Angle-Resolved Thermal Dissociative Sticking of Light Alkanes on Pt

Article pubs.acs.org/JPCC

Angle-Resolved Thermal Dissociative Sticking of Light Alkanes on Pt(111): Transitioning from Dynamical to Statistical Behavior Jason K. Navin, Scott B. Donald, and Ian Harrison* Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, United States S Supporting Information *

ABSTRACT: Gas-surface reactivity involving small molecules can exhibit significant dynamical deviations away from statistical behavior that complicate quantitative modeling of catalytic processes. This study examines dissociative chemisorption of light alkanes to determine if a transition toward statistical behavior can be identified at some threshold level of molecular complexity. Angle-resolved thermal dissociative sticking coefficients (arDSCs) were measured for methane, ethane, and propane on Pt(111) using effusive molecular beams at a temperature of 700 K. The ar-DSCs were peaked around the direction of the surface normal, and the angular variation flattened with increasing alkane size from roughly cos12ϑ to only a 20% variance with angle. Precursor-mediated microcanonical trapping models of the gas-surface reactivity were used to simulate the ar-DSCs while maintaining consistency with other nonequilibrium supersonic and effusive molecular beam experiments. This work indicates that dissociative chemisorption of ethane is dynamically biased similar to methane, wherein the mean vibrational efficacy for promoting reaction relative to normal translational energy is 0.40 and molecular translations parallel to the surface and rotations are spectator degrees of freedom. In contrast, propane’s reactivity shows no discernible evidence for dynamical deviations away from statistical behavior.

I. INTRODUCTION

S(T ) =

The activation of light alkanes at transition metal catalyst surfaces is a topic of lively interest1 based on its connection to hydrogen and synthesis gas production through steam reforming2 and the possibility of olefin production through catalytic dehydrogenation.3 The initial C−H bond cleavage occurring in alkane dissociative chemisorption to yield cochemisorbed alkyl and hydrogen products is often considered to be the rate-limiting step in industrial catalytic processes involving alkanes. Moreover, alkane dissociative chemisorption4,5 is a model system for activated polyatomic gas-surface reactions for which molecular complexity can be varied and multidimensional experimental measurements can be used to challenge emerging theoretical models6−8 of gas-surface reactivity. In this report, angle-resolved thermal dissociative sticking coefficients, S(ϑ;T), for light alkanes impinging on Pt(111) at a temperature of 700 K are measured and compared to predictions of precursor-mediated microcanonical trapping (PMMT) models7,9,10 of the gas-surface reactivity. Although the S(ϑ;T) measurements were made using a heated effusive molecular beam to impinge alkane molecules with a gas temperature Tg equal to the surface temperature Ts of a Pt(111) surface held in an ultrahigh vacuum, surface analysis chamber, the measurements directly characterize the thermal dissociative sticking relevant to high pressure catalysis.11,12 Averaging the S(ϑ;T) measurements over the angular flux distribution of an ambient gas hitting a surface under thermal equilibrium conditions allows for calculation of the thermal dissociative sticking coefficient S(T): © 2014 American Chemical Society

∫ S(ϑ; T ) cosπ ϑ dΩ

(1)

The reactivity of small molecules at surfaces is oftentimes nonstatistical and significantly influenced by reaction dynamics,13−15 which complicates quantitative modeling of catalytic and chemical vapor deposition processes. Both mode-specific16 and bond-selective17 chemistry have been demonstrated for methane dissociative chemisorption on metals. For the benchmark H2/Cu(111) and CH4/Pt(111) reactive systems,12,18 dynamical biases reduce the thermal dissociative sticking coefficients of interest to high pressure catalysis by 2 and 1 orders of magnitude, respectively, as compared to the expectations of statistical transition state theory. It is important to develop kinetic models that can handle and recognize such significant dynamical biases when they occur to advance the scientific design of catalysts and catalytic processes, and to forge better connection between experiments and electronic structure theory calculations. There are relatively few experimental studies of gas-surface reactivity for alkanes larger than methane,4,5,19,20 and an open question is at what level of molecular complexity does the alkane/surface reactivity cease to be appreciably influenced by dynamics and transition toward more purely statistical behavior. For supersonic molecular beams of C2−C5 alkanes incident on Pt(111) at such high translational energies, 80 kJ/mol ≤ Et ≤ 550 kJ/mol, that neither the surface temperature nor Received: June 6, 2014 Revised: August 15, 2014 Published: September 4, 2014 22003

dx.doi.org/10.1021/jp505660p | J. Phys. Chem. C 2014, 118, 22003−22011

The Journal of Physical Chemistry C

Article

solid angle, d2N(ϑ)/dΩ dt, that varied as ∼cos1.3ϑ, which, when projected onto the Pt(111) surface, oriented normal to the beam’s centerline, gave an incident molecular flux, d2N(ϑ)/dA dt, that varied as ∼cos4.3ϑ across the surface. The net effusive beam flux was determined by comparison to flux from a calibrated leak. With the effusive beam doser and surface temperatures set equal to 700 K, the cleaned Pt(111) surface was positioned 12.7 mm in front of the effusive beam orifice before gas dosing began. A typical gas impingement flux for methane along the beam centerline at the Pt(111) surface was 1.3 × 1015 cm−2 s−1 or 0.87 ML/s where 1 ML = 1.5 × 1015 cm−2 is the areal density of Pt(111) atoms. After dosing, AES was used to measure the C reaction product coverage left behind on the surface as a function of distance (angle) away from where the beam centerline hit the surface. Heated beam molecules that missed the Pt(111) surface, or did not react upon initial collision with the surface, raised the ambient chamber pressure and were assumed to be rapidly thermalized to the chamber wall temperature prior to any further possible collisions with the surface. The reactive contribution from this “cold” ambient alkane gas flux to the C deposition on the surface was subtracted11 when calculating the 700 K S(ϑ;T) values.

