Selectivity of chemisorbed oxygen in C-H bond activation and CO oxidation and kinetic consequences for CH4-O2 catalysis on Pt and Rh clusters

Article abstract of DOI:10.1016/j.jcat.2011.06.011

Rate measurements, density functional theory (DFT) within the framework of transition state theory, and ensemble-averaging methods are used to probe oxygen selectivities, defined as the reaction probability ratios for ^O reactions with CO and CH

Full text of DOI:10.1016/j.jcat.2011.06.011

Journal of Catalysis 283 (2011) 10–24
Contents lists available at ScienceDirect
Journal of Catalysis
journal homepage: www.elsevier.com/locate/jcat
Selectivity of chemisorbed oxygen in C–H bond activation and CO oxidation
and kinetic consequences for CH4–O2 catalysis on Pt and Rh clusters
a,
Ya-Huei (Cathy) Chin a, Corneliu Buda b, Matthew Neurock b,c, , Enrique Iglesia
⇑
⇑
a Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, USA
b Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22904, USA
c Department of Chemistry, University of Virginia, Charlottesville, VA 22904, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 March 2011
Revised 4 June 2011
Accepted 12 June 2011
Available online 12 August 2011
Rate measurements, density functional theory (DFT) within the framework of transition state theory, and
ensemble-averaging methods are used to probe oxygen selectivities, defined as the reaction probability
ratios for Oꢀ reactions with CO and CH4, during CH4–O2 catalysis on Pt and Rh clusters. CO2 and H2O are
the predominant products, but small amounts of CO form as chemisorbed oxygen atoms (Oꢀ) are depleted
from cluster surfaces. Oxygen selectivities, measured using 12CO–13CH4–O2 reactants, increase with O2/
CO ratio and Oꢀ coverage and are much larger than unity at all conditions on Pt clusters. These results
suggest that Oꢀ reacts much faster with CO than with CH4, causing any CO that forms and desorbs from
metal cluster surfaces to react along the reactor bed with other Oꢀ to produce CO2 at any residence time
required for detectable extents of CH4 conversion. Oꢀ selectivities were also calculated by averaging DFT-
derived activation barriers for CO and CH4 oxidation reactions over all distinct surface sites on cubo-octa-
hedral Pt clusters (1.8 nm diameter, 201 Pt atoms) at low Oꢀ coverages, which are prevalent at low O2
pressures during catalysis. CO oxidation involves non-activated molecular CO adsorption as the kineti-
cally relevant step on exposed Pt atoms vicinal of chemisorbed Oꢀ atoms (on ꢀ–Oꢀ site pairs). CH4 oxida-
tion occurs via kinetically relevant C–H bond activation on ꢀ–ꢀ site pairs involving oxidative insertion of a
Pt atom into one of the C–H bonds in CH4, forming a three-centered HC3–Pt–H transition state. C–H bond
activation barriers reflect the strength of Pt–CH3 and Pt–H interactions at the transition state, which cor-
relates, in turn, with the Pt coordination and with CH3ꢀ binding energies. Ensemble-averaged Oꢀ selectiv-
ities increase linearly with O2/CO ratios, which define the Oꢀ coverages, via a proportionality constant.
The proportionality constant is given by the ratio of rate constants for O2 dissociation and C–H bond acti-
vation elementary steps; the values for this constant are much larger than unity and are higher on larger
Pt clusters (1.8–33 nm) at all temperatures (573–1273 K) relevant for CH4–O2 reactions. The barriers for
the kinetically relevant C–H bond dissociation step increase, while those for CO oxidation remain
unchanged as the Pt coordination number and cluster size increase, and lead, in turn, to higher Oꢀ selec-
tivities on larger Pt clusters. Oxygen selectivities were much larger on Rh than Pt, because the limiting
reactants for CO oxidation were completely consumed in 12CO–13CH4–O2 mixtures, consistent with lower
CO/CO2 ratios measured by varying the residence time and O2/CH4 ratio independently in CH4–O2 reac-
tions. These mechanistic assessments and theoretical treatments for Oꢀ selectivity provide rigorous evi-
dence of low intrinsic limits of the maximum CO yields, thus confirming that direct catalytic partial
oxidation of CH4 to CO (and H2) does not occur at the molecular scale on Pt and Rh clusters. CO (and
H2) are predominantly formed upon complete O2 depletion from the sequential reforming steps.
Ó 2011 Elsevier Inc. All rights reserved.
Keywords:
CH4
Catalytic partial oxidation
Methane combustion
Platinum
Rhodium
CO oxidation
Density functional theory
C–H bond activation
Transition state theory
Oxygen selectivity
1. Introduction
attractive thermoneutral route to H2–CO mixtures suitable as reac-
tants in methanol and Fischer–Tropsch syntheses [1,2]. H2 and CO
The direct catalytic partial oxidation (CPOX) of methane is
may form via direct CH4–O2 reactions, as proposed based on high
CO selectivities (CO/CO2 > 90%) in short monolith reactors [3,4].
These direct paths seem inconsistent with the fast reactions of
H2 and CO with chemisorbed oxygen atoms (Oꢀ) at the conditions
required for CH4 activation. H2–CO mixtures with direct partial
oxidation stoichiometries (H2/CO = 2) can also form (with the same
overall reaction enthalpy) via initial CH4 combustion to CO2 and
H2O and their subsequent reactions with the remaining CH4 [5].
mildly exothermic (
D
Horeaction ¼ ꢁ35:9 kJ molꢁ1) and provides an
⇑
Corresponding authors. Addresses: Department of Chemical Engineering,
University of Virginia, Charlottesville, VA 22904, USA (M. Neurock). Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, CA
94720, USA. Fax: +1 510 642 4778 (E. Iglesia).
E-mail addresses: mn4n@virginia.edu (M. Neurock), iglesia@berkeley.edu (E.
Iglesia).
0021-9517/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcat.2011.06.011

