Atomistic Adsorption of Oxygen and Hydrogen on Platinum Catalysts

Article pubs.acs.org/JPCC

Atomistic Adsorption of Oxygen and Hydrogen on Platinum Catalysts by Hybrid Grand Canonical Monte Carlo/Reactive Molecular Dynamics Lili Gai,† Yun Kyung Shin,† Muralikrishna Raju,‡ Adri C. T. van Duin,† and Sumathy Raman*,§ †

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States § ExxonMobil Research and Engineering Co., 1545 Route 22 East, Annandale, New Jersey 08801, United States S Supporting Information *

ABSTRACT: The reactivity of a metal catalyst depends strongly on the adsorbate coverage, making it essential for the reactivity models to account for the in situ structures and properties of the catalyst under reaction conditions. The use of first principle based thermodynamic approaches to describe adsorbate−adsorbate interaction though attractive for its technical rigor is tedious and computationally demanding especially for metal nanoparticles. With the advent of empirical reactive force fields (ReaxFF), there is a great deal of interest to advance simulation approaches like hybrid grand canonical Monte Carlo reactive molecular dynamics (GCMC/RMD) that enable efficient use of ReaxFF to model the adsorptive states. The predictive ability of GCMC/RMD relies upon the quality of the force field, which in turn depends upon the training set used for its parametrization. To this end, we investigate the adsorption behavior of O and H over the Pt catalysts using the newly developed Pt/O/H ReaxFF. We assess the thermodynamic stability of Pt-adsorbates by GCMC/RMD and provide insight on the atomic composition of in situ catalysts. The theoretical adsorption isotherms of O and H are derived in many Pt surfaces over a wide range of reference gas pressures (e.g., 10−20 atm to 10 atm) relevant to the observed real catalysis, including the Pt(111), unreconstructed and reconstructed Pt(110) surfaces, and even Pt nanoparticles of different sizes and shapes. The force field is further evaluated to predict the relative binding energies of O on Pt(321) surface, while it has not been trained for this kinked surface. For both oxygen and hydrogen atoms, adsorption occurs initially at the Pt surface, followed by subsurface and bulk. Examination of the equilibrated structures discloses the contribution of different sites on the surface, subsurface, and the bulk regions during adsorption at various applications. The adsorption behavior obtained in this paper agrees with the DFT and/ or the experimental data reported in the literature, which validates the Pt/O/H ReaxFF and demonstrates its applicability in catalytic reactions coupled with time acceleration tools. Based on the derived adsorption isotherm, one can infer the relative affinity of O, H, or OH species, and thus prepare appropriate structures at the specified reaction conditions for further investigation of the catalytic reactions by molecular dynamics and for designing experimental conditions for optimal catalyst performance.

1. INTRODUCTION Platinum has a special place in surface science and catalysis due to its ability to perform both oxidizing and reducing reactions without losing its metallic character and has been widely applied in various industrially important reactions, such as hydrocarbon oxidation and dehydrogenation, reduction of automobile exhaust gases,1 fuel cells,2 and reforming in petroleum industry.3 The reactivity of a catalyst is often a strong function of the coverage of adsorbates. Oxidation activity, for example, has been related with different metal− oxygen surface states (i.e., surface adsorbed oxygen, surface oxide films, and even bulk metal oxides) for many metallic catalysts involving Ru,4−7 Ag,8,9 Pd,10,11 and Pt.12−14 Similarly, © XXXX American Chemical Society

the affinity between hydrogen and metal catalysts is also of great significance in chemical processes including hydrogenation, hydrogenolysis, and dehydrogenation, and subsurface hydrogen is shown to be important, especially in hydrogenation reactions on Pd and Ni nanoparticles.15−19 Compared to monometallic catalysts, alloys offer additional opportunities for catalyst development. Alloys can show distinct chemical properties and electronic structures that do not belong to either of their parent metals. Specifically, the Received: January 31, 2016 Revised: April 17, 2016

A

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short-range pair interactions, long-range and multibody effective interactions to capture the behavior of minority adsorbate species that are expected to be essential reaction intermediates. Due to the required computational resources, quantum mechanical description of systems with those first-principlebased modeling techniques are still limited to small systems of typically a hundred atoms. The steady state DFT investigations involve repeated computations of extensive potential energy surfaces for each of the potentially feasible catalyst surface structures and coverages, and it still cannot account for surface reconstruction or environmentally induced segregation, unless the researcher has a strong chemical insight into explicitly consider such starting configurations. Alternatively, ab initio derived force field based techniques, in particular the class of bond-order dependent reactive force fields (ReaxFF)44−46 are becoming attractive, as they are able to describe reactions and provide reasonably accurate energetics, reaction barriers, and structures for larger molecules or surfaces with reduced symmetry at a small fraction of the computational cost. In addition, the reactive force fields are potentially promising because of their high transferability. For example, Pt/H parameters developed here are fully transferable with previously developed Pt/O parameters, making them extendable to a Pt/ O/H system or a future Pt/C/H/O system describing hydrocarbon or even the simple CO oxidation on Pt catalysts. In addition, this also exemplifies the fact that the force field development is modular in nature, and in doing so, efforts are made especially to preserve the Pt/O and Pt/H force field parameters intact. Similarly, the Pt/O/H force field will be merged further with the Pt/C force field to obtain Pt/C/H/O force field without impacting the parameters of both sets. Newly added cross terms will account for the added interactions in the Pt/C/H/O force field. The ReaxFF bond-order dependent formalism combines the bond order concept with a geometry-dependent, polarizable charge calculation, enabling the description of all possible bonding scenario viz., covalent, metallic, and/or ionic bonds. This capability, if successful, has a potential to improve the interactions among researchers and increase the leveraging of modeling and characterization data during the course of catalyst development. For the organic systems involving covalent bonds among carbon, hydrogen and oxygen, the ReaxFF C/H/O force field has demonstrated its ability to describe the singly, doubly, triply bonded carbons, allenic, ketenic, and aromatic carbons, ring fusion carbons with added terms, where needed, in the energy expression.47 This highlights the fact that force field development should be general and not focused on a particular system. However, it should be tested for a particular application in mind by comparing its prediction with high-level DFT results. The existing literature on ReaxFF highlights the need for force field validation and potential retraining as a first step in any application of ReaxFF. Essentially, the transferability of ReaxFF is dependent on the comprehensiveness of the training data set used in its development. If the training set, for example, only contains structures and energies related to surface-chemistry, the affiliated ReaxFF parameters may not necessarily be reliable for bulk materials, and as such should be validated for such systems before its application. Considering the complexity of viable local bonding/coordination environments around a metal surface, subsurface or oxide interface, it is worthwhile understanding the strengths and challenges of the two options, namely, (i) having an extended training set