molecular internal energy influenced the reactivity, Madix and co-workers21 found that the dissociative sticking coefficients scale with the normal translational energy, En = Et cos2 ϑ, just as is the case for methane.22 This is a key experimental finding that underpins the typical theoretical assumption that for light alkanes reacting on smooth close-packed metal surfaces, molecular translations parallel to the surface can be treated as spectator degrees of freedom. A dynamically biased (d-) PMMT model for dissociative chemisorption of methane on Pt(111), which assumes that molecular translations parallel to the surface and rotations are spectator degrees of freedom and the vibrational efficacy for promoting reaction relative to normal translational energy is 0.40, suffices to replicate10 and predict12 a wide range of dissociative sticking coefficients measured in supersonic and effusive molecular beam experiments, as well as the methane product state distributions7 from thermal associative desorption of coadsorbed methyl radicals and hydrogen atoms using the principle of detailed balance. Although vibrational cooling during the expansion of supersonic molecular beams is negligible for methane,7,22,23 uncertainty in the extent of vibrational cooling24,25 in supersonic beams of larger alkanes makes quantitative modeling and interpretation of the larger alkane supersonic beam/surface reactivity somewhat contentious.21 Effusive molecular beam measurements of dissociative sticking coefficients for C1−C3 alkanes on Pt(111), S(ϑ = 0°;Tg,Ts) = Sn(Tg,Ts), for beams incident along the direction of the surface normal, and with independently varied Tg and Ts, are more amenable to quantitative theoretical analysis7,19,20 because the initial reactant energy distributions are simple thermal ones defined by Tg and Ts. Here, we report S(ϑ;T) measurements for C1−C3 alkanes on Pt(111), which, when combined with prior Sn(Tg,Ts) measurements, provide useful constraints to refine theoretical models of the gas-surface reactivity. The main finding from PMMT analysis of this multidimensional dissociative sticking data is that the methane and ethane reactivity display strong evidence for dynamical biases away from statistical behavior, which the propane reactivity does not.

III. THEORETICAL METHODS Figure 1 provides a schematic overview for the PMMT models of activated dissociative chemisorption.7,18,27 The precursor

II. EXPERIMENTAL METHODS Experiments were performed using an ultrahigh vacuum (UHV) surface analysis chamber equipped for Auger electron spectroscopy (AES) using a double pass cylindrical mirror analyzer, thermal programmed desorption, residual gas analysis, and effusive molecular beam dosing. The UHV chamber had a base pressure of 1 × 10−10 Torr. The 10 mm diameter Pt(111) crystal was cleaned prior to experiments by cycles of Ar+ ion sputtering at Ts = 600 K, exposure to ∼10−7 Torr of O2 at 800 K, and annealing to 1200 K in good UHV, until no contaminants were detectable by AES. Methane, ethane, and propane were all obtained from Matheson Tri-Gas and had a purity of 99.999%. Ethane and propane were used without further purification, but methane was further purified by flowing through a Supelco filter (model 2-2450-U), capable of removing trace amounts of reactive impurities. The molecular beam doser7 and methodology11 for making effusive molecular beam measurements of alkane dissociative sticking coefficients have been described in detail elsewhere, and only a brief synopsis follows. Alkane dissociative chemisorption at 700 K was assumed to lead exclusively to desorbing H2 gas and chemisorbed C products. The effusive molecular beam doser had a 0.076 mm thick end-wall with a 0.5 mm diameter orifice that resulted in a calculated26 molecular flux distribution in

Figure 1. Schematic describing the energetics and reaction scheme for precursor-mediated microcanonical trapping (PMMT) models of alkane dissociative chemisorption. Upon striking the surface, an impinging molecule interacts with a small number of local surface oscillators, s, forming a transient precursor complex (PC) that, treated on a microcanonical basis, can go on to react, desorb, or exchange energy with the surrounding metal. See text for further details. 22004



Article

Figure 2. Angle-resolved thermal dissociative sticking coefficients measured (points) for light alkanes on Pt(111) at 700 K are compared to various kinds of PMMT model predictions (lines). See Table 1 for PMMT model parameters and how they were fixed.

for this kind of energy transfer.19,20 A complication for small molecules is they can exhibit dynamical biases away from statistical behavior, and a dynamically biased (d-) PMMT model has been developed to treat such cases.7,10,18 Some PMMT model parameters typically need to be derived from experiments, but parametrization has been reduced by the use of density functional theory (DFT) calculated transition state vibrational frequencies. For alkanes with DFT determined transition state frequencies, statistical (s-) PMMT models require two parameters, {E0, s}, where E0 is the reaction threshold energy and s is the number of surface oscillators in the PC; a master equation (ME) PMMT model needs an additional PC-surface energy transfer parameter α;27 and a dPMMT model has required three parameters for methane, {E0, s, ηv}, where ηv is the efficacy of molecular vibrational energy to promote reactivity relative to translational energy directed along the surface normal.7 Once these few parameters are determined by PMMT simulations to a limited set of

complexes (PC) in these models are transient gas-surface collision complexes composed of an impinging molecule interacting with a small number of local surface oscillators. PCs are assumed to have their exchangeable energy microcanonically randomized if their energy is sufficient to gain access to the strongly state-mixing regions of the reactive PES near the transition state, at least a collective sense when averaged over the ensemble of collision complexes formed.18,28−30 The PCs formed are transiently trapped between the transition states for desorption and dissociative chemisorption (reaction) and are assumed to go on to desorb or react with Rice−Ramsperger−Kassel−Marcus (RRKM)31 microcanonical rate constants. For activated dissociative chemisorption of sufficiently small molecules, ultrafast desorption time scales at energies sufficient to react allow energy transfer between the PCs formed and the surrounding surface to be ignored,7,18,27 but for larger molecules a master equation approach is required to account 22005



