Scaling Relations and Kinetic Monte Carlo Simulations To Bridge the

Subscriber access provided by EAST TENNESSEE STATE UNIV

Article

Scaling Relations and Kinetic Monte Carlo Simulations to Bridge the Materials-Gap in Heterogeneous Catalysis Mikkel Jørgensen, and Henrik Grönbeck ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b01194 • Publication Date (Web): 22 Jun 2017 Downloaded from http://pubs.acs.org on June 27, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Catalysis is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 24

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

ACS Catalysis

Scaling Relations and Kinetic Monte Carlo Simulations to Bridge the Materials-Gap in Heterogeneous Catalysis Mikkel Jørgensen∗ and Henrik Grönbeck∗ Department of Physics and Competence Centre for Catalysis, Chalmers University of Technology, 412 96 G¨ oteborg, Sweden E-mail: [email protected]; [email protected]

Abstract Scaling relations combined with Kinetic Monte Carlo Simulations are used to study catalytic reactions on extended metal surfaces and nanoparticles. The reaction energies are obtained by Density Functional Theory calculations where the site-specific values are derived using generalized coordination numbers. This approach provides a way to handle the materials-gap in heterogeneous catalysis. CO oxidation on Platinum is investigated as an archetypical reaction. The kinetic simulations reveal clear differences between extended surfaces and nanoparticles in the size range 1-5 nm. The presence of different types of sites on nanoparticles results in a turnover frequency that is orders of magnitudes larger than on extended surfaces. For nanoparticles, the reaction conditions determine which sites that dominate the overall activity. At low pressures and high temperatures, edge and corner sites determine the catalytic activity, whereas facet sites dominate the activity at high pressures and low temperatures. Furthermore, the ∗

To whom correspondence should be addressed

1

ACS Paragon Plus Environment

ACS Catalysis

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

reaction conditions are found to determine the particle-size dependence of the turnover frequency. Keywords: Microkinetic modeling, Kinetic Monte Carlo, Density Functional Theory, CO oxidation, Platinum Nanoparticles, Scaling relation, Generalized Coordination Number.

Introduction Heterogeneous catalysis plays a central role in modern society. Catalytic technologies are used in chemical and fuel production and are key in emission control systems. One wellknown example is the three-way catalytic converter (TWC) for abatement of emissions from gasoline vehicles, which has been critical for improved air quality in urban areas. 1 Atomistic level understanding has proven important for catalyst development. Experimentally, such knowledge has over the last decades been obtained by the surface science approach where reactions are studied on extended surfaces. 2 Common surface science techniques often require high vacuum conditions, which results in a pressure-gap with respect to the technically relevant operating conditions. Another issue is the materials-gap arising from the fact that technical catalysts generally consist of nano-meter sized metal particles dispersed on oxide supports. A technical catalyst has a multitude of sites, whereas a single crystal surface only has a few. Considerable efforts have been made in the past to close the materials-gap by fabrication of well-defined nanoparticles. 3–5 The development of Density Functional Theory (DFT) calculations has made it possible to study catalytic reactions from first principles. 6 Systematic work on extended surfaces has established universal scaling relations where trends in catalytic performance has been related to the electronic structure. 7,8 Moreover, first-principles data from extended surfaces have provided input to models of reaction kinetics. 9–17 These atomistic models bridge the pressure-gap but not the materials-gap as nanoparticles contain a range of different sites