geometries of the alloy structures might be changed due to the formation of heteroatom bonds and the new average metal− metal bond length.20 The surfaces of the alloy are often rough with inborn strain effects and associated with relaxations, reconstructions, and segregation.21 These unique properties may result in enhanced activity or selectivity, as is exemplified by a recent study on catalyst development for the oxygen reduction reaction (ORR), which shows 1 order of magnitude increase in ORR activity on the Pt3Ni(111) surface compared to a pure Pt(111) surface.22 In addition to the extended surfaces, finely dispersed nanoparticles emerge as attractive alternatives to improve the catalytic performance.21,23 Nanoparticles provide an increased surface area for catalytic reactions compared to bulk materials. Besides this relatively straightforward benefit, the use of nanoparticles introduces additional factors to consider while rationalizing their catalytic activity, including the heterogeneous surface sites (different on facets, steps and edges), quantum size effects, and various particle shapes.23−26 Consequently, it is essential to understand the compositions, properties and especially the conditions associated with different adsorbate coverages for developing correct models of surface reactivity qualitatively and quantitatively. In recent years, experiments and theory together have provided a wealth of insight into the complex relationship between the compositions of transition metals and their catalytic reactivity. High symmetry metal facets such as (111) and (100) are the convenient models of real catalysts. Consequently, they have been studied more often than the lower symmetry stepped or kinked surfaces by both surface science experiments and modeling using density functional theory (DFT). Equilibrium models are often employed to infer on surface compositions and reaction steps relevant to observed catalysis, although they do not fully depict the dynamic surfaces under reaction conditions.27 Comparing with bulk material surfaces, nanoparticles present additional complexity, since there is a larger number of diverse adsorption site types available (such as different facets, edges and corners), which results in a wider range of adsorbate interactions requiring to be addressed. The current theoretical evidence of the shape and size effects on nanoparticle activity is deduced from ideal surface models and hypothetical coverages of adsorbates.28,29 A more direct explanation requires information on the adsorbate distribution on the nanoparticle, which is not straightforward from experiments and/or DFT modeling. Such a direct explanation would require simulating the binding, diffusion and reactions of adsorbates under realistic catalytic operation conditions using a simulation technique that can account for adsorbate−adsorbate interactions.30 In the first principle based simulations related to this topic,27 DFT calculations are utilized to quantify the thermodynamics of different surface compositional states, with a correlation to the gas phase composition.31 Although this approach allows the study of thermodynamics of much adsorbate behavior such as oxygen on Pt, Pd, Ag, and Ru surfaces,5,9,32−35 metal oxide films, bulk oxides of Pd, Pt, and Cu,36−39 and hydrogen into the subsurface and bulk regions of Ni, Pd, Ru, and Pt systems,15−19,40−42 the clarification of many relevant coverage states remains as a challenge for any specific system. On the other hand, the computationally intensive, cluster expansion method (CE) has been applied to construct effective adsorbate−adsorbate interactions on nanoparticles and predict adsorption isotherms for nanocatalysts.28,30,43 CE considers B

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The Journal of Physical Chemistry C upfront and aiming for a more comprehensive force field or (ii) starting with a more focused training set, and performing forcefield retraining and validation as a routine initial process in any ReaxFF application. Historically, the second option, continuous force-field retraining, has often been employed as it reduces the initial effort for force field development. In spite of the significant ReaxFF literature, the lack of understanding in the retraining process can be daunting for new users of this method. In this work, en route to exploring the first comprehensive, option, we have developed the Pt/H ReaxFF parameters and combined with Pt−O and Pt−Pt parameters from Fantauzzi et al.,48 and evaluate the applicability of the Pt/O/H reactive force field in predicting (i) the binding energies of O and H in both high coordination and low coordination steps and kink surfaces (Pt(321)); (ii) the adsorption isotherms of O and H on Pt(111), Pt(110) surfaces and Pt nanoparticles of different sizes and shapes using the GCMC/RMD technique.49 We explore both systems that are representative for the systems included in the training set and the coordinations that lie outside the training set (Pt(321)) to fully enhance the predictive power of this empirical force field. In the following section, we summarize the earlier work on the development of Pt/O and Pt/H ReaxFF. The subsequent section describes briefly the ReaxFF formalism, GCMC/RMD technique and the methodology for deducing XRD spectra. The Results and Discussion section covers a validation of binding energies of O and H at various Pt surface sites and provides an indication of additional data needed for retraining to improve the predictive power. This is followed by the GCMC/RMD results and the derived adsorption isotherms of O and H on relevant Pt systems. 1.1. History of the ReaxFF Pt/O and Pt/H Force Field Parametrization. The ReaxFF Pt/O force field was initially described by Valentini et al.,50 aiming for studying the adsorption dynamics of molecular oxygen on the Pt(111) surface. The training set is relatively limited and includes the equations of state and heats of formation for PtO and PtO2 condensed phases, binding energies of O on typical Pt(111) surface sites (top, bridge, fcc, and hcp sites), binding energy of O2 molecule, and dissociation barriers. The Pt−Pt and Pt/O interactions were described in the training set using two different levels of DFT. The author51 further computed the adsorption isotherms on the Pt(111) facet by standard GCMC method with the Pt/O ReaxFF reoptimized to explicitly include the lateral interaction energies and improve the binding energy of oxygen atom. The Pt/O force field was subsequently retrained by Fantauzzi et al.,48 with a more rigorous training set and a consistent level of DFT-PBE for both Pt−Pt and Pt−O parameters. The training set for Pt−Pt interaction contains equations of state for fcc, hcp, bcc, simple cubic, diamond, and β-tungsten bulk phases of Pt and accurately accounts for atomic structure, material properties and relative formation energies of bulk Pt phases. In addition, they demonstrated the transferability of Pt−Pt parameters by computing the surface energies of low Miller-index surfaces with their relative thermodynamic stability as (111) > (100) > (110). The Pt−O parameters were optimized to reliably describe various bulk platinum oxides, i.e., α-PtO2, β-PtO2, PtO, and Pt3O4, and oxygen behavior on Pt(111) terraces and the {111} and {100} steps connecting them (modeled by Pt(221) and Pt(335)). Additional training was performed to quantify the influence of coverage on the

binding energy of fcc-adsorbed oxygen on the Pt(111) surface, with p(3 × 3), p(2 × 2), (√3 x √3)R30, and p(2 × 1) overlayer structures included. The transferability of Pt−O parameter was demonstrated using oxygen diffusion profile comparison from nudged elastic band calculations using DFT, diffusion barriers, and relevant diffusion coefficients. The ReaxFF Pt/H force field was described by Ludwig et al.52 by parametrizing Pt−Pt and Pt−H interactions based on DFT calculations. The DFT data set also contains equations of states for various phases of Pt metal (e.g., fcc, bcc, a15, simple cubic and diamond phases), binding energy for Pt3 to Pt35 clusters, hydrogen binding energy at Pt(111) surface sites, bond dissociation energy of H−Pt in (H3N)2PtHCl, H2 dissociative adsorption on a flat Pt12 cluster, and H2 dissociation and formation. The author calculated the thermodynamic stability of hydrogen dissociated on various Pt surfaces e.g., Pt(111), Pt(100), Pt(110), Pt(211), Pt(311), Pt(331), Pt(332), and Pt(533), which verified that the Pt/H force field is capable of predicting qualitatively energetics for systems beyond the data included in the training set. The Pt/O parameters by Fantauzzi et at.48 are used in this work as the basis for Pt/H force field development. We kept the Pt−Pt and Pt−O terms fixed−ensuring complete transferability with the Fantauzzi et al. Pt/O ReaxFF results. Because the ReaxFF parameters for the Pt interaction have been redescribed in the Pt/O force field, to obtain a combined Pt/ O/H force field, the Pt/H interaction with new Pt parameters are reparameterized to reproduce a DFT data set for Pt/H systems, including the hydrogen binding energy on Pt(111) surface and subsurfaces, and the hydrogen coverage dependentbinding energy on Pt(111).