Article

experimental data, they can be used to simulate or predict reactivity under any other arbitrary thermal or nonequilibrium experimental conditions.7,18 For all of the PMMT models of alkane dissociative chemisorption considered in this Article, molecular translations parallel to the surface were treated as spectator degrees for freedom. The ME PMMT models used an exponential down energy transfer function27 in which the α parameter is roughly the average energy transferred per PC/ phonon interaction involving PC energy loss,32 and the PC/ phonon interactions were assumed to occur at 3 times the mean phonon frequency of platinum. DFT electronic structure theory calculations defining the transition state geometry, energetics, and transition state vibrational frequencies for methane dissociative chemisorption on Pt(111) have been performed earlier7,33 for methane on Pt(111) using the Perdew−Becke−Ernzerhof (PBE)34,35 functional. With identical protocol, DFT calculations were performed for ethane and propane dissociative chemisorption on Pt(111) using the Vienna ab initio Software Package36−39 (VASP) with a plane-wave basis set. Exchange and correlation effects were treated within the generalized gradient approximation (GGA) of the PBE functional. Calculations were performed using the projector-augmented wave40,41 method with a plane-wave cutoff of 400 eV. The metal substrate was modeled as four layers of a 4 × 4 unit cell, corresponding to 64 metal atoms, with periodic boundary conditions and a large vacuum space separating repeating images. Reaction pathways were searched with the nudged elastic band42 method and further optimized using the dimer43 method. Calculations were considered converged when all forces were smaller than 0.05 eV/Å. Ultimately, a consistent set of DFT calculations using the PBE functional defined transition state properties for the light alkanes of these experiments. The DFT calculated transition state vibrational frequencies, defined by the local curvature of the reactive potential at the transition state, are likely to be relatively robust quantities because they are based on changes of energies for small local changes in configuration. These frequencies are used within the PMMT modeling. In contrast, the threshold energies for reaction calculated by DFT are less reliable because they are defined by the difference in energy between two very different configurations, the separated reactants and the transition state. Typical accuracies for DFT computed threshold energies for reaction have recently been estimated at ±30 kJ/mol for popular functionals.44 Moreover, the DFT calculations with the PBE functional do not explicitly account for van der Waals interactions, which can be anticipated to become more significant with increasing alkane size.19,20 For these reasons, the PMMT modeling treats the reaction threshold energy, E0, as a free parameter to be extracted from experiments.

Table 1. Model Parameters for Alkane Dissociative Chemisorption on Pt(111)

CH4 C2H6

C3H8

model

E0 (kJ/mol)

s

ηv

d-PMMT7 s-PMMT ME s-PMMT d-PMMT ME d-PMMT s-PMMT ME s-PMMT

58.9 33.8 33.8 42.3 42.3 23.6 21.9

2 2 2 2 2 2 2

0.40

α (cm−1)

350 0.40 0.40

60 1000

fit expts S(En,TN)22 Sn(Tg,Ts)20 Sn(Tg,Ts)20 Sn(Tg,Ts)20 Sn(Tg,Ts)20 Sn(Tg,Ts)20 Sn(Tg,Ts)20

PMMT models for the light alkanes plotted in semilogarithmic fashion. With increasing alkane size, the S(ϑ;T) increase and their angular variation diminishes rapidly. The methane S(ϑ;T) data were measured in separate experiments7,12 with two different effusive molecular beam dosers. The methane d-PMMT model7 parameters were fixed by optimizing simulations to Luntz and Bethune’s CH4/ Pt(111) supersonic molecular beam measurements22 of S(⟨En⟩;TN, Ts = 800 K) for hyperthermal mean normal translational energies in the 20 kJ/mol < ⟨En⟩ < 120 kJ/mol range with nozzle temperatures of TN = 300 and 680 K. The resulting d-PMMT model predicts the S(ϑ;T) relatively well and also replicates Sn(Tg,Ts) effusive beam measurements, other supersonic molecular beam measurements, and the methane product state distributions from thermal associative desorption of coadsorbed methyl radicals and hydrogen using the principle of detailed balance.7 The d-PMMT model treats molecular translations parallel to the surface and rotations as spectator degrees for freedom, and required imposition of a vibrational efficacy for promoting reaction relative to normal translational energy of ηv = 0.40. Alternate PMMT models were unable to quantitatively reconcile the S(ϑ;T) data with other kinds of CH4/Pt(111) reactivity measurements.7,12 The ethane S(ϑ;T) measurements are compared to the predictions of several PMMT models in Figure 2b. The models used DFT calculated transition state vibrational frequencies,45 and the remaining parameters were optimized to the ethane effusive molecular beam measurements of Sn(Tg,Ts) as shown in Figure 3. Statistical models assume rotations were active degrees of freedom were only slightly inferior to dynamical models in replicating the Sn(Tg,Ts) measurements, but the statistical models fail to predict the S(ϑ;T) angular variation. Figure 3 shows the significant improvement in describing the Sn(Tg,Ts) data that is introduced by explicitly treating the PCto-surrounding-surface energy transfer in a master equation approach. The d-PMMT simulation of Figure 3a overestimates the variation of Sn(Tg,Ts) with Tg. Energy transfer tends to thermalize the PCs toward the surface temperature. By including this effect, the ME d-PMMT model of Figure 3b is able to replicate the experimental data, and its Sn(Tg,Ts) predictions are closer to its thermal S(T = Tg = Ts) predictions than those for the d-PMMT model of Figure 3a. Although both dynamical models predict the S(ϑ;T) data measured at 700 K quite well, only the ME d-PMMT model succeeds at adequately replicating the Sn(Tg,Ts) data. The dynamical PMMT models for ethane treated molecular translations parallel to the surface and rotations as spectator degrees for freedom, and imposed a vibrational efficacy of ηv = 0.40, just as was the case for methane.