2


Page 2 of 24

Page 3 of 24

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

ACS Catalysis

with various properties. 18–20 The potential importance of different sites for reaction kinetics have been demonstrated with Kinetic Monte Carlo simulations using schematic reactionparameters. 21,22 These simulations considered connected low-index facets, and showed that complex kinetic behavior could arise from inter-facet diffusion and differences in sticking coefficients between facets. 21,22 Kinetic Monte Carlo simulations of small metal clusters have also been performed, 15,23 demonstrating cluster-size effects on catalytic activity. To further enhance the understanding of catalytic reactions over nanoparticles there is a need to introduce a reaction-energy-landscape that efficiently considers the energetics of the different sites. However, complete mapping of the energy-landscape is still unfeasible. In connection to this challenge, it has recently been demonstrated that adsorption energies on nanoparticles can be described accurately by generalized coordination numbers (CN). 24,25 Thus, a reasonable energy landscape of a nanoparticle can be constructed with low computational cost. In the present work, we combine scaling relations for reaction energies based on generalized coordination numbers and kinetic Monte Carlo simulations to study catalytic reactions on nanoparticles. This Scaling Relation Monte Carlo (SRMC) approach is applied to CO oxidation over Pt(111) and Pt nanoparticles in the size-range 1-5 nm. CO oxidation over platinum is an archetypical reaction, and numerous experimental and theoretical studies have elucidated the nature of CO oxidation on metallic surfaces. 1 It is well-known that the reaction proceeds via a Langmuir-Hinselwood mechanism, 1,26,27 and may exhibit complex behavior such as bistable kinetics 28,29 and oscillations. 30,31 Our results show that the kinetics over nanoparticles is markedly different from that of extended surfaces. In particular, the simulations predict that nanoparticles are active over a wider range of reaction conditions. This is a direct consequence of the range of coordination numbers present on nanoparticles. Furthermore, the most active site is found to vary with reaction conditions: Low-coordinated sites are most active at high temperatures, whereas high-coordinated sites are beneficial at low temperatures. Similarly, for low pressures the low-coordinated sites are most active, whereas

3


ACS Catalysis

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

the high-coordinated dominate the activity at high pressures. The connection between reaction conditions and most active sites results in a size dependent Turnover Frequency (TOF). At low pressures, small particles have the highest TOF, whereas large particles have the highest TOF at high pressures. The introduced method is computationally cheap and straightforward to generalize to other catalytic reactions and nanoparticles. Furthermore, the approach provides a way to bridge the materials-gap as extended surfaces and nanoparticles are treated within the same framework.

Computational Method Density Functional Theory Density Functional Theory calculations are performed using the Vienna Ab-Initio Simulation Package (VASP) 32–35 in the Projector-Augmented Wave (PAW) scheme, 36 where the number of valence electrons are: Pt(10), O(6) and C(4). The calculations employ the Generalized Gradient Approximation with the RPBE 37 exchange-correlation functional. Although, the RPBE functional wrongly predicts the fcc site as most stable for CO adsorption, 38 it reproduces the experimentally obtained binding energy. Convergence with respect to plane-wave kinetic cutoff, k-point density, and vacuum layerwidth is ensured by probing oxygen chemsiorption in a (2×2) supercell. The O chemisorption energy is converged within 0.05 eV for a plane-wave cutoff of 450 eV, a (6 × 6 × 1) k-point grid, and a 12 ˚ A vacuum separating periodic repetitions of the slab. The slab is modeled by four atomic layers, which is sufficient for converged surface energies. The lattice constant is calculated to be 4.00 ˚ A, which is determined in the bulk fcc unit-cell using a (12 × 12 × 12) k-point grid. Structures are optimized using the Atomistic Simulation Environment (ASE) 39 with the BFGS Line-Search Algorithm until all forces are below 0.05 eV/˚ A. The two bottom layers 4


Page 4 of 24

Page 5 of 24

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

ACS Catalysis

are fixed to emulate a bulk surface. Vibrational energies are determined in the Harmonic Approximation using two-point finite differences with a displacement of 0.01 ˚ A. Adsorbates are considered non spin-polarized, and adsorption energies are corrected with zero-point energies from the vibrational energy calculations. Gas-phase molecules are optimized in a (30 ˚ A × 30 ˚ A × 30 ˚ A) cell using the proper spin-states: Singlet (CO and CO2 ) and triplet (O2 ). Energy barriers are evaluated using Climbing Image Nudged Elastic Band (NEB) 40 method from the VTST tools. 41 Seven images are used, and initial interpolations are performed by the Image Dependent Pair Potential method. 42 The transition states are optimized until all forces are below 0.05 eV/˚ A.

Kinetic Monte Carlo We perform Kinetic Monte Carlo 43,44 (KMC) simulations with the First Reaction Method 43 (FRM). In the FRM, occurrence-times are generated for each possible reaction. Every reaction is executed chronologically, while updating new possible reactions after each simulationstep. The occurrence-time tβα of an event taking the system from state α to state β is evaluated by the rate-constant 45 Wβα :

tβα = t −

1 lnu Wβα

(1)

Where t is the current simulation-time, and u is a random uniform number on the interval ]0, 1]. The simulations are done by explicitly considering all sites, on a truncated octahedral nanoparticle, which is cut in half to describe the geometry of a supported particle. All the considered particles are shown in the Supporting Information. Each site is associated with a generalized coordination number CN. CN is a generalization of the conventional coordination number that additionally accounts for the coordination numbers of the nearest neighbors.