2. THEORY AND METHODS 2.1. ReaxFF Method. The ReaxFF force field utilized in the present work was developed to help bridge the gap between the quantum chemical (QC) methods and the experiment. ReaxFF is a bond order dependent force field with instantaneous connectivity for the chemical bonds that are formed or broken from the atomic local environment and is suitable to examine the energetics of various chemical reactions. In the ReaxFF formalism, the overall system energy is described by physically meaningful many-body empirical potential terms such as the bond, angle, torsion, and the long-range interaction terms such as van der Waals and Coulomb interactions using a bond-orderdependent potential energy formulation in conjunction with time-dependent, polarizable charge descriptions, to continuously describe bond formation and cleavage in a wide range of chemical environments. The dependence of these energy contributions on bond order ensures that the overall system energy is a continuous function of the interatomic distances, so that there are no discontinuities as bonds or other potential energy contributions vanish or appear. Furthermore, it ensures that the potential energy surface is differentiable, thus enabling direct calculation of interatomic forces. The full expressions for each of these terms are best described in the ReaxFF hydrocarbon work by Chenoweth et al.47 All force field parameters describing energy terms are optimized against the DFT data using a single-parameter based parabolic extrapolation method. 2.2. DFT Calculations. To construct the ReaxFF training set for the Pt/O/H force field parametrization, we performed DFT calculations, by employing the Vienna ab initio simulation package (VASP), a periodic DFT code with localized basis sets C

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compiled as the external routine called by the in-house GCMC code.59 LAMMPS is highly parallelized and thus better for simulations of fairly massive systems, compared to the stand-alone ReaxFF used by Senftle et al.49,55 Energy minimization is conducted with a conjugate gradient relaxation of forces, with a convergence criteria of 0.5−1 kcal/mol between steps.49,55 As can be seen from the flowchart in Scheme 1, the hybrid GCMC/RMD method is consisted of the following steps: (1) perform a MC trial move, (2) energy minimization in LAMMPS, (3) accept or reject new coordinates generated after energy minimization, and (4) iterate until the system energy converges at equilibrium. Specifically, the following MC moves are performed in the GCMC/RMD method: (1) insertion of an adsorbent atom into the system at a random position, (2) deletion of a randomly selected adsorbent atom, and (3) displacement of an adsorbent atom to a new random position. The above MC trial moves are accepted or rejected based on the following criteria:

comprised of linear combinations of Gaussian functions, within the generalized gradient approximation (GGA) exchangecorrelation functional developed by Perdew, Burke and Ernzerhof (PBE).53 Core states were described using the projector augmented wave (PAW) method.54 The energy cutoff is 600 eV and a 3 × 3 × 1 Monkhorst−Pack mesh is used for kpoint sampling. Spin polarization is employed to describe properly the magnetic structure of the metal system. For the calculation of hydrogen binding energy on Pt(111) surface and subsurface layer, a p(2 × 2) Pt(111) slab with seven layers is constructed. This corresponds to a surface coverage (θ) of 1/4 ML when there is one adsorbate per unit cell. In order to examine the effect of hydrogen coverage on the energetics of the Pt(111) surface, the surfaces including one, two, three and four surface hydrogen atoms on top site are considered, which corresponds to the surface coverage of 0.25, 0.50, 0.75, and 1.0 ML. For the construction of surfaces with lower hydrogen coverage (0.0625 ML), a 4 × 4 supercell with one surface hydrogen atom is used. The slab surface is separated by a vacuum space of 10 Å thick. Adsorption is allowed on only one surface, and the adsorbate and the four top layers of the slab are relaxed in the calculations for the binding energy of hydrogen on Pt(111) surface. 2.3. Grand Canonical Monte Carlo/Reactive Molecular Dynamics (GCMC/RMD). To investigate the atomic gas adsorption behavior on various Pt systems, we performed hybrid GCMC/RMD simulations with the developed Pt/O/H ReaxFF. This GCMC/RMD approach was introduced earlier by Senftle et al. and utilized successfully to investigate the gas adsorption behavior on palladium.49,55 The ensemble used is μVTNPt, with constant temperature (T), volume (V), gas chemical potential (μ), and number of Pt atoms. In the hybrid GCMC/RMD method, MD-based energy minimization using ReaxFF is performed after every MC trial move to relax the whole system before applying the acceptance criteria, as shown schematically in Scheme 1. According to the previous study49,55

⎧ ⎫ V exp[−β(Enew − Eold − μ)]⎬ Pinsertion = min⎨1, 3 ⎭ ⎩ Λ (N + 1) (1)

⎧ N Λ3 ⎫ exp[−β(Enew − Eold + μ)]⎬ Pdeletion = min⎨1, V ⎭ ⎩

(2)

Pmove = min{1, exp[−β(Enew − Eold)]}

(3)

where V is the volume of the system, N is the number of exchangeable atoms in the system before the MC move, Λ is the thermal de Broglie wavelength of the adsorbent atoms, β is the Boltzmann factor given by β = 1/(kbT), Eold is the potential energy of the system before the MC trial move, Enew is the potential energy of the system after the energy minimization, and μ is the chemical potential of the particle reservoir. In this study, μ for atomic gas is related to T and P by the following equation:

Scheme 1. Flow Chart of the Hybrid GCMC/RMD Method

1 (μ (T , p)) 2 X2 ⎤ ⎛ pX ⎞ 1⎡ = ⎢μ X (T , p0 ) + kBT ln⎜ 02 ⎟ − Ed ⎥ ⎥⎦ 2 ⎢⎣ 2 ⎝p ⎠

μX (T , p) =

(4)

where μX2(T,p0) is the standard chemical potential with the ideal gas entropy at T and p0, which is available from the JANAF thermodynamic tables,60 and Ed is the total energy of an isolated X2 molecule. Generally, Ed is calculated from ReaxFF parameters, namely 129.1 kcal/mol for O2 molecule and 108.7 kcal/mol for H2 molecule. But we made slightly adjustment of the Ed for the H2 molecule to keep consistent comparison with the previous work,55 i.e., a value of 105.1 kcal/ mol calculated from DFT. For the adsorption of OH group on Pt(111), the reference molecule used is hydrogen peroxide (H2O2). In addition, the energy minimization step conducted prior to applying the acceptance criteria introduces a bias in the MC algorithm. Consequently, to counter the bias and to maintain the detailed balance, the system volume V used in eqs 1 and 2 is replaced by Vacc, which is the volume accessible to the GCMCinserted atoms, according to Lachet et al.61 The accessible volume Vacc is calculated using the following expression:

and our preliminary tests, the number of MC iterations required to reach the equilibrium is reduced appreciably with the hybrid method, compared to standard GCMC simulations without energy minimization. Since the majority of the system is occupied by Pt atoms and is not accessible to adsorbates, standard GCMC simulations without energy minimization suffer from low acceptance rates, especially for the insertion. Here, the ReaxFF potential calculation and the energy minimization are performed in LAMMPS,56−58 which is D

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4 Vacc = V − NPt πrPt 3 3

low coverage would contribute to the optimization of Pt−Pt−H and Pt−H−Pt valence angle parameters. On the other hand, the energetics of the surfaces at higher coverage would contribute to the optimization of all valence angle parameters. To verify the Pt/O/H force field, we examine the H2 dissociative adsorption and the surface hydrogen diffusion behavior over Pt(111) surface as typical of catalytic processes. The hydrogen binding energy was calculated with eq 9 for the surface sites (fcc, hcp, bridge and top), first subsurface sites (octahedral and tetrahedral) and second subsurface sites (octahedral and tetrahedral). The negative binding energy indicates that the hydrogen bound surface is more stable than the system of the bare metal surface and the gaseous molecular hydrogen. As shown in Figure 1, the formation of surface