IV. RESULTS AND DISCUSSION Measurements of angle-resolved thermal dissociative sticking coefficients for methane, ethane, and propane on Pt(111) at 700 K are compared to PMMT model predictions in Figure 2. The PMMT model parameters are listed in Table 1 and were fixed by optimizing simulations to pre-existing supersonic22 or effusive20 molecular beam experiments. Polynomial cosine fits to the experimental measurements and PMMT predictions of S(ϑ;T) are given in Figure 2a−c, which allow the angular variation of the different S(ϑ;T) curves to be visually and analytically assessed. Figure 2d presents the experimental S(ϑ;T) data and the predictions of the most successful 22006



Article

Figure 3. Normal incidence, effusive molecular beam dissociative sticking coefficients, Sn(Tg,Ts), measured (points) for ethane on Pt(111) as a function of surface temperature at several different gas temperatures20 are compared to PMMT simulations (lines).

Figure 4. Normal incidence, effusive molecular beam dissociative sticking coefficients, Sn(Tg,Ts), measured (points) for propane on Pt(111) as a function of surface temperature at several different gas temperatures20 are compared to PMMT simulations (lines).

The modest angular variation of the propane S(ϑ;T) measurements of Figure 2c falls within the range of predictions of the statistical PMMT models, which used DFT calculated transition state vibrational frequencies45 and whose parameters were optimized to the Sn(Tg,Ts) experiments20 of Figure 4. Explicitly treating the PC/surface energy transfer is more important for the propane reactivity than for ethane, and only the ME s-PMMT was able to quantitatively replicate the propane Sn(Tg,Ts) experiments. The ME s-PMMT model’s S(ϑ;T) prediction has a slightly shallower angular variation than the experiments but remains within the one standard deviation experimental error bars. The statistical models assume that rotational energy is exchangeable and active in promoting dissociative chemisorption. Dynamical PMMT models were not attempted for propane because the ME s-PMMT model already adequately represents the experiments with less parametrization. Table 2 compares alkane thermal dissociative sticking coefficients, S(T), at 700 K calculated using eq 1 and the polynomial cosine fits to the experimental S(ϑ;T) measurements, and by the optimal PMMT models of Figure 2d whose parameters were fixed by other kinds of supersonic or effusive molecular beam experiments. The S(T) values derived from the different kinds of experiments are in broad agreement with one

Table 2. Thermal Dissociative Sticking Coefficients S(T) at 700 K for CnH2n+2/Pt(111) based on CH4 C2H6 C3H8

S(ϑ;T)

PMMT of other expts

1.03 × 10−5 2.2 × 10−4 1.0 × 10−3

9.97 × 10−6 1.4 × 10−4 2.2 × 10−3

another. The thermal dissociative sticking increases rapidly with alkane size. According to DFT calculations with the PBE functional, the reaction threshold energy for dissociative chemisorption of the light alkanes on Pt(111) is ∼76 kJ/mol and varies by less than ±1 kJ/mol across the alkanes. In contrast, the reaction threshold energies derived from PMMT analysis of experiments decline monotonically with increasing molecular size from 58.9 kJ/mol for methane to 21.9 kJ/mol for propane. These DFT calculations do not account for van der Waals interactions whose inclusion would likely bring electronic structure calculated E0 values into better agreement with experiments (Table 3). In earlier work,19,20 we demonstrated that the experimental activation energies for dissociative chemisorption of these light alkanes fell with increasing molecular size with a linear relationship between the activation energies and the molecular desorption energies. Arguing that the molecular 22007



Article

Table 3. Comparison of E0 Values Calculated by DFT Using the PBE Functional (Vibrational Zero-Point Energy Corrected)45 with Values Derived from the Optimal PMMT Modeling of Experiments

where the Pt surfaces were believed to be essentially clean (i.e., having vanishingly small adsorbate coverages). Thermal dissociative sticking coefficients for methane on these Pt nanocatalysts calculated54 under the assumption that dissociative chemisorption rate-limits the steam reforming experiments are S(T = 700 K) = 3.4 × 10−8 for 6.3 nm diameter Pt nanoparticles49 and 3.6 × 10−8 for 1.9−2.3 nm diameter Pt nanoparticles,53 where the temperature extrapolations used Wei and Iglesia’s measured 75 kJ/mol activation energy for the steam reforming rate constant. The 350-fold discrepancy between the surface science determination of S(T = 700 K) for Pt(111) and the nanocatalyst kinetics evaluation for the presumably more open and reactive nanocatalyst surfaces suggests that either the number of surface sites that can turn over on the operating nanocatalysts is surprisingly limited or the initial dissociative chemisorption of methane is not ratelimiting. The latter possibility is reasonable to consider because the entropic cost for accessing the transition state for methane dissociative chemisorption on Pt(111) is modest (e.g., translations parallel to the surface and rotations are spectator degrees of freedom),7,10,12 and DFT calculations55−57 find the energetic barrier is considerably less than those for some subsequent CHx decomposition steps. The angle resolved thermal dissociative sticking coefficients measured in the effusive beam experiments are precisely those applicable to high pressure catalytic reactors where frequent intermolecular collisions maintain thermal equilibrium energy distributions for the reagents. The simplest theoretical model for thermal dissociative sticking on smooth planar surfaces is the one-dimensional (1-D) model proposed by van Willgen58 wherein only normal translational energy, En = Et cos2 ϑ, is used to surmount the threshold energy for dissociative chemisorption, E0, on a reactive potential energy surface that is presumed to be uncorrugated across the surface plane. Assuming that every incident molecule capable of surmounting the barrier with En ≥ E0 successfully reacts:

threshold energy for dissociative chemisorption CH4 C2H6 C3H8

DFT (kJ/mol)