5


ACS Catalysis

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

Page 6 of 24

Each Pt atom in the outermost layer of the particle constitutes one site. All sites in the kinetic simulations have a nearest-neighbor list, which constitute a global connectivity pattern. Alternative implementations have been described previously. 46–48 The site is a coarse-grained entity containing both fcc, hcp, bridge, and ontop positions. Consequently, the detailed adsorption position is not considered in the simulations. This is an approximation, as CO and O adsorb at different sites within one coarse grained cell. As the preferred adsorptionsite of CO and O are different for Pt(111), Pt(100) and the edge sites, the scaling is done from the ontop site on Pt(111). Using the ontop site instead of the preferred adsorption site results at most in an energy difference of 0.18 eV. We study CO oxidation and the considered reactions are: adsorption and desorption of CO and O2 , reaction of CO and O to form CO2 , and adsorbate-diffusion. The reaction scheme is given by:

CO(g) + ∗ ↔ CO∗ O2 (g) + 2∗ ↔ 2O∗

(2)

CO∗ + O∗ → CO2 (g) + 2 ∗ . Rate constants for adsorption are evaluated using the expression from collision theory:

ads =√ Wi,j

si,j pi 2πMi kB T

(3)

Where i is the species, j is a site-index, pi is the pressure, si,j is the sticking coefficient, and Mi is the mass of the impinging molecule. The rate constants of adsorption events are evaluated using the sticking coefficients reported in Refs. 49,50 Thus, the sticking coefficient of O2 is 0.1 on the facets and 1 on corners and edges. Similarly, CO has a sticking coefficient of 0.9 on the facets and 1 on corners and edges. The sticking coefficients implicitly account for molecular precursor states. Rate constants for desorption are evaluated from the adsorption rate constants and the 6


Page 7 of 24

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

ACS Catalysis

equilibrium constants:

des Wi,j,α

ads Wi,j,α = , Ki,j,α

Ki,j,α

"

ads ads −Ei,j,α − T Sigas − Si,j = exp kB T

#

.

(4)

ads Ei,j,α is the adsorption energy of species i on site j with the system in state α, Sigas is the ads ideal-gas entropy of the molecule in the gas phase, Si,j is the entropy in of the adsorbed ads molecule, and Ki,j,α is the equilibrium constant. Both Sigas and Si,j are evaluated in the Harads monic Approximation, as described in Ref. 51 Ei,jα depends on the generalized coordination

number 24,25 through a scaling relation, which is fitted to results on extended surfaces. The rate constant for the reaction [CO∗ + O∗ → CO2 (g)] is calculated by Transition State Theory 52 (TST). r Wj,α

kB T Z TS exp = h Z IS

−Ej,α kB T

,

(5)

where Ej,α is the activation energy of CO oxidation on site j in state α, Z TS is the partition function of the transition state, and Z IS is the partition function of the initial state. Z IS and Z TS are evaluated on the Pt(111) surface in the Harmonic Approximation 51 from the DFTderived vibrational frequencies. Ej,α is evaluated by a BEP relation between the transition state and co-adsorbed CO and O. 12 Rate constants for diffusion are calculated by TST as in (5), and diffusion barriers of CO and O are calculated on Pt(111) in a (3x3) cell. A barrier of 0.08 eV is found for diffusing CO from the bridge to the fcc site, and a barrier of 0.58 eV is found for O diffusing from the fcc to the hcp site. In the simulations, diffusion barriers between different types of sites are adjusted by the differences in adsorption energies. KMC simulations with very different barriers are not computationally feasible, and we increase the diffusion barriers of CO while ensuring convergence (see Supporting Information). This approach has been applied previously 15,17 and was theoretically justified in Refs. 45,53–55 The reaction energies depend on the coverage and adsorbate distribution. To account for this, we include nearest-neighbor adsorbate-adsorbate interactions as a perturbation to 7