(5)

where NPt is the number of Pt atoms and rPt is the atomic radius of the Pt atom. For a detailed introduction and discussion of the hybrid GCMC/RMD method used, see refs 49 and 61. 2.4. X-ray Diffraction Characterization. To characterize the structural changes of the Pt systems, we use Debye’s equation62 to compute X-ray diffraction (XRD) patterns with eq 6. I = I0 ∑ fi f j

sin(drij) drij

ij

(6)

In eq 6, I is the diffraction intensity at angle 2θ, I0 is the incident intensity, f i is X-ray scattering factor for the atoms in the system, d is the diffracted wave vector 4π sin θ/λ, and rij are distances between all atom pairs. The X-ray scattering factor f i was computed using the analytic function as follows: ⎛ sin θ ⎞ ⎟ = f⎜ ⎝ λ ⎠

4

⎛

∑ aiexp⎜−bi i=1

⎝

sin 2 θ ⎞ ⎟+c λ2 ⎠

(7)

The coefficients ai and bi were obtained from Cromer et al.63 The diffraction data is plotted as a function of 2θ. 2.5. Thermodynamics Calculation. To predict the stability of the different Pt slab surfaces, we calculated the clean surface energy according to eq 8 as follows: 1 γslab = (Eslab − NPtE bulk ) (8) 2A where γslab is the surface energy of clean Pt slab, the Eslab is the energy of the Pt slab, NPt is the number of Pt atoms in the slab, Ebulk is the energy per Pt atom, and A is the surface area. In addition, the binding energy (Eb) for atomic adsorbates is calculated to estimate the relative affinity at various surface sites as follows: 1 E b = Eσ − Eslab − Egas (9) 2 where σ represents any specific configuration of adsorbates (O or H) at different adsorption sites, Eslab is the energy of the clean Pt slab surface, and Egas is the energy of the isolated O2 or H2 molecule. According to this convention, negative binding energies indicate exothermic process.

Figure 1. Hydrogen binding energy on Pt(111) surface (fcc, hcp, bridge, top), first subsurface (octahedral: oct, tetrahedral: tet), and second subsurface (octahedral: oct,́ tetrahedral: tet)́ at θH = 0.25 ML.

hydrogen is exothermic: hydrogen is most strongly bound to the top and the fcc sites (−10.4 and −10.2 kcal/mol, respectively), and less strongly bound to the hcp (−8.0 kcal/ mol) and bridge sites (−9.1 kcal/mol). The binding energy at all four sites differs only slightly in energy by 1−2 kcal/mol with no strong preference for a specific surface site as reported in other works.64−66 On the other hand, it can be seen that the formation of subsurface hydrogen is endothermic, which indicates that the interior sites of Pt would not be favorably occupied by hydrogen unlike Pd. Pd is the only metal considered with a strong subsurface binding energy. Thus, adsorbed hydrogen atoms on the Pt surface would not diffuse spontaneously into the subsurface layers and further into bulk region. We also note that in ReaxFF, hydrogen appears to prefer spacious interstitial binding sites in the subsurface region, allowing for the octahedral sites to become more favorable binding sites, whereas the tetrahedral sites are the preferred sites in DFT. The valence angle interaction between Pt−H bonds due to the insertion of hydrogen into the interstitial site can create internal stress. It is expected that hydrogen inserted into the octahedral site induces less internal stress compared to the tetrahedral site, resulting in the lower system energy. Results on the dependence of the hydrogen adsorption on the coverage for the Pt(111) surface are shown in Table 1. The H binding energy at atop site was calculated in the H coverage range between θH = 1/16 and 1.0 ML. It is observed that the binding energy tends to be less sensitive to the surface coverage, increasing from −10.4 to −8.0 kcal/mol. The binding energy is most negative at θH = 0.25 ML and increases as the coverage increases. Note, the complete list of H binding energies at different sites on Pt(111), Pt(100), and Pt(110) surfaces and Pt cuboctahedrons of different sizes (Pt13, Pt55, and Pt147) is provided in the Supporting Information. To verify the Pt/H force field, we examined the molecular hydrogen dissociative adsorption on Pt(111) surface. As shown

3. RESULTS AND DISCUSSION 3.1. ReaxFF Force Field Development. The Pt/O/H ReaxFF force field is developed by reoptimizing the Pt/H force field52 and combining to the Pt/O force field.48 For the reoptimization of the Pt/H force field, atom parameters (Pt and H) and bond parameters (Pt−Pt and H−H) are kept fixed to the initial values, whereas the other force field parameters between Pt and H atom type such as Pt−H bond, Pt−Pt−H, Pt−H−Pt, H−H−Pt, and H−Pt−H valence angles, and Pt−H van der Waals long-range interaction terms, are reoptimized to reproduce the following DFT data set: hydrogen binding energy on Pt(111) surface (fcc, hcp, bridge and top) and firstand second-subsurfaces (tetrahedral and octahedral sites) at 0.25 ML, and the thermodynamic stability of adsorbed hydrogen on Pt(111) at different coverages of 0.0625 to 1.0 ML. Given that the interaction of adsorbed hydrogen with neighboring hydrogen is negligible at coverage lower than 0.25 ML, the energetics and the structures for hydrogen binding at E

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connecting them (modeled by Pt(221) and Pt(335)).48 To further evaluate the applicability of the force field in predicting surface properties for other relevant asymmetry Pt surfaces, we calculate the surface energy and oxygen binding energy for the kinked Pt(321) surface. The Pt(321) surface is also an ideal model for understanding structure effects in catalytic oxidation, and the oxygen adsorption behavior is investigated by many experimental works.70−72 The Pt(321) surface is unique and composed of three-atomwide (111) terraces that are interrupted by zig-zagged atomic steps. There are five symmetry-distinct surface atoms, labeled as atom 1, 2, 3, 4, 5, corresponding to Pt−Pt coordination numbers of 6, 8, 9, 10, and 11, respectively, following the convention used by Bray et al. (see Figure 4a).73 The clean

Table 1. Coverage-Dependent Hydrogen Binding Energy (kcal/mol) at Atop Site on Pt(111) Surfacea

a

θH, ML

ReaxFF

DFT

1/16 1/4 1/2 3/4 1.0

−9.8 −10.4 −9.2 −8.5 −8.0

−11.2 −12.4 −11.9 −11.4 −10.9

Molecular hydrogen is used as a reference state.

in Figure 2, when H2 approaches close to the top site on the Pt surface, hydrogen atoms dissociate toward to the nearest bridge

Figure 2. Reaction pathway for the dissociative adsorption of H2 on Pt(111) surface in ReaxFF and in DFT.

sites, which is found to be the dissociation pathway with the lowest energy barrier in DFT.67 The barrier for the dissociation of H2 on the Pt(111) surface is found to be 1.6 kcal/mol, which agrees well with the DFT value (1.4 kcal/mol). From the potential energy profile along the dissociation pathway, it is expected that the molecular hydrogen will almost spontaneously dissociate into the atoms and forms Pt−H bonds with a reaction energy of −9.7 kcal/mol. In addition, hydrogen diffusion behavior across the surface sites on Pt(111) is investigated (refer to Figure 3). Three H

