and methoxy was attached on the aluminum atom of the (100)-γ-Al2O3 surface. For the case of acetate and formate, the O–Al bond dissociation retains another O–Al bond on the surface. As a result, the remaining O–Al bond becomes flexible and thus it performs a rotation that enables the oxygen atom of the carbonyl group to interact with another empty orbital of the aluminum atom. As the rotation that took place occurred right after the bond dissociation, the process is analogous to ballet.

Figure 3

Figure 3. Representative metadynamics snapshots of (a) acetate, (b) formate, and (c) methoxy diffusion on (100)-γ-Al2O3 surface.

Similar to the case of the acetate diffusion mechanism, in the beginning, O–Al, the bond between formate and the (100)-γ-Al2O3, was dissociated. Unlike the case of acetate, where oxygen is the only atom that can interact with the surface, herein, the hydrogen atom has a tendency to interact with the surface oxygen atoms. Such an interaction is slightly weaker with a bond length of 1.82 Å, whereas the O–Al bond length between formate and the surface is 1.75 Å. Once the H–O interaction is complete, the formate moiety is destabilized, leading to the dissociation of the second O–Al. Therefore, generally, formate diffusion is facilitated by a ballet jumping motion that originates from the formation of the H–O bond.
In contrast with the acetate and formate cases, the methoxy radical has only one O–Al bond with the (100)-γ-Al2O3 surface. As shown in Figure 3c, at first, the radical rotates until it finds a good conformation to promote O–Al bond dissociation. Once it is detached from the surface, it performs a random vehicular diffusion (68,69) until a proper orientation is identified for it to be re-adsorbed on to the surface. The random motion on the surface increases the degree of freedom, in particular, for reorienting and forming the O–Al bond.
To further investigate these three mechanisms, the free energy diffusion surfaces were re-constructed and are shown in Figure 4. The free energy barriers, ΔF, are summarized in Table 5. As shown in Figure 4a, there are two activated complexes formed during acetate diffusion, with diffusion barriers of 8.01 and 25.31 kcal/mol, respectively. These transition states refer to the dissociation of the O–Al bonds, indicating that each O–Al bond has a different strength, with a ratio ΔFf2Ff1 of 3.16. A lower ΔFf2Ff1 ratio represents faster diffusivity as the second bond dissociation O–Al is the rate-determining step of the overall diffusion process. On the other hand, owing to the dissociations facilitated by the H–O surface interaction, the formate diffusion exhibits a lower ΔFf2Ff1 of 1.90, leading to faster diffusivity than the acetate radical. The third step of formate diffusion involves the dissociation of a relatively weak H–O bond, which is represented by a low free energy barrier of 5.73 kcal/mol.

Figure 4

Figure 4. Reconstructed free energy surfaces of (a) acetate, (b) formate, and (c) methoxy diffusion.

Table 5. Estimated Free Energy Barriers of Acetate, Formate, and Methoxy Diffusion on the (100)-γ-Al2O3 Surface in kcal/mol
speciesΔFf1ΔFf2ΔFf3ΔFf2Ff1ΔFb1ΔFb2ΔFb3
acetate8.0125.31 3.169.5910.97 
formate6.8212.955.731.9019.287.421.58
methoxy15.46   25.45  
As described above for the case of methoxy diffusion, only one O–Al bond was dissociated with a moderately high free energy barrier of 15.46 kcal/mol. The ΔFf1 of methoxy diffusion is higher than that of formate diffusion, but still lower than that of acetate. As the methoxy radical performs Brownian diffusion before it is re-adsorbed to the surface, the transition state becomes broader with a few noises as the marks of the small vehicular diffusion barrier. The Brownian diffusion is rather random; therefore, the free energy barrier for methoxy diffusion hardly converges, that is, with a standard deviation of 2.5 kcal/mol.
Note that the ΔF values listed in Table 5 are in the range of experimental values, namely, 5.74–26.05 kcal/mol. (34,70−72) Moreover, in agreement with the TPO experiment, removing acetate radicals is more difficult compared to removing enolate, aliphatic ester, and acetone. (34) Based on the MD simulation at the DFTB level, for the case of the acetate radical, the surface atom configuration, in particular, surface O–Al–O angles where the oxy-carbon was adsorbed (α and β), is primarily responsible for the O–Al bond dissociation. As shown in Figure 5a,b, when the O–Al bond dissociates, namely, when nO–Al reaches zero, α decreases from 105 to 85°, while β increases from 70 to 85°. On the other hand, for the case of formate as shown in Figure 5c,d, the α and β angles do not change significantly, in particular, α is relatively stable at 82°, while β slightly increases from 84 to 88°. In this case, the surface atoms provided a lower driving force for facilitating formate diffusion. As explained previously, formate diffusion is partly facilitated by the interaction between the hydrogen atom of the formate and the oxygen atom on the surface; hence, the diffusion takes place with less efforts from the surface. In stark contrast, as shown in Figure 5e,f, both, the α and β angles, do not change significantly during methoxy diffusion. Although methoxy diffusion is not the fastest among the adopted oxy-carbon species, the surface atoms have a low contribution to the overall diffusion process.