ACS Catalysis

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

the adsorption energies. The adsorbate-adsorbate interactions are calculated on the Pt(111) surface, and lowered by a factor 0.5 on the corners and edges to model geometrical effects (0.5 is the cosine of 60◦ ). For CO-CO, the repulsion is 0.19 eV per CO neighbor, for O-O it is 0.32 eV per O neighbor and for CO-O it is 0.30 eV per neighbor. The repulsions are calculated as the difference in average adsorption energy between a system with two adsorbed molecules and one molecule, both evaluated in the optimal positions (see Supporting Information). For extended Pt(111) surface, there is only one type of site with CN 7.5 for ontop and 6.94 for fcc. 24,25 Periodic boundary conditions are applied to simulate the infinite geometry of Pt(111), and the simulations are converged with respect to cell-size in a (12 × 12) cell (See Supporting Information). For each data point (temperature, pressure, particle-size), we run 16 identical simulations initiated with full CO coverage. The resulting steady-state configurations are averaged to obtain the final results, and error-bars are taken as the standard deviation between the simulations. By running different simulations for each data point a larger part of configuration space is explored as compared to running one long simulation. Table 1: Table of simulation parameters. The table shows parameters used in the Kinetic Monte Carlo simulations. CN is the generalized coordination number. Energies are in eV and vibrational energies in meV. Parameter Adsorption energy CO Adsorption energy O Reaction barrier CO-CO repulsion O-O repulsion CO-O repulsion Vibrational energies CO Vibrational energies O Vibrational energies TS CO diffusion barrier O diffusion barrier CO diffusion barrier addition Sticking coefficient CO Sticking coefficient O2

Values −1.36 + 0.252(CN − 7.5) −0.95 + 0.218(CN − 7.5) 2.95 − 0.824(EO + ECO ) 0.19 0.32 0.30 (17.8, 18.3, 36.3, 36.3, 39.7, 216.8) (47.3, 47.6, 55.1) (7.3, 19.9, 36.4, 40.4, 50.5, 54.6, 65.1, 245) 0.08 0.58 0.50 facets : 0.9, edges and corners: 1.0 facets : 0.1, edges and corners: 1.0

8


Page 8 of 24

Page 9 of 24

ACS Catalysis

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

ACS Catalysis

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

and CN. The interior of the Pt(111) surface has the highest CN and represents a limit. On the extended Pt(111) surface, RPBE predicts CO to be bridge bonded with an adsorption energy of -1.36 eV, accounting for zero-point motion. However, the site-preference is weak and the remaining sites (fcc, hcp, ontop) are within 0.07 eV of the bridge site. O prefers to bind fcc with an adsorption energy of -0.95 eV, with respect to molecular oxygen in the gas phase. The site-preference is stronger for O, which prefers fcc over hcp and bridge by 0.40 and 0.65 eV, respectively. The multiple sites on a nanoparticle results in a varying energy landscape that can be described by the CN. The linear scaling relation is shown in Figure 1 (b), where the slope is 0.25 eV for CO and 0.22 eV for O. These results are obtained using model-surfaces with various CN (see Supporting Information). The difference in ontop CN between Pt(111) facets and corners is 3.25, which corresponds to an adsorption energy difference of 0.81 eV for CO and 0.72 eV for O. Thus, the geometrical site-distribution influences the reaction landscape significantly. A molecule that initially adsorbs on an inner-terrace site will diffuse to the outer terrace, further to the edge, and finally occupy corner sites. Consequently, the undercoordinated sites should have a higher average coverage than facet-sites. The expression for the adsorption energies used in the simulations is given in Table 1. The adsorption energies on the particle determine the transition state energy for CO2 formation. In Figure 1 (c), the transition state energy is given with respect to the binding energies of CO and O. The linear correlation constitutes a Brønsted-Evans-Polanyi (BEP) relation with a slope of 0.82. The BEP relation was obtained by straining (100), (111) and (211) surfaces and linear regression. In addition to the unstrained Pt(111), Pt(100) and Pt(211), Pt(111) was considered with 1, 2 and 3 % compressive strain and Pt(100) with 1 and 2 % compressive strain. The reaction barrier is 1.08 eV on unstrained Pt(111), with respect to CO and O in separate cells. Using this reference and the BEP relation, the barrier is corrected for adsorbate-adsorbate interactions during the simulations. The fact that the three considered surfaces fall on the same line suggests that the detailed structure