Figure 4. (a) Clean Pt(321) surface with five distinct atoms labeled as 1, 2, 3, 4, and 5 and hollow sites labeled as a−e; (b) atomic O binding energy at different surface sites and the correlation with average Pt−Pt coordination of the binding site. Site name definition: first letter means h-hollow, b-bridge, and a-atop, and the number means the connected labeled atoms; Note, for DFT points, the labels for site names are omitted and are the same as the corresponding ReaxFF points; for example, for the hcp-like line, the three red circles (from left to right) are b12, hb, and hc sites, respectively, while for the fcc-like line, the three red circles (from left to right) are b21, ha, and hd sites, respectively.

surface energy is calculated to be 128.7 meV/A2 using a 13layer Pt(321) model by ReaxFF, which is about 20% larger than the Pt(111) surface (104.9 meV/A2 from Fantauzzi et al.). Compared to the reported DFT data (110.2 meV/A2),73 the Pt/O ReaxFF slightly underestimates the surface stability of Pt(321) but reproduce qualitatively the generally agreed trend for surface thermodynamic stability, i.e., Pt(111) > Pt(321). In addition, the O binding energy was calculated using a 2 × 2 supercell with 20 Pt atoms per layer, corresponding to O coverage of 0.05 ML with one oxygen atom on the surface. The results are shown for a wide variety of sites available on the Pt(321) surface in Figure 4b, and the corresponding structures of Pt(321)-O are provided in Figure 5. Due to the five distinct surface atoms, there are more bridge and hollow site types on Pt(321), compared to high-symmetry surfaces. To distinguish the sites on Pt(321) surfaces, we follow the same convention as the previous work by Bray et al. and Fajin et al.,73,74 i.e., the order of surface atom numbers in the site label is given from left to right and top to bottom shown in Figures 4a and 5 (see b21 and b12 sites). As shown in Figure 4b, the general trend for O binding energy predicted by ReaxFF is similar to the reported DFT data for the Pt−Pt coordination number of 7.5−9. The ReaxFF appears to underestimate the surface stability for a1, b12, and b21 sites by more than 0.3 eV. The reason is that the atop and bridge sites are not stable for O adsorption in the current Pt/O force filed, and the surface energies for those structures were not explicitly included in the ReaxFF

Figure 3. Energy barriers for hydrogen diffusion (top-to-fcc, top-tobridge, and top-to-hcp) on Pt(111) surface in ReaxFF and in DFT. The direction of the arrow (red) indicates the direction of the hydrogen diffusion.

diffusion pathways were identified: top-to-fcc, top-to-bridge, and top-to-hcp pathways. The energy barriers for diffusion between top and various sites calculated in ReaxFF are found to be 3.8−3.9 kcal/mol, which is slightly higher than the experimental (1.6 kcal/mol)68 and theoretical (2.1−3.0 kcal/ mol)69 values. Although we slightly overestimate the available experimental and theoretical results, we expect that H atom diffuses relatively freely on the Pt surface because the barrier that H has to surmount to diffuse from site to site is reasonably small. 3.2. Applicability of Pt/O ReaxFF to the Pt(321) Surface. In the training set of the Pt/O ReaxFF, the oxygen binding energy was explicitly accounted for the flat, highsymmetry Pt(111) terraces and the {111} and {100} steps F

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Figure 6. Equilibration of the GCMC/RMD simulation for Pt(111)-O system at T = 300 K and p = 10−11 atm. The relative energy is calculated relative to the clean Pt slabs and the oxygen chemical potential, i.e., Relative Energy = Esystem,n0 − Ecleanpt − n0μ0.

Figure 5. Structures of atomic O (red) bound in the 12 binding sites on Pt(321) surface (orange).

temperature and pressure specified by the chemical potential of the oxygen reservoir. The surface structures of the Pt catalyst are examined during the GCMC/RMD simulations, as shown in Figure 7a. We

parametrization. Thus, the adsorption behavior on Pt(321) predicted by ReaxFF is only in qualitative agreement with the results from DFT. For a quantitative agreement, the Pt/O force field need to be retrained with some of the binding energies from sites on Pt(321) in the training set. Such a retrained force field would then enable us to study adsorption characteristics of oxygen on Pt(321) kinked surfaces. In addition, one should include the barriers for diffusion from one adsorption site to the other in the training set if one is interested in capturing the description of adsorption and diffusion behavior on Pt(321) surfaces appropriately using ReaxFF. 3.3. Monte Carlo Simulation of Gas Adsorption on Pt Slab Surfaces. The adsorption behavior of O and H on extend Pt slab surfaces is quite important in catalysis reactions, since they can provide atomic structure and composition of in situ catalysts under oxidation and reduction. With the developed Pt/O/H ReaxFF, we performed the GCMC/RMD simulations to examine the surface behavior of Pt−O, Pt−H and Pt−OH, especially in the extent of atomic uptake on Pt slabs as a function of gas partial pressures. 3.3.1. Pt(111) Slab. For the extended slab system, the simulation starts with a clean Pt(111) slab in a 22.3 Å × 38.7 Å × 40 Å simulation box. The system constructed is similar to the model used by Valentini et al.,51,59 which is composed of six atomic layers in the z direction, and for each layer, there are 8 × 16 atoms in the x−y plane, giving a total of 768 Pt atoms. The supercell dimension along the z−axis was set large enough to mimic a surface exposed to vacuum. The orthogonal fcc lattice is constructed with optimized Pt−Pt lattice spacing from ReaxFF (unit cell = 3.947 Å). All the models used assume fcc structures, if not otherwise stated. In the GCMC/RMD simulations, adsorbates are allowed to insert, delete, or move until the system reached thermodynamic equilibrium, where the chemical potentials of the adsorbate in the simulation box and in the imaginary reservoir are equal. For the oxygen adsorption, two sets of temperature 300 and 500 K are investigated. The equilibration of GCMC/RMD simulation is first examined and one example system is shown in Figure 6. The equilibrium of the simulation is reached when the number of oxygen atoms and the system energy converges. As shown in Figure 6, the MC simulation is converged in the range of 2.0 × 105 ∼ 4.0 × 105 MC trial iterations. For the convergence of the energy, we follow a similar criterion as stated in the previous work,49 i.e., the energy change in the system is roughly less than 20 kcal/mol over the final 1000 MC trial moves. With the converged simulations, we obtained the equilibrium O coverage and the atomic phase structures at the

Figure 7. (a) Atomic structure of Pt−O system at T = 300 K, top, p = 10−14 atm (top view), bottom, p = 10−8 atm (side view); (b) O coverage on Pt(111) surfaces; Getman et al. from ref 75. Note, the O coverage is provided only at typical pressures, instead of a pressure gradient with the same intervals.