PMMT (kJ/mol)

77.2 75.3 75.3

58.9 42.3 21.9

desorption energies of the physisorbed molecules are reasonable experimental estimates of the van der Waals stabilization energies of the chemisorbed products of dissociative chemisorption, the linear correlation between the activation energies and molecular desorption energies is consistent with an Evans−Polanyi relationship wherein the products (and transition states) are increasingly stabilized by van der Waals interactions as alkane size increases. Measurements of thermal dissociative sticking coefficients for alkanes incident on well-defined metal surfaces are rare.5 Rodriguez and Goodman46 provide the only example for an alkane on Pt(111) where their thermal bulb measurements for ethane extrapolate to give S(T = 700 K) = 1.2 × 10−6, which is several orders of magnitude less than the values calculated in Table 2 based on our effusive molecular beam experiments. The Goodman bulb experiments were performed by varying the surface temperature from 515 to 635 K at 1 Torr total pressure, comprised of 0.01 Torr ethane and 0.99 Torr argon, under the assumption that ethane striking the surface would be thermalized to the surface temperature by gas-phase collisions occurring in the near vicinity of the surface. It could be that the ethane gas temperature was not completely thermalized to the surface temperature in the Goodman experiments.47 The Sn(Tg,Ts) data of Figure 3b certainly show that Tg can strongly influence dissociative sticking, but the Goodman S(T = 700 K) is even less than the Sn(Tg = 300 K, Ts = 700 K) of Figure 3b. Aside from this discrepancy of unknown origin, Table 2 S(T) values are in reasonable accord with measurements for light alkanes on other surfaces. The methane S(T = 700 K) = 1.0 × 10−5 on Pt(111) is somewhat higher than the expectations of S(T = 700 K) = 3.5 × 10−6 and 1.5 × 10−6 for methane on the close-packed Ru(0001) and Ni(111) surfaces, respectively, based on Egeberg and co-workers’s thermal bulb experiments.48 Alkane dissociative chemisorption is a structure-sensitive reaction,5,49 and the close-packed Pt(111) surface should be less reactive than the more open Pt(110) surface. Weinberg and Sun’s50,51 low pressure ambient gas measurements of S(Tg = 300 K, Ts = 700 K) on Pt(110) for methane, ethane, and propane yielded values of 1.9 × 10−5, 6.3 × 10−4, and 2.1 × 10−3, respectively. Luntz and Winters’s52 measurements of S(Tg = 300 K, Ts = 700 K) on Pt(110) were 1.9 and 3.9 times higher for methane and ethane. These nonequilibrium S(Tg = 300 K, Ts = 700 K) measurements provide lower bounds on the thermal dissociative sticking coefficients, S(T = 700 K), of the alkanes on Pt(110). Consequently, Table 2 results are consistent with the light alkanes being less reactive on Pt(111) as compared to Pt(110). An interesting additional comparison for the methane thermal dissociative sticking coefficient is possible based on catalysis kinetic studies49,53 at 1 bar total pressure, which examined steam reforming of methane on Pt nanocatalysts on ZrO2 oxide supports over a 773−973 K temperature range

∞

S(ϑ; T )vW =

∫E /cos ϑ (kBT )−2 Et e−E /k T dEt t

B

2

0

⎛ = ⎜1 + ⎝ ⎧ (E ⎨ 0 ⎩ (E 0

E0 ⎞ −E0 / kBT ⎟e kBT ⎠ + kBT cos2 ϑ) 2

+ kBT ) cos ϑ

e−(E0 tan

2

⎫ ⎬ ⎭

ϑ)/(kBT )

(2)

where the expression in the curly braces is the angular variation of the van Willigen S(ϑ;T)vW normalized to its value along the direction of the surface normal. The experimental variation of S(ϑ;T)/S(0°;T) for the alkanes in Figure 2 can be admirably fit by the van Willigen functional form with threshold energies of E0 = 37.9, 11.9, and 3.7 kJ/mol for methane, ethane, and propane. However, with these E0 values the van Willigen model predicts absolute dissociative sticking coefficients that are 120, 875, and 660 times higher than the experimental values for methane, ethane, and propane. Moreover, all of these alkanes exhibit strong variations in Sn(Tg,Ts) when Ts is varied independently from Tg (e.g., Figures 3 and 4).7,19,20 Although the 1D model fails to quantitatively capture the multidimensional nature of the dissociative sticking, it provides a simple motivation for the qualitative relationships between the sharpness of the S(ϑ;T)/S(0°;T) angular variation, the reaction threshold energy, and the availability of normal translational 22008



Article

would eliminate any angular variation of S(ϑ;T). This limit has clearly not been reached for the light alkanes examined here. Dynamical effects that restrict the assembly of active exchangeable energy that PCs can use to surmount the activation barrier to dissociative chemisorption enhance the relative importance of normal translation energy and sharpen the angular variation of S(ϑ;T). Figure 2 measurements and modeling indicate that both methane and ethane react in a dynamically biased fashion wherein rotations and parallel translations can be approximated as spectator degrees of freedom and the mean vibrational efficacy is ηv = 0.40. In contrast, propane’s reactivity shows no discernible deviation away from statistical behavior wherein only parallel translations are approximated as spectator degrees of freedom. The spectator status of rotational energy and the dynamical discounting of vibrational energy combine to reduce the methane thermal dissociative sticking coefficient by an order of magnitude as compared to statistical expectations.7,12 The finding that the ethane/Pt(111) reactive system also behaves dynamically points to the complexity of accurately predicting the catalytic behavior of polyatomic molecules at surfaces. More optimistically, the propane/Pt(111) observations encourage the idea that simpler statistical models may suffice to handle the gas-surface reactivity of polyatomic molecules of propane’s size and larger.