10


Page 10 of 24

Page 11 of 24

ACS Catalysis


ACS Catalysis

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

on nanoparticles and address the effect of particle size. By comparisons with the extended Pt(111) surface, it is possible take a step towards bridging the materials-gap. We start by analyzing the the Turnover Frequency (TOF), which is a fundamental measure of the catalyst performance and enables comparison between catalysts with a different number of active sites. The TOF is shown with respect to temperature in Figure 2 for two particle sizes and the extended Pt(111) surface. The particle sizes are 2.8 nm and 3.6 nm (dispersion of about 35%), which correspond to typical sizes present in a technical catalyst. For both surfaces and nanoparticles, the TOF shows a typical light-off behavior where a certain temperature is required before the reaction starts. The nanoparticle-TOF ranges between 0 at low temperatures and 106 s−1 site−1 above 1100 K. At temperatures above 1200 K, the TOF declines slowly with increasing temperature. The Pt(111) surface has a TOF between 0 and 103 s−1 site−1 , and the TOF declines more rapidly above 1200 K with increasing temperature. The surface and nanoparticles have a similar TOF below 600 K, where the value varies between 0 and 102 s−1 site−1 . However, above 800 K the TOFs for the nanoparticles and Pt(111) differ by three orders of magnitudes. The large difference in TOF between the nanoparticle and Pt(111) is owing to the existence of different types of sites on the nanoparticle, which is an obvious consequence of the finite size. The difference of three orders of magnitudes in TOF is remarkable, and shows that reaction kinetics on nanoparticles is difficult to capture with extended surfaces. The fact that nanoparticle kinetics differs from the superposition of the individual facets was also emphasized in Ref. 21,22 The slow decrease of the TOF on nanoparticles with temperature is an effect of the high adsorption energies on low-coordinated sites such as edges and corners. Thus, the multitude of different sites on a nanoparticle prevent the reaction from becoming adsorption-limited. This is the reason for high activity over a wider temperature interval than on the extended Pt(111) surface. The faster declination on Pt(111) is an effect of the low coverage on highcoordinated sites at elevated temperatures. To unravel the origin of the catalytic activity, the site-specific coverages is a natural

12


Page 12 of 24

Page 13 of 24

ACS Catalysis


ACS Catalysis

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

starting point. Figure 3 shows the coverages of CO (top) and O (bottom) as a function of temperature for a 2.8 nm particle and extended (111) surface. Generally, the CO coverages span the entire range between 0.00 and 0.99. The coverages are ordered by CN: The (111) surface and (111) facet on the nanoparticle have the lowest coverage, the (100) has a higher coverage, and edges and corners have the highest coverage. Furthermore, the temperature required to desorb CO completely varies with over 700 K between the sites. When a sufficient amount of CO has desorbed, oxygen has free sites for dissociation. The CN determines the maximal O coverage, which is lowest for the (111) surface, higher on (100), and finally highest for the edges and corners. The difference in CO coverage is small for nanoparticles and Pt(111). For O, however, the coverage is significantly larger on the extended (111) surface as compared to the (111) facet on the nanoparticle, which is due to the higher TOF on the nanoparticle that rapidly converts oxygen to CO2 . The coverages and TOFs vary with temperature, which signals that the active site changes with temperature on the nanoparticle. As the reaction requires both CO and O to proceed, facets are expected to be active at low temperatures, whereas edges and corners are expected to be active at high temperatures.

Reaction Regimes The significantly different coverages on the sites suggest a difference in the kinetic behavior of these sites. Therefore it becomes interesting to analyze which sites are responsible for the catalytic activity and how this changes with reaction conditions. In Figure 4, the catalytic activity for the 2.8 nm particle is plotted at a temperature above light-off (850 K) as a function of pressure and CN. The result is also represented by coloring of the nanoparticle. To facilitate comparisons between different pressures, the activity is normalized to the maximal activity at each pressure. The activity is, furthermore, divided by the number of sites of the given CN to compare sites of different abundances. Corners are the most active sites below 10−2 mbar, whereas edges are highly active from 10−1 14