observe that most of the oxygen atoms occupy hollow sites on the slab surface, as suggested by the DFT data.21 In addition, the oxygen coverage is calculated at different oxygen pressures for a specified temperature, as shown in Figure 7b. The O coverage (θ) is calculated based on the monolayer atom number. The overall O coverage has increased at higher partial pressure for both temperatures. In a recent study,75 selected coverage was obtained on Pt(111) at an O2 pressure of 0.1 Torr (≃ 1.3 × 10−4 atm), and our simulation result obtained at 500 K (θ = 0.61 ML) is comparable to the reported experiment data (θ = 0.54 ML at slightly higher temperature of 518 K, shown in Figure 7b).75 Comparing to the simulation results given by Valentini et al.51 that tend to underestimate the experiment values (such as θ ≃ 0.32 ML at 500 K with a higher pressure of 10−3 atm), the current Pt−O ReaxFF shows higher O coverage and agrees closely with the experiment data. The ReaxFF parameters in the training set used by Valentini et al. are limited, compared to the current Pt−O ReaxFF. In addition, the GCMC/RMD method with energy minimization utilized here helps reach the equilibrium with reduced MC trial moves. In addition, during the GCMC/RMD simulations, we observe that the surface morphology of the Pt slab surface changed significantly with increasing oxygen uptake, while the rest of the central layers remained in an ordered state, i.e., some surface Pt atoms are lifted up and small Pt−O clusters are formed on top of the metal surface as suggested previously (see Figure 7a, bottom).76−78 For the current system, it takes longer G

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The Journal of Physical Chemistry C time for the GCMC/RMD simulations to get converged for O coverages of above 0.6 ML (especially when oxygen chemical potential is closer to the one corresponding to the bulk PtO2 formation, i.e., 0.64 ev from ReaxFF).48 Thus, for a relatively high O coverage (>0.6 ML), it is possible that the Pt−O structures obtained are at its metastable states, and the coverage obtained is qualitative. Based on the adsorption isotherm obtained, we can get prior knowledge of the relative affinity of O on Pt surfaces and thus fabricate the Pt−O structures at the specified conditions for further molecular dynamics simulations of catalytic reactions. In addition, we also studied the process of atomic H adsorption on Pt(111) slabs by the GCMC/RMD approach. Examining the adsorption process, H atoms can sit on the top, bridge (tilted-bridge) and hollow sites on the surface at the early stage of the simulation or at lower H coverage (see Figure 8a), in correspondence with the data reported in Figure 1. As

Figure 9. (a) Atomic structure of Pt−OH system at T = 300 K, top, p = 10−22 atm (top view), bottom, p = 10−10 atm (top view); (b) hydroxyl group coverage on Pt(111) surfaces at T = 300 K.

behavior is examined by GCMC/RMD simulations on different Pt(110) surfaces, including unreconstructed Pt(110) and three other reconstructed structures, i.e., (1 × n) missing-row structures with n = 2−4. The models constructed are similar to Zhu et al.84 Specifically, the unreconstructed model labeled as Pt(110)-(1 × 1), contains 5 × 8 atoms in x-y direction, with a total number of 12 layers. For Pt(110)-(1 × 2), there are also a total number of 12 layers, and those slabs with reconstructed surfaces as (1 × 3) and (1 × 4) have 14 layers in z-directions. In all cases, the separation distances between the slabs are set at approximately 20 Å. First, we examined and compared the surface structures of the four different systems at a similar O coverage (e.g., about 0.65 ML), as shown in Figure 10. Specifically, the oxygen atoms

Figure 8. (a) Atomic structure of Pt−H system at T = 300 K, top, p = 7.7 × 10−9 atm (top view), bottom, p = 10−4 atm (top view); (b) H coverage on Pt(111) surfaces at different pressures, experiment data from ref 79.

the H coverage is increased, there is a larger portion of H atoms adsorbed on the top sites (see Figure 8a). The H coverage at 300 K over different pressures is presented in Figure 8b, which is in good agreement with the trend reported previously.79 At lower hydrogen pressure ( 10 atm, the surface is saturated with H atoms and H atoms began to penetrate into the subsurfaces (not shown here). To validate the Pt/O/H force field for the further application to catalytic systems, we also studied the adsorption isotherm of hydroxyl group on Pt(111) surface, which is another key intermediate agent in oxidation/reduction reactions. Examining the equilibrium structures at 300 K, most of the hydroxyl groups occupy the top sites of the surfaces via O−Pt, and some on bridge sites (see Figure 9a), which agrees with the DFT calculations.80 It is also observed that the OH groups tend to form clusters or chains through H bonding, as indicated by DFT.81 In addition, the coverage of the hydroxyl group is calculated, as presented in Figure 9b. The OH coverage is in the range of 0.6−0.8 over the pressure range of 10−22 atm to ∼10−10 atm, which is the overall experimental coverage for the observed OH overlayer.82 3.3.2. Pt (110) Slab. Another low-index Pt slab, Pt(110), is also of great interest to surface science, especially the reconstruction of Pt(110) induced by adsorbates is quite important to catalysis process.83−85 Thus, oxygen adsorption

Figure 10. Top and side view of different Pt(110)-O structures; (a) (1 × 1) surface, (b) (1 × 2) surface, (c) (1 × 3) surface, and (d) (1 × 4) surface; T = 300 K, and the oxygen coverage is around 0.65 ML for all the structures shown.

are observed to occupy both the hollow and bridge sites on Pt(110)-(1 × 1) surfaces, with hollow sites as the preferred sites. For Pt(110)-(1 × 2) surfaces, almost all the oxygen atoms occupy the hollow sites. For Pt(110)-(1 × 3) and Pt(110)-(1 × 4) surfaces, the oxygen atoms sit at the long bridge sites at the bottom layer in the trough and the hollow sites for other layers. The above observations for the Pt(110) systems with missing rows are in good agreement with the reported DFT trend by Zhu et al.,84 while it is also reported that the oxygen atoms sit at the bridge sites of Pt(110)-(1 × 1) surfaces, which is slightly different from our result. As shown in Figure 10a, the adsorbed O atoms on the Pt(110)-(1 × 1) surface introduced obvious reconstruction and distortion to the surface Pt atoms (e.g., atoms come closer in the 100 directions), as expected during the adsorption process.84 With the rearranged Pt surface, oxygen atoms are able to place themselves in the hollow sites. H

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H adsorption are mainly the valley hollow sites (especially (1 × 3) and (1 × 4) systems), which are less preferable compared to the bridge sites on ridges, as indicated by the DFT calculation.86 In summary, the above results obtained by the ReaxFF method demonstrate similar behavior or trend comparing to the data reported from DFT and/or experimental results. The ReaxFF and GCMC/RMD method together is a valuable tool to explore the structure and morphology of the active catalyst states in reacting environment. Most importantly, the GCMC/ RMD simulations take just a small fraction of time required by DFT method. 3.4. Monte Carlo Simulation of Gas Adsorption on Pt Nanoparticles. Besides the slab systems, we also simulated the adsorption behavior on different Pt nanoparticles (PtNPs) in order to investigate the size and shape effects on the uptake of atomic oxygen and hydrogen. The surface of the PtNPs is made up of different facets and under-coordinated sites at corners and edges, all of which are associated with the reactivity. Given sufficient prior knowledge, the catalytic reactivity and selectivity can be controlled by rational design of the sizes and shapes of the PtNPs.87−89 3.4.1. Pt Nanospheres of Different Sizes. To investigate the size effect, we studied the O adsorption behavior on Pt nanospheres in the range of 1 nm to ∼3 nm. Specifically, we utilized Pt nanospheres with four different sizes of 1.0, 1.5, 2.1, and 3 nm in diameter, corresponding to a total of 43, 135, 321, and 935 Pt composed of (111), (110), and (100) facets and edges between them, and the clean structure of the nanosphere at a size of 2.1 nm is provided as an example in Figure 14a.

For the other three Pt(110) systems with missing rows (Figure 10b-d), the surfaces are more open with valley hollow sites exposed to O adsorption, and they do not have much surface reconstruction. Besides, the oxygen coverage is calculated for all the Pt(110) systems at 300 K to quantify the results, as shown in Figure 11.