energy to surmount the reaction barrier as temperature is varied. The multidimensional PMMT models recognize that energy from other degrees of freedom beyond normal translation can also contribute toward surmounting the energetic barrier to reaction. For thermal dissociative chemisorption of methane on Pt(111) at 700 K, the fractional energy uptakes, the fraction of the mean active total energy of the successfully reacting PCs formed that derives from a particular degree of freedom, f j = ⟨Ej⟩R/⟨Etot⟩R, are 52% from surface phonons, 28% from molecular normal translation, and 20% from molecular vibrations according to the d-PMMT model7 that quantitatively replicates a wide variety of experiments. With increasing alkane size, the angular variation of the thermal dissociative sticking coefficient broadens because the threshold energy for reaction diminishes and the relative importance of normal translational energy to promote reactivity diminishes in comparison to other forms of energy that do not depend on the gas-surface collision angle. Although the translational energy distribution of molecules striking the surface under thermal equilibrium conditions is independent of incident angle, the distribution of normal translational energy varies with angle as: P(En , Tϑ) = (RTϑ)−2 En e−En / RTϑ where Tϑ = T cos2 ϑ (3)

■

For normal incidence (ϑ = 0°), the normal translational energy distribution is identical to the usual flux weighted Maxwell− Boltzmann distribution of translational energy at temperature T. However, as the angle of incidence increases, the effective temperature of the normal translational energy distribution, Tϑ = T cos2 ϑ, falls rapidly. In the S(ϑ;T) experiments, the effective temperature of the normal translational energy distribution varies with molecular incident angle even though the temperature of all other degrees of freedom remains fixed at T. This independent scanning of the normal translational energy temperature from the temperature of the other degrees of freedom distinguishes the S(ϑ;T) experiments from the Sn(Tg,Ts) experiments. Although the fractional energy uptake from normal translational energy is relatively modest at only 28% for thermal dissociative chemisorption of methane on Pt(111),7 the relative availability of En, drawn primarily from the high energy tail of P(En,Tϑ), depends strongly on the angledependent Tϑ. A nonlinear alkane of N atoms has 3N − 6 vibrational modes, and so in going from methane to ethane to propane the number of vibrational modes doubles and then triples its initial value of 9 for methane. Given that vibrational energy is efficacious in helping to surmount the activation barrier to thermal dissociative chemisorption, with increasing alkane size the energy used to surmount the reaction barrier will eventually derive almost exclusively from vibrations, and the angular variation of S(ϑ;T) will become vanishingly small. Another phenomenon that tends to broaden S(ϑ;T) is increasing gas-surface energy transfer, which works toward thermalizing the incident molecule’s energetic modes toward the surface temperature prior to reaction (e.g., Figures 3 and 4). The desorption lifetime at reactive energies is the typical time over which gas-surface energy transfer is possible, and the rate of energy transfer is governed by the α parameter within the PMMT modeling. Both this desorption lifetime and α increase with alkane size. In the limit of sufficiently high gas-surface energy transfer,27 a gas may be thermalized to the surface temperature independent of its initial gas characteristics, which

ASSOCIATED CONTENT

S Supporting Information *

GGA-DFT calculated transition state geometries for ethane and propane dissociative chemisorption on Pt(111), tables of transition state vibrational frequencies, and a table of experimental vibrational frequencies for the gas-phase alkanes that were used in d-PMMT calculations. A table of the GGADFT calculated classical and vibrational zero-point energy corrected threshold energies for dissociative chemisorption for methane, ethane, and propane is also provided. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Phone:(434) 924-3639. Fax: (434) 924-3710. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by National Science Foundation (NSF) grant no. CHE-1112369 and an AES Graduate Fellowship in Energy Research for J.K.N. Electronic structure calculations were performed using the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant no. ACI-1053575, and the Stampede supercomputing system at TACC/UT Austin, funded by NSF grant no. ACI-1134872.

■

REFERENCES

(1) Bond, G. C. Metal-Catalysed Reactions of Hydrocarbons; Springer: New York, 2006. (2) Rostrup-Nielsen, J.; Christiansen, L. J. Concepts in Syngas Manufacture; World Scientific: Singapore, 2011. (3) Sun, P. P.; Siddiqi, G.; Vining, W. C.; Chi, M. F.; Bell, A. T. Novel Pt/Mg(In)(Al)O Catalysts for Ethane and Propane Dehydrogenation. J. Catal. 2011, 282, 165−174. 22009