Page 14 of 24

Page 15 of 24

ACS Catalysis


ACS Catalysis


Page 16 of 24

Page 17 of 24

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

ACS Catalysis

mbar. At high pressures, both edges and (111) facet sites are active. We note that highcoordinated sites are inactive at low pressures, which is caused by low adsorbate-coverages at the given reaction conditions. At higher pressures, the facets and edges are the only active sites because the corners are poisoned. Figure 4 shows that a CN of 6.69 has a low activity at all pressures. This CN corresponds to the outer-perimeter of the (111) facets. The relatively low TOF of this site is due to rapid adsorbate-diffusion to other sites, before forming CO2 with an adsorbate on a neighboring site. At a fixed pressure, the most active sites change with temperature. Commercial emission control catalysts typically have a size distribution centered around 2 nm for aged catalysts. 56 Therefore, it is interesting to investigate the kinetic behavior at various sizes. Figure 5 shows the TOF for particle sizes in the range from 1.2 to 5.2 nm at two pressures: 10−3 mbar and at 101 mbar. At 10−3 mbar, the total TOF originates from edges and corners, and declines with particle size. At 101 mbar, the total TOF primarily comes from edges and facets and grows instead with particle size. The size dependence of the TOF is related to differences in coverages on the facets. At the considered temperature (850 K), a pressure of 10−3 mbar is too low to sustain CO and O coverages, which makes the facets inactive. The fact that the TOF depends on particle diameter means that a hierarchy of most active particle-sizes exists. At low pressures, smaller particles are more efficient as they have a larger fraction of corner and edges. However, at high pressures large particles have a higher TOF thanks to the contribution from (100) and (111) facets. It should be noted that the TOF is calculated per active site, and not per gram Pt, which makes large particles more expensive to fabricate. The obtained hierarchy of active particle sizes agrees with the findings of Ref. 57 that observed a size-dependent activity-hierarchy of active species in Au catalysts for CO oxidation. The effect for Pt particles is not as pronounced as for Au particles as only lower-coordinated sites are active on Au. Geometrical finite-size effects cause a difference between nanoparticle-facets and extended surfaces that depends on reaction conditions. At 101 mbar and 850 K, the TOF of the (111)

17


ACS Catalysis

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

facet of the 1.2 nm particle is 4.5 × 103 s−1 site−1 whereas the TOF on the extended Pt(111) surface is 1.2 × 103 s−1 site−1 . Lowering the pressure to 10−3 mbar yields a completely inactive nanoparticle-facet, whereas the extended surface has a TOF of 0.12 s−1 site−1 . The zero contribution from facets to the activity of the particle is due diffusion of adsorbates to the corners and edges. This observation emphasizes that nanoparticle facets behave fundamentally different than extended surfaces, which is in agreement with previous simulations using schematic reaction landscapes. 21,22 When discussing how the TOF scales with particle-size, a distinction should be made between geometrical finite-size effects and electronic finite-size effects. Our results highlight the importance of geometrical finite-size effects. In addition to the geometrical effects, electronic finite-size effects may affect the reactivity at sizes below ∼1.5 nm. 20

Conclusions In this paper, we have taken a step towards bridging the materials-gap, by modeling CO oxidation kinetics over Pt nanoparticles with a Scaling Relation Monte Carlo (SRMC) method. The reaction energies were obtained with Density Functional Theory calculations using the scaling relation of adsorption energies in the generalized coordination number, and the kinetics was investigated using Kinetic Monte Carlo simulations. The SRMC method enables us to simulate the kinetics of nanoparticle catalysis and to investigate the active sites as a function of reaction conditions. Taking the detailed energy landscape into account implies that the thermodynamic and kinetic relationships on the various sites can be described. The simulations reveal that the kinetic behavior on nanoparticles and extended surfaces is fundamentally different. The nanoparticles are more active than extended surfaces, which is related to the presence of both high and lowcoordinated sites. When the activity of the facets is limited by adsorption, the edges and corners dominate the reaction, whereas the reaction proceeds over the facets when the edges

18


Page 18 of 24

Page 19 of 24

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

ACS Catalysis

and corners are poisoned. Thus, the reaction is not adsorption-limited on the nanoparticle as opposed to the extended Pt(111) surface. The results demonstrate that extended surfaces cannot fully capture the dynamics of catalytic reactions on nanoparticles. The simulations predict different reaction regimes for the CO oxidation reaction. At low pressures or high temperatures, the reaction proceeds over corners and edges. At high pressures or low temperatures, the reaction proceeds most rapidly on the facets and edges. Investigation of the size dependence reveals a hierarchy of most active particle-sizes: Small particles yield the highest Turnover Frequency (TOF) at low pressures, whereas the large particles give the highest TOF at high pressures. The present work provides insight into the dynamics of catalysis on metallic nanoparticles, and take a step towards bridging the materials-gap. Moreover, the results provide information to enhance understanding of chemical reactions on nanoparticles, and can be useful in future catalyst design based on atomistic understanding.

Acknowledgement Financial support is acknowledged from Chalmers Area of Advance Nanoscience and Nanotechnology and the Swedish Research Council. The calculations were performed at PDC (Stockholm) and C3SE (Göteborg) via a SNIC grant. The Competence Centre for Catalysis (KCK) is hosted by Chalmers University of Technology and is financially supported by the Swedish Energy Agency and the member companies AB Volvo, ECAPS AB, Haldor Topsøe A/S, Scania CV AB, Volvo Car Corporation AB, and Wärtsilä Finland Oy.