Figure 5

Figure 5. Probability density distribution of the correlation between α and β angles and the coordination number of oxygen atom, nO–Al of acetate (a,b), formate (c,d), and methoxy species (e,f).

3.4. Coverage Dependence on the Barriers to Acetate Diffusion

The surface coverage affects the estimated barriers of acetate diffusion as summarized in Table 6. At a low surface coverage, namely, 0.83%, the free energy barriers for the dissociations of the second and first O–Al bonds are 11.23 and 20.92 kcal/mol, respectively. The first intermediate state, where one O–Al bond remains adsorbed on the surface, is more stable than the initial state, as implied by the backward free energy barrier of 17.79 kcal/mol. The first intermediate state is even more stable than the final state where the remaining O–Al bond is dissociated. Conversely, despite the high free-energy dissociation of the second O–Al bond, the backward reaction requires a lower energy of 5.28 kcal/mol. Hence, the second O–Al bond dissociation is an endergonic process with ΔFf2 > 0, which indicates that a larger thermal energy is required to induce spontaneity.
Table 6. Estimated Free Energy Barriers (ΔF) and Free Energy Differences (ΔF) of Acetate Diffusion at Different Surface Coverage Levels
surface coverage [%]ΔFf1 [kcal/mol]ΔFf2 [kcal/mol]ΔFb1 [kcal/mol]ΔFb2 [kcal/mol]ΔFf1 [kcal/mol]ΔFf2 [kcal/mol]
0.8311.2320.9217.795.28–6.5615.64
1.674.3914.417.613.77–3.2210.64
9.174.6115.291.805.922.809.37
As the surface coverage increases to 1.67%, both ΔFf1 and ΔFf2 decrease to 4.39 and 14.41 kcal/mol, respectively. Similarly, the barriers for backward processes also decrease to 7.61 and 3.77 kcal/mol. Overall, such changes lead to an increase in the free energy difference for the first dissociation process, namely, −3.22 kcal/mol. This indicates that the dissociation of the first O–Al bond becomes more energy demanding. On the other hand, the dissociation of the second bond requires a lower energy than the one at the coverage of 0.83%, with a free energy difference of 10.64 kcal/mol. Overall, at a surface coverage of 1.67%, a lower temperature will be sufficient to promote the entire diffusion process as the total free energy difference, ΔFf1 + ΔFf2 of 7.42 kcal/mol, is smaller than the one at 0.83% surface coverage, namely, 9.08 kcal/mol. The decrement in ΔFf2 helps mitigate the increment in ΔFf1. It is speculated that such decrement stems from the surface deformation when an additional acetate molecule is adsorbed on the surface.
When the surface coverage is further increased to 9.17%, the dissociation barriers of the first and second O–Al bonds slightly increase to 4.61 and 15.29 kcal/mol, respectively. These increments are, however, insignificant, at 0.22 and 0.88 kcal/mol, respectively. Such values are still within the statistical error of metadynamics sampling and re-weighting. In contrast, the backward process for the first dissociation step is reduced significantly from 7.61 to 1.80 kcal/mol. As the backward process is easier, the first dissociation process becomes thermodynamically unfavorable with a free energy difference of 2.80 kcal/mol. The difficulty with dissociating the first O–Al bond may arise from the steric hindrance between the acetate moieties. On the other hand, the second dissociation process is slightly easier than that with a surface coverage of 1.67%, with a free energy difference of 9.37 kcal/mol. As acetate diffusion is difficult at 9.17% surface coverage, one needs to control and minimize the growth of the acetate radical on the Al2O3 surface.