Article

(4) Weinberg, W. H. Alkane Activation on Transition-Metal Surfaces - Beams, Bulbs, and New Insights. Langmuir 1993, 9, 655−662. (5) Weaver, J. F.; Carlsson, A. F.; Madix, R. J. The Adsorption and Reaction of Low Molecular Weight Alkanes on Metallic Single Crystal Surfaces. Surf. Sci. Rep. 2003, 50, 107−199. (6) Jackson, B.; Nave, S. The Dissociative Chemisorption of Methane on Ni(111): The Effects of Molecular Vibration and Lattice Motion. J. Chem. Phys. 2013, 138, 174705. (7) Donald, S. B.; Navin, J. K.; Harrison, I. Methane Dissociative Chemisorption and Detailed Balance on Pt(111): Dynamical Constraints and the Modest Influence of Tunneling. J. Chem. Phys. 2013, 139, 214707. (8) Nattino, F.; Ueta, H.; Chadwick, H.; van Reijzen, M. E.; Beck, R. D.; Jackson, B.; van Hemert, M. C.; Kroes, G.-J. Ab Initio Molecular Dynamics Calculations versus Quantum-State-Resolved Experiments on CHD3 + Pt(111): New Insights into a Prototypical Gas−Surface Reaction. J. Phys. Chem. Lett. 2014, 5, 1294−1299. (9) Bukoski, A.; Abbott, H. L.; Harrison, I. Microcanonical Unimolecular Rate Theory at Surfaces. III. Thermal Dissociative Chemisorption of Methane on Pt(111) and Detailed Balance. J. Chem. Phys. 2005, 123, 094707. (10) Donald, S. B.; Harrison, I. Dynamically Biased RRKM Model of Activated Gas-Surface Reactivity: Vibrational Efficacy and Rotation as a Spectator in the Dissociative Chemisorption of CH4 on Pt(111). Phys. Chem. Chem. Phys. 2012, 14, 1784−1796. (11) Cushing, G. W.; Navin, J. K.; Valadez, L.; Johánek, V.; Harrison, I. An Effusive Molecular Beam Technique for Studies of Polyatomic Gas-Surface Reactivity and Energy Transfer. Rev. Sci. Instrum. 2011, 82, 044102. (12) Navin, J. K.; Donald, S. B.; Tinney, D. G.; Cushing, G. W.; Harrison, I. Communication: Angle-resolved Thermal Dissociative Sticking of CH4 on Pt(111): Further Indication that Rotation is a Spectator to the Gas-Surface Reaction Dynamics. J. Chem. Phys. 2012, 136, 061101. (13) Rettner, C. T.; Auerbach, D. J.; Tully, J. C.; Kleyn, A. W. Chemical Dynamics at the Gas-Surface Interface. J. Phys. Chem. 1996, 100, 13021−13033. (14) Killelea, D. R.; Utz, A. L. On the Origin of Mode- and BondSelectivity in Vibrationally Mediated Reactions on Surfaces. Phys. Chem. Chem. Phys. 2013, 15, 20545−20554. (15) Muiño, R. D.; Busnengo, H. F. Dynamics of Gas-Surface Interactions: Atomic-Level Understanding of Scattering Processes at Surfaces; Springer: New York, 2013. (16) Beck, R. D.; Maroni, P.; Papageorgopoulos, D. C.; Dang, T. T.; Schmid, M. P.; Rizzo, T. R. Vibrational Mode-Specific Reaction of Methane on a Nickel Surface. Science 2003, 302, 98−100. (17) Killelea, D. R.; Campbell, V. L.; Shuman, N. S.; Utz, A. L. Bondselective Control of a Heterogeneously Catalyzed Reaction. Science 2008, 319, 790−793. (18) Donald, S. B.; Harrison, I. Rice-Ramsperger-Kassel-Marcus Simulation of Hydrogen Dissociation on Cu(111): Addressing Dynamical Biases, Surface Temperature, and Tunneling. J. Phys. Chem. C 2014, 118, 320−337. (19) Cushing, G. W.; Navin, J. K.; Donald, S. B.; Valadez, L.; Johanek, V.; Harrison, I. C-H Bond Activation of Light Alkanes on Pt(111): Dissociative Sticking Coefficients, Evans-Polanyi Relation, and Gas-Surface Energy Transfer. J. Phys. Chem. C 2010, 114, 17222− 17232. (20) Cushing, G. W.; Navin, J. K.; Donald, S. B.; Valadez, L.; Johánek, V.; Harrison, I. Addition/Correction to: C-H Bond Activation of Light Alkanes on Pt(111): Dissociative Sticking Coefficients, Evans-Polanyi Relation, and Gas-Surface Energy Transfer (vol 114, pg 17222, 2010). J. Phys. Chem. C 2010, 114, 22790−22790. (21) Weaver, J. F.; Krzyzowski, M. A.; Madix, R. J. Direct Dissociative Chemisorption of Alkanes on Pt(111): Influence of Molecular Complexity. J. Chem. Phys. 2000, 112, 396−407. (22) Luntz, A. C.; Bethune, D. S. Activation of Methane Dissociation on a Pt(111) Surface. J. Chem. Phys. 1989, 90, 1274−1280.