Supporting Information Available Details on coverage dependence of adsorbate energies. Elaboration on scaling-relation calculations. Kinetic Monte Carlo simulation convergence tests. of charge via the Internet at http://pubs.acs.org/.

19


This material is available free

ACS Catalysis

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

References (1) Royer, S.; Duprez, D. ChemCatChem 2011, 3, 24–65. (2) Larsen, J. H.; Chorkendorff, I. Surf. Sci. Rep. 1999, 35, 163–222. (3) Libuda, J.; Meusel, I.; Hoffmann, J.; Hartmann, J.; Piccolo, L.; Henry, C. R.; Freund, H.-J. J. Chem. Phys. 2001, 114, 4669–4684. ¨ (4) Osterlund, L.; Grant, A. W.; Kasemo, B. Lithographic Techniques in Nanocatalysis. In Nanocatalysis; Heiz, U., Landman, U., Eds.; Springer: Berlin, 2007; p. 269–341. (5) Papp, C. Catal. Lett. 2017, 147, 2–19. (6) Nørskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H. Nat. Chem. 2009, 1, 37–46. (7) Hammer, B.; Nørskov, J. K. Adv. Catal. 2000, 45, 71–129. (8) Hammer, B.; Nørskov, J. K. Nature 2002, 376, 238–240. (9) Jørgensen, M.; Grönbeck, H. ACS Catal. 2016, 6, 6730–6738. (10) Van den Bossche, M.; Grönbeck, H. J. Am. Chem. Soc. 2015, 137, 12035–12044. (11) Honkala, K.; Hellman, A.; Remediakis, I. N.; Logadottir, A.; ans S. Dahl, A. C.; Christensen, C. H.; Nørskov, J. K. Science 2005, 307, 555–558. (12) Falsig, H.; Hvolbæk, B.; Kristensen, I. S.; Jiang, T.; Bligaard, T.; Christensen, C. H.; Nørskov, J. K. Angew. Chem., Int. Ed. 2008, 47, 4835–4839. (13) Heard, C. J.; Hu, C.; Skoglundh, M.; Creaser, D.; Grönbeck, H. ACS Catal. 2015, 6, 3277–3286. (14) Loffreda, D.; Delbecq, F.; Vigné, F.; Sautet, P. Angew. Chem., Int. Ed. 2005, 44, 5279–5282. 20


Page 20 of 24

Page 21 of 24

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

ACS Catalysis

(15) Yang, L.; Karim, A.; Muckerman, J. T. J. Phys. Chem. C. 2013, 117, 3414–3425. (16) Rogal, J.; Reuter, K.; Scheffler, M. Phys. Rev. B. 2008, 77, No. 155410. (17) Piccinin, S.; Stamatakis, M. ACS Catal. 2014, 4, 2143–2152. (18) Yudanov, I. V.; Sahnoun, R.; Neyman, K. M.; Rösch, N. J. Phys. Chem. B. 2003, 107, 255–264. (19) Kleis, J.; Greeley, J.; Romero, N. A.; Morozov, V. A.; Falsig, H.; Larsen, A. H.; Mortensen, J. J.; Dulak, M.; Thygesen, K. S.; Nørskov, J. K.; Jacobsen, K. W. Catal. Lett. 2011, 141, 1067–1071. (20) Li, L.; Larsen, A. H.; Romero, N. A.; Morozov, V. A.; Glinsvad, C.; Abild-Pedersen, F.; Jacobsen, K. W.; Nørskov, J. K. J. Phys. Chem. Lett. 2013, 4, 222–226. (21) Zhdanov, V. P.; Kasemo, B. Surf. Sci. 1998, 405, 27–37. (22) Persson, H.; Thormählen, P.; Zhdanov, V. P.; Kasemo, B. J. Vac. Sci. Technol. A 1999, 17, 1721–1726. (23) Nikbin, N.; Austin, N.; Vlachos, D. G.; Stamatakis, M.; Mpourmpakis, G. Catal. Sci. Technol. 2015, 5, 134–141. (24) Calle-Vallejo, F.; Mart´ınez, J. I.; Garc´ıa-Lastra, J. M.; Sautet, P.; Loffreda, D. Angew. Chem., Int. Ed. 2014, 53, 8316–8319. (25) Calle-Vallejo, F.; Loffreda, D.; Koper, M. T. M.; Sautet, P. Nat. Chem, 2015, 7, 403– 410. (26) Engel, T.; Ertl, G. J. Chem. Phys. 1978, 69, 1267–1281. (27) Campbell, C.; Ertl, G.; Kuipers, H.; Segner, J. J. Chem. Phys. 1980, 73, 5862–5873.