4. Conclusions

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In conclusion, metadynamics simulations at the DFTB level successfully revealed molecular mechanisms of acetate, formate, and methoxy diffusion on a (100)-γ-Al2O3 surface. The present study has examined three diffusion mechanisms that depend on unique interactions between the oxy-carbon radical with the surface. Although acetate and formate have the same functional group, namely, carboxylate (−COO), they exhibit different diffusion mechanisms. For these carboxylic species, the oxygen atoms were attached asymmetrically, where the O–Al bonds had nonequivalent strength. The acetate diffusion uniquely mimics a ballerina dancer, namely, one O–Al bond rotation occurs immediately after another O–Al bond dissociates. The acetate radical displays the slowest diffusivity among the other oxy-carbon species adopted in the present work. Further investigation shows that the spontaneity of the O–Al bond dissociation is affected by the surface coverage. Increasing the surface coverage to 9.17% leads to nonspontaneous O–Al bond dissociation. Although further investigation to elucidate this phenomenon has not been carried out, it is speculated that the steric hindrance between acetate residues is at play in suppressing the acetate diffusion. The present work suggests that removing the acetate species from the surface is easier at an early stage of its growth, that is, when the surface coverage less than 9%.
On the other hand, the formate radical exhibits the fastest diffusion by forming the O–H bond between the hydrogen atom of the formate radical with the surface oxygen atom. The nature of its fast diffusion, however, is experimentally unobservable, as the diffusion of the formate radical is indistinguishable among the other oxy-carbon species. (26) The present work suggests that it is easier to remove the formate radical from the (100)-γ-Al2O3 surface than the acetate or methoxy species. In contrast to the acetate and formate cases, the methoxy radical performs Brownian diffusion. As only one O–Al bond dissociates, Brownian diffusion occurs right after dissociation. Despite the dissociation of only one O–Al bond, the process is slower than formate diffusion due to the lack of surface deformation during methoxy diffusion. Overall, the order of diffusivity among the adopted oxy-carbon species is acetate < methoxy < formate. While the order was not experimentally confirmed, it was reported that the acetate radical exhibits the slowest diffusion. (34)

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  • Corresponding Author
    • Hiromi Nakai - Element Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyotodaigaku-Katsura, Kyoto 615-8520, JapanWaseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo 169-8555, JapanDepartment of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japanhttp://orcid.org/0000-0001-5646-2931 Email: [email protected]
  • Authors
    • Aditya W. Sakti - Element Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyotodaigaku-Katsura, Kyoto 615-8520, JapanWaseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo 169-8555, Japan
    • Chien-Pin Chou - Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo 169-8555, Japan
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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Some of the presented calculations were performed at the Research Center for Computational Science (RCCS), Okazaki Research Facilities, Institutes of Natural Sciences (NINS). This work was supported in part by a Grant-in-Aid for Scientific Research (S) “KAKENHI Grant Number JP18H05264” from the Japan Society for the Promotion of Science (JSPS). This work was also supported by Element Strategy Initiative “JPMXP0112101003” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Abbreviations

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MTD

metadynamics

MD

molecular dynamics

DFTB

density-functional tight-binding

DC-DFTB

divide-and-conquer-density-functional tight-binding

References

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  • Abstract

    Figure 1

    Figure 1. Representative (a) small and (b) large-size slab models adopted in the present work.

    Figure 2

    Figure 2. Adsorbed methoxy (#1–#2), ethoxy (#3–#5), formate (#6–#9), acetate (#10–#13), propionate (#14–#17), and bicarbonate (#18–#20) species on (100)-γ-Al2O3 obtained from geometry optimizations at the DFTB3-D3(BJ) level.

    Figure 3

    Figure 3. Representative metadynamics snapshots of (a) acetate, (b) formate, and (c) methoxy diffusion on (100)-γ-Al2O3 surface.

    Figure 4

    Figure 4. Reconstructed free energy surfaces of (a) acetate, (b) formate, and (c) methoxy diffusion.

    Figure 5

    Figure 5. Probability density distribution of the correlation between α and β angles and the coordination number of oxygen atom, nO–Al of acetate (a,b), formate (c,d), and methoxy species (e,f).

  • References

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