(23) Bronnikov, D. K.; Kalinin, D. V.; Rusanov, V. D.; Filimonov, Y. G.; Selivanov, Y. G.; Hilico, J. C. Spectroscopy and Non-equilibrium Distribution of Vibrationally Excited Methane in a Supersonic Jet. J. Quant. Spectrosc. Radiat. Transfer 1998, 60, 1053−1068. (24) Mayer, P. M.; Baer, T. A Photoionization Study of Vibrational Cooling in Molecular Beams. Int. J. Mass Spectrom. Ion Processes 1996, 156, 133−139. (25) Stevens, W. R.; Bodi, A.; Baer, T. Dissociation Dynamics of Energy Selected, Propane, and i-C3H7X+ Ions by iPEPICO: Accurate Heats of Formation of i-C3H7+, i-C3H7Cl, i-C3H7Br, and i-C3H7I. J. Phys. Chem. A 2010, 114, 11285−11291. (26) Pauly, H. Other Low-Energy Beam Souces. In Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University Press: New York, 1988; Vol. 1, pp 83−123. (27) Bukoski, A.; Blumling, D.; Harrison, I. Microcanonical Unimolecular Rate Theory at Surfaces. I. Dissociative Chemisorption of Methane on Pt(111). J. Chem. Phys. 2003, 118, 843−871. (28) Ukraintsev, V. A.; Harrison, I. A Statistical Model for Activated Dissociative Adsorption: Application to Methane Dissociation on Pt(111). J. Chem. Phys. 1994, 101, 1564−1581. (29) Bunker, D. L.; Hase, W. L. On Non-RRKM Unimolecular Kinetics: Molecules in General, and CH3NC in Particular. J. Chem. Phys. 1973, 59, 4621−4632. (30) Freed, K. General Discussion. Faraday Discuss. 1979, 67, 231− 235. (31) Forst, W. Unimolecular Reactions: A Concise Introduction, 1st ed.; Cambridge University Press: Cambridge UK, 2003. (32) Miller, J. A.; Klippenstein, S. J. Master Equation Methods in Gas Phase Chemical Kinetics. J. Phys. Chem. A 2006, 110, 10528−10544. (33) Nave, S.; Tiwari, A. K.; Jackson, B. Methane Dissociation and Adsorption on Ni(111), Pt(111), Ni(100), Pt(100), and Pt(110)-(1 × 2): Energetic Study. J. Chem. Phys. 2010, 132, 054705. (34) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (35) Perdew, J. P.; Burke, K.; Ernzerhof, M. Erratum: Generalized Gradient Approximation Made Simple (Vol 77, pg 3865, 1996). Phys. Rev. Lett. 1997, 78, 1396−1396. (36) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (37) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (38) Kresse, G.; Hafner, J. Ab-Initio Molecular-Dynamics Simulation of the Liquid-Metal Amorphous-Semiconductor Transition In Germanium. Phys. Rev. B 1994, 49, 14251−14269. (39) Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics for LiquidMetals. Phys. Rev. B 1993, 47, 558−561. (40) Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953−17979. (41) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (42) Henkelman, G.; Uberuaga, B. P.; Jonsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901−9904. (43) Henkelman, G.; Jonsson, H. A Dimer Method for Finding Saddle Points on High Dimensional Potential Surfaces Using Only First Derivatives. J. Chem. Phys. 1999, 111, 7010−7022. (44) Yang, K.; Zheng, J. J.; Zhao, Y.; Truhlar, D. G. Tests of the RPBE, revPBE, tau-HCTHhyb, omega B97X-D, and MOHLYP Density Functional Approximations and 29 Others Against Representative Databases for Diverse Bond Energies and Barrier Heights in Catalysis. J. Chem. Phys. 2010, 132, 164117. (45) See the Supporting Information. (46) Rodriguez, J. A.; Goodman, D. W. Dissociative Adsorption And Hydrogenolysis of Ethane Over Clean And Ni-Covered Pt(111). J. Phys. Chem. 1990, 94, 5342−5347. 22010



Article

(47) Nielsen, B. O.; Luntz, A. C.; Holmblad, P. M.; Chorkendorff, I. Activated Dissociative Chemisorption of Methane on Ni(100) - a Direct Mechanism under Thermal Conditions. Catal. Lett. 1995, 32, 15−30. (48) Egeberg, R. C.; Ullmann, S.; Alstrup, I.; Mullins, C. B.; Chorkendorff, I. Dissociation of CH4 on Ni(111) and Ru(0001). Surf. Sci. 2002, 497, 183−193. (49) Wei, J. M.; Iglesia, E. Mechanism And Site Requirements for Activation and Chemical Conversion of Methane on Supported Pt Clusters and Turnover Rate Comparisons Among Noble Metals. J. Phys. Chem. B 2004, 108, 4094−4103. (50) Sun, Y. K.; Weinberg, W. H. Kinetics of Dissociative Chemisorption of Methane and Ethane on Pt(110)-(1 × 2). J. Vac. Sci. Technol., A 1990, 8, 2445−2448. (51) Weinberg, W. H.; Sun, Y. K. Quantification of Primary Versus Secondary C-H Bond-Cleavage in Alkane Activation - Propane on Pt. Science 1991, 253, 542−545. (52) Luntz, A. C.; Winters, H. F. Dissociation of Methane and Ethane on Pt(110) - Evidence for a Direct Mechanism under Thermal Conditions. J. Chem. Phys. 1994, 101, 10980−10989. (53) Jones, G.; Jakobsen, J. G.; Shim, S. S.; Kleis, J.; Andersson, M. P.; Rossmeisl, J.; Abild-Pedersen, F.; Bligaard, T.; Helveg, S.; Hinnemann, B.; et al. First Principles Calculations and Experimental Insight Into Methane Steam Reforming Over Transition Metal Catalysts. J. Catal. 2008, 259, 147−160. (54) Abbott, H. L.; Harrison, I. Dissociative Chemisorption and Energy Transfer for Methane on Ir(111). J. Phys. Chem. B 2005, 109, 10371−10380. (55) Michaelides, A.; Hu, P. Insight Into Microscopic Reaction Pathways in Heterogeneous Catalysis. J. Am. Chem. Soc. 2000, 122, 9866−9867. (56) Chen, Y.; Vlachos, D. G. Hydrogenation of Ethylene and Dehydrogenation and Hydrogenolysis of Ethane on Pt(111) and Pt(211): A Density Functional Theory Study. J. Phys. Chem. C 2010, 114, 4973−4982. (57) Zhu, T. W.; van Grootel, P. W.; Filot, I. A. W.; Sun, S. G.; van Santen, R. A.; Hensen, E. J. M. Microkinetics of Steam Methane Reforming on Platinum And Rhodium Metal Surfaces. J. Catal. 2013, 297, 227−235. (58) Van Willigen, W. Angular Distribution of Hydrogen Molecules Desorbed From Metal Surfaces. Phys. Lett. A 1968, 28, 80−81.

22011


Angle-Resolved Thermal Dissociative Sticking of Light Alkanes on Pt

Recommend Documents