21


ACS Catalysis

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

Page 22 of 24

(28) Vogel, D.; Spiel, D.; Suchorski, Y.; Trinchero, A.; Schlögl, R. Angew. Chem., Int. Ed. 2012, 51, 10041–10044. (29) Wrobel, R. J.; Becker, S.; Weissv, H. J. Phys. Chem. C 2012, 116, 22287–22292. (30) Ertl, G.; Norton, P. R.; R¨ ustig, J. Phys. Rev. Lett. 1982, 49, 177–180. (31) Zhdanov, V. P.; Kasemo, B. J. Catal. 2003, 214, 121–129. (32) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169–11186. (33) Kresse, G.; Furthmuller, J. Comp. Mater. Sci. 1996, 6, 15–50. (34) Kresse, G.; Hafner, J. Phys. Rev. B. 1993, 47, 558–561. (35) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775. (36) Blöchl, P. Phys. Rev. B 1994, 50, 17953–17979. (37) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Phys. Rev. B 1999, 59, 7413–7421. (38) Feibelman, P.; Hammer, B.; Nørskov, J. K.; Wagner, F.; Scheffler, M.; Stumpf, R.; Watwe, R.; Dumesic, J. J. Phys. Chem. B 2001, 105, 4018–4025. (39) Bahn, S. R.; Jacobsen, K. W. Comput. Sci. Eng. 2002, 4, 56–66. (40) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. J. Chem. Phys. 2000, 113, 9901–9904. (41) Henkelman

Group

at

the

University

of

Texas

at

Austin

Home

Page.

http://theory.cm.utexas.edu, (accessed Nov 16, 2015). (42) Smidstrup, S.; Pedersen, A.; Stokbro, K.; Jónsson, H. J. Chem. Phys. 2014, 140, No. 214106. (43) Gillespie, D. T. J. Comput. Phys. 1976, 22, 403–434. (44) Fichthorn, K. A.; Weinberg, W. H. J. Chem. Phys. 1991, 95, 1090–1096. 22


Page 23 of 24

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

ACS Catalysis

(45) Jansen, A. P. J. An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions; Springer: Berlin, 2012; p. 162–163. (46) Kunz, F. M., L. Kuhn; Deutschmann, O. J. Chem. Phys. 2015, 143, No. 044108. (47) Hoffmann, M. J.; Matera, S.; Reuter, K. Comput. Phys. Commun. 2014, 185, 2138– 2150. (48) Stamatakis, M.; Vlachos, D. G. J. Chem. Phys. 2011, 134, No. 214115. (49) Campbell, C.; Ertl, G.; Kuipers, H.; Segner, J. Surf. Sci. 1981, 107, 207–219. (50) Yeo, Y.; Vattuone, L.; King, D. J. Chem. Phys. 1997, 106, 392–401. (51) Jørgensen, M.; Grönbeck, H. J. Phys. Chem. C 2017, 121, 7199–7207. (52) Eyring, H. Chem. Rev. 1935, 17, 65–77. (53) Stamatakis, M.; Vlachos, D. G. Comput. Chem. Eng. 2011, 35, 2602–2610. (54) Chatterjee, A.; Voter, A. F. J. Chem. Phys. 2010, 132, No. 194101. (55) Dybeck, E. C.; Plaisance, C. P.; Neurock, M. J. Chem. Theory Comput. 2017, 13, 1525–1538. (56) Pingel, T. N.; Fouladvand, S.; Heggen, M.; Dunin-Borkowski, R. E.; Jäger, W.; Westenberger, P.; Phifer, D.; McNeil, J.; Skoglundh, M.; Grönbeck, H.; Olsson, E. ChemCatChem 2017, doi: 10.1002/cctc.201700479. (57) He, Q.; Freakley, S. J.; Edwards, J. K.; Carley, A. F.; Borisevich, A. Y.; Mineo, Y.; Haruta, M.; Hutchings, G. J.; Kiely, C. J. Nat. Commun. 2016, 7, No. 12905.

23


ACS Catalysis


Page 24 of 24

Scaling Relations and Kinetic Monte Carlo Simulations To Bridge the

Recommend Documents