Figure 11. Comparison of O coverage on different Pt(110) surfaces at T = 300 K.

The oxygen coverage is calculated based on the number of unconstructed surface atoms (i.e., 4 × 8 = 32 for (1 × 3) surface and 5 × 8 = 40 for the rest). For the four different systems, the O coverage is comparable over all the pressures studied, with slightly higher O coverage for the (1 × 2) system at θ < 0.8 ML. Compared to the Pt(111) surface discussed above, it is more easily for oxygen atoms to deposit on Pt(110) surface, and the catalysis is more likely to occur around Pt(110) surfaces under ultra high vacuum of oxygen. Similarly, we also examined H adsorption behavior on these different Pt(110) systems. Most H sit at the tilted bridge sites on the Pt(110) surfaces, especially those sites on the ridges, as given in Figure 12. The hydrogen coverage is calculated for all

Figure 12. Atomic structures of Pt(110)-H systems at T = 300 K and p = 10−12 atm, (a) (1 × 1) surface, (b) (1 × 2) surface, (c) (1 × 3) surface, and (d) (1 × 4) surface; all top views.

Figure 14. (a) Whole (top) and cross section (bottom) structures of the 2.1 nm nanosphere, left, initial configuration, middle, equilibrium configuration of Pt−O at T = 300 K and p = 10−18 atm, right, equilibrium configuration of Pt−O at T = 300 K and p = 10−9 atm; (b) XRD pattern of the three structures given in (a).

the Pt(110) systems, and higher coverage is obtained for the Pt(110)-(1 × 1) surface, compared to the reconstructed surfaces, as shown in Figure 13. For the three reconstructed systems, the surfaces are more open, and the available sites for

First, the GCMC/RMD simulations are performed at 300 K over a wide range of oxygen pressure from 10−20 atm to 10−1 atm. The equilibrium structure of each simulation was examined to estimate the oxygen uptake on the surface, in the subsurface and bulk regions of Pt nanospheres. The O/Pt ratio increases as the oxygen pressure is increased, and the surface hollow sites are first occupied, then the subsurface sites, and later the bulk sites as shown in Figure 14a. The calculated radial distribution of local O for the nanoparticles of different sizes at selected pressures is provided in Figure 15. Radial distribution of local O refers to the number of oxygen atoms within a specified radius relative to the center of the nanoparticle. There is a clear distinction between O loading on the surface and in the bulk-like region, as demonstrated by the narrow distribution of O with a peak around the outer shell

Figure 13. Comparison of H coverage on different Pt(110) surfaces at T = 300 K. I

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Figure 15. Radial distribution of local oxygen atoms relative to the center of the nanospheres after GCMC/RMD simulations at T = 300 K for Pt nanospheres at sizes of (a) D = 1.5 nm, (b) D = 2.1 nm, (c) D = 3.0 nm; Color code for pressures: black, 10−20 atm, brown, 10−18 atm, blue, 10−16 atm, orange, 10−14 atm, red, 10−11 atm, magenta, 10−9 atm, turquoise, 10−1 atm. The dash and solid line is a guide for surface oxide and bulk oxide.

Figure 16. Radial distribution of local hydrogen atoms relative to the center of the nanospheres after GCMC/RMD simulations at T = 300 K, (a) D = 1 nm, (b) D = 1.5 nm, (c) D = 2.1 nm. Color code for pressures: black, 10−15 atm, brown, 10−11 atm, green, 10−9 atm, blue, 10−7 atm, red, 10−5 atm, orange, 10−3 atm; The dash and solid line is a guide for surface hydride and bulk hydride.

Figure 17. Radial distribution of Pt atoms relative to the center of the PtNPs, (a) octahedron, (b) cuboctahedron, and (c) cubic; insets are the corresponding structure of PtNPs. Note: the edge length for cuboctahedron is roughly defined as the distance between the two paralleled (100) surfaces here.

adsorption88 as will be discussed in the following section. The net effect of reducing the particle size is destabilizing the particle structure.90 Furthermore, the X-ray diffraction (XRD) spectrum of the PtNPs is calculated (eq 6 and 7) to characterize the three different structures obtained, including the clean PtNPs, PtNPs with oxygen atoms on surface sites and PtNPs with oxygen atoms in bulk regions, as shown in Figure 14. For the clean Pt nanosphere in Figure 14a, the XRD pattern shows the characteristic property of the crystalline Pt fcc phase with four typical peaks, (111), (200), (220), and (311).91 With the O atoms adsorbed on the surface (Figure 14b), the typical peaks become wider and lower, and as the pressure increases to 10−9 atm, the XRD pattern only shows two wider peaks, which corresponds to the structure of fully oxidized Pt (Figure 14a).92,93

and the wide distribution of O along the radius. For the 1.5 nm cluster, the bulk oxide forms fully at very low pressures of 10−20 atm, supported by the wide distribution of O atoms along the radius (shown in Figure 15a), while for the 3 nm cluster (Figure 15c), O atoms are adsorbed on the surface mainly in the region of 14−18 Å away from the center at 10−20 atm, and the surface sites are saturated and O began to penetrate into the subsurface at a much higher pressure of 10−11 atm. The medium size of 2.1 nm cluster exhibits bulk oxide around p = 10−16 atm (Figure 15b). For the smallest 1 nm cluster, bulk oxide forms at the very low pressure of 10−20 atm as expected (data not shown here). This kind of size dependence is attributed to the decreased surface sites for O adsorption when reducing the particle size. In addition, the percentage of surface atoms on the edge and corners is increased as particle size is reduced, which are the more effective sites for oxygen J

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The Journal of Physical Chemistry C The H adsorption behavior is also examined on the PtNPs at three different sizes of 1.0, 1.5, and 2.1 nm in diameter. The GCMC/RMD simulations are performed at 300 K over a wide range of hydrogen pressures from 10−15 atm to 10−3 atm. The radial distribution of local hydrogen atoms in each nanoparticle is calculated, and the distribution at selected pressures is shown in Figure 16. Similar adsorption behavior as discussed for oxygen adsorption is obtained with hydrogen adsorption, i.e., the onset pressure of bulk hydride goes higher for bigger PtNPs. For the smallest clusters of 1 nm size (Figure 16a), the bulk hydride formation starts at about p = 10−11 atm, while it starts around 10−7 atm and 10−5 atm for the 1.5 nm cluster (Figure 16b) and 2 nm cluster (Figure 16c), respectively. Comparing to the H adsorption behavior on Pd nanospheres,55 the pressure for Pt bulk hydride formation is much higher as expected, indicating that the general trend predicated by GCMC/RMD is reasonable compared to other metals. 3.4.2. Pt Nanoparticles of Different Shapes. To examine the shape effect on atomic adsorption behavior, we employed three different types of PtNPs including octahedron, cuboctahedron and cubic. The three PtNPs have a similar edge length of approximately L = 2.3 nm, corresponding to a total number of 489, 695, and 864 Pt atoms, respectively. The three clean models along with their initial radial distribution of local Pt atom are shown in Figure 17. The structural details of the PtNPs are summarized in Table 2. Each nanoparticle was placed in a 50 Å × 50 Å × 50 Å periodic box.

Figure 18. Atomic structures of PtNPs-O after GCMC/RMD simulations at T = 500 K and p = 10−15 atm for (a) octahedron, (b) cuboctahedron, and (c) cubic.

corners, and some of the hollow sites in the (111) facets are occupied, while the center of the perfect (100) facets is free of oxygen atoms. In summary, for the O adsorption, the sites to be occupied follow the order, edge (corners) > (111) > (100). The trend obtained here are in good agreement with the experiment data,87,88 and it also provides the atomic-level structures of the Pt−O systems with various catalyst shapes. To quantify the above observations, we calculated the fraction of atoms standing on the surface, and the percentage of surface atoms on corners and edges, as shown in Table 2. The O coverage is also calculated and shown in Table 2. For the three models with a similar size of 2.3 nm, the percentage of surface atoms located on corners and edges, NE+C%, is approximately 35% for the octahedron, 33% for the cuboctahedron model, and 18% for the cubic model. Thus, octahedron nanoparticles among the three are expected to be the most active catalyst for O adsorption under ultra low pressures. This is in good agreement with the calculated O coverage, i.e., the highest coverage is obtained for the octahedron, followed by the cuboctahedron and then the cubic model. The intrinsically larger fraction of edges and corners for octahedron and cuboctahedron explains the higher O coverage.94 In addition, the (111) facet is also one of the reasons for higher O coverage in an octahedron model. Moreover, when switching to the reduction environment, the adsorption behavior of hydrogen atoms on different PtNPs becomes interesting and hence is examined at 300 K. At a pressure of 10−16 atm, a very different behavior of H adsorption is observed as demonstrated in Figure 19. For octahedron

Table 2. Structural Properties of the PtNPs, Surface O Coverage at 500 K, 10−15 atm and Surface H Coverage at 300 K, 10−16 atm

octahedron cubooctahedron cubic

facets

NTa

NS

NE+C%

O coverage

H coverage

111(8) 111(8) 100(6) 100(8)

489 695

258 290

∼35% ∼33%

∼40% ∼36%

23% 30%

864

364

∼18%

∼26%

35%

a

Where NT is the total number of Pt atoms, NS, is the total number of surface Pt atoms, and NE+C% is the percentage of surface atoms located on corners and edges;

To have a better comparison of the adsorption behavior among different shapes, it is necessary to keep the surface coverage of oxygen below 1.0 ML (i.e., only partial surface sites are occupied). The GCMC/RMD simulations are conducted at both 300 and 500 K. Due to the relatively small size of PtNPs used, oxidized Pt can be formed very easily and it is found to be at ultra low pressures for 300 K (below p = 10−25 atm). Thus, we reported the O adsorption behavior on these different PtNPs obtained from GCMC/RMD simulations at 500 K. Note, in practical applications with larger PtNPs, we expect to see similar behavior at much higher pressures. We take the case of p = 10−15 atm as an example and the corresponding equilibrium configurations are provided in Figure 18. As shown in Figure 18, the edges and corners of cubic nanoparticles are occupied by oxygen atoms, while the surface sites of (100) facets are barely occupied, indicating that the edges and corners are the more active sites for O adsorption, compared to (100) facets. For the octahedron model, while occupying the edges and corners, O also sits on some of the hollow sites of the (111) facets, indicating (111) surface sites are preferable to (100) surface sites. For the cuboctahedron model, the edges,

Figure 19. Atomic structures of PtNPs-H after GCMC/RMD simulations at T = 300 K and p = 10−16 atm for (a) octahedron, (b) cuboctahedron, and (c) cubic.

(Figure 19a), only partial sites on the edges and corners are occupied by the hydrogen, and surface sites of (111) facets are almost free of hydrogen, while for the cubic model (Figure 19c), besides the edges and corners, bridge sites on the (100) facets especially those sites closer to the edges and corners are also occupied, but not fully saturated at this pressure. For the cuboctahedron (Figure 19b), the edges, corners, and some of the bridge sites on the (100) facets are occupied, while sites on (111) facets are almost clean. Although octahedron model has K

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considering all possible coordination around platinum. Understanding its performance together with the challenges in parametrizing the atomic interactions will help appreciate aptly the significance of the currently practiced retraining approach.

higher fraction of surface atoms on the edges and corners, those sites near (111) facets is less preferred compared to the sites near (100) facets. This can be explained by the fact that the H adsorption is preferred on Pt(100) over Pt(111).95,96 Thus, for reactions related to hydrogen-transfer catalyzed by PtNPs, the cubic PtNPs would expect a better affinity to the hydrogen at ultra low pressures. The H coverage is also calculated (see Table 2), and the highest coverage is obtained for cubic, followed by cuboctahedron and then octahedron. In summary, the most active sites of each Pt nanoparticle as catalysts are edges and corners due to its insufficient coordination.13 In addition, among varied shapes, the catalytic activities also depend on the adsorbed species, due to their different affinity with the facets of PtNPs. With these in mind, the catalytic properties of Pt can be controlled through shapeselective synthesis. In this work, our simulation results are focused on the thermodynamic equilibrium structures and thus coverage isotherms are derived for the validation of the force field. In practical catalytic processes, the reactions may occur along with the adsorption process of O or H on the catalysts. Thus, the tools described here can also be utilized to generate random configurations during the adsorption process, which can be used for further molecular dynamics investigations. In addition, the tools and fields reported here can be readily extended to other systems relevant for surface catalysis, where for example multiple species could get adsorbed on the surface including the adsorption behavior of molecules on the metal catalyst. Moreover, we will study the complex structures of the supported Pt catalysts in future work, which are always the form of catalysts in industrial applications, with maximized surface-volume ratio. We can provide the actual structure of the metal cluster supported on graphene and study how this affects the adsorption and diffusion behavior of adsorbates, and thus catalytic properties of the catalyst cluster.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01064. Binding energy of hydrogen on various Pt surfaces, the binding energy of oxygen for some static structures with direct comparison with DFT data, as well as the ReaxFF reactive force field parameters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (908) 7302512. Fax: (908) 730-3323. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant from the Corporate Strategic Research, ExxonMobil Research and Engineering, Clinton, NJ. We like to thank Joshi, Yogesh V, and Md Mahbubul Islam for useful discussions.

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REFERENCES

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4. CONCLUSIONS The surface chemistry between noble metal such as Pt and gas (oxygen and hydrogen) plays a critical role in numerous heterogeneous catalytic reactions. The Pt/O/H reactive force field is developed to describe the adsorption behavior of species containing O and H on/in surfaces, subsurface and bulk regions of Pt catalysts. The hybrid GCMC/RMD simulations are then performed to derive theoretical adsorption isotherms of O and H in relevant Pt slabs and nanoparticles, for the validation of the force field and its further application in catalytic reactions. The adsorption behavior or trend obtained in this paper agrees with the reported DFT or experiment data. Besides, the size and shape effects of PtNPs on the adsorption behavior are assessed, and atomic-level structures are provided for equilibrium adsorption to complement the experimental work. The identified trend of adsorption on diverse types of surface sites in this work, would contribute to the systematic understanding of structure effects of catalysts. Additionally, we can get prior knowledge of the relative affinity of O and H on different Pt surfaces, and thus prepare appropriate structures at the specified conditions for further molecular dynamics investigation of catalytic reactions. This study suggests reactive force field coupled with time acceleration tools as a robust option to infer the active states of the catalysts and stresses on the importance of force field validation as a key step in any application of RMD. Future work will be directed to the force field development from a more comprehensive training set L

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