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
11
These sequential combustion and reforming reactions can proceed
within axial conduction distances in a reactor, thus enabling the
thermal coupling of exothermic and endothermic reactions with-
out the direct molecular coupling implied by catalytic partial oxi-
dation. The discrimination between direct and indirect routes to
H2 and CO from CH4–O2 reactants is made difficult by the ubiqui-
tous presence of temperature and concentration gradients within
packed-beds, monoliths, or catalyst pellets, caused by fast endo-
thermic and exothermic reactions [6–8] and by thermodynamic
constraints that corrupt the intended chemical origins and the
mechanistic interpretations of measured rates and selectivities
[9,10].
Pt and Rh dispersions, defined as the atomic ratios of the ex-
posed metal atoms to total metal atoms, were measured from vol-
umetric H2 uptakes (2–14 kPa, 313 K) (Quantasorb chemisorption
analyzer) and determined by extrapolation of strong H2 adsorption
isotherms to zero pressures using a 1:1 H:Msurface adsorption stoi-
chiometry [11]. Mean metal cluster diameters were calculated
from these dispersion values by assuming hemispherical particles
and the bulk densities of Pt (21.45 g cmꢁ3
(12.41 g cmꢁ3) metals [12].
) [12] and Rh
2.2. Catalytic rate and selectivity measurements
Here, we address the persistent controversies regarding the
occurrence of direct catalytic partial oxidation on Pt and Rh cata-
lysts by measuring rates and selectivities for CH4–O2 reactions un-
der conditions of strict kinetic control. Only trace amounts of CO
were detected at any conditions that retained measurable O2 con-
centrations in the reactor effluent. The yields of CO reflect the
ratios of rate constant for CO and CH4 reactions with O2, described
here in terms of the relevant elementary steps and their rate and
equilibrium constants. These ratios, measured using 13CH4–
12CO–O2 mixtures, showed much higher rate constants for 12CO
oxidation than for 13CH4 oxidation at all O2 pressures and oxygen
surface coverages. These conclusions are consistent with ensem-
ble-averaged ratio of rate constants derived in the framework of
transition state theory using DFT-calculated activation barriers of
CO and CH4 oxidation steps on Pt clusters. These experimental
and theoretical data indicate that H2 and CO do not form directly
from CH4–O2 mixtures because any CO that desorbs from catalyst
surfaces would form CO2 via subsequent oxidation along the cata-
lyst bed at all residence times required for measurable CH4 conver-
sions. Partial oxidation products (CO and H2) are exclusively
formed from subsequent reactions of CO2 and H2O with CH4 after
depletion of the limiting O2 reactant on Pt and Rh catalysts at
CH4 conversions of practical interest.
CH4 conversion turnover rates (per exposed metal atom) and
selectivities (on a carbon basis) were measured on a packed-bed
of catalyst particles held within a quartz tube (8.1 mm ID) fitted
with an axial concentric thermowell that contains a K-type ther-
mocouple. SiO2 granules (Davison Chemical, Chromatographic Sil-
ica Media, CAS #112926-00-8, 280 m2 gꢁ1, <100
lm) were used as
intrapellet diluents for Pt/SiO2, Pt/Al2O3, and Rh/Al2O3 catalysts
(100–300 SiO2/catalyst ratios) by mixing, pelletizing, and sieving
to retain 100–180 lm agglomerates. These pellets were then
mixed loosely with quartz granules (Fluka, #84880, 1000–4700
quartz/catalyst ratios) of similar size and placed in the quartz tube,
forming the packed catalyst bed. The catalyst bed (containing
0.15–0.25 mg of Pt/Al2O3 or Rh/Al2O3) was heated in flowing He
(Praxair, UHP grade, 1.67 cm3 sꢁ1) at 0.083 K sꢁ1 to reaction tem-
peratures. Reactant mixtures were prepared using 25% CH4/He
(Matheson Certified Plus Grade), 5% O2/He (Praxair, Certified
Standard), and He (Praxair, UHP grade). Individual flow rates were
metered using electronic mass flow controllers (Porter, type 201).
13CH4 (Isotec, 99% 13C purity), 1% 12CO/He (Praxair, Certified
Standard), and 5% O2/He (Praxair, Certified Standard) were used
in 13CH4–12CO–O2 isotopic experiments. CH4, CO, H2, O2, and CO2
molecules were measured by thermal conductivity detection after
chromatographic separation (Agilent 3000A Micro GC with chan-
nels equipped with 5A and Porapak Q columns). 13CO2, 12CO2,
13CO, and 12CO concentrations were measured by mass selective
detection after similar chromatographic separation (Agilent
5973N MSD and 6890 GC).
2. Experimental and theoretical methods
2.1. Synthesis and characterization of Pt and Rh catalysts
2.3. Density functional theory methods
Pt and Rh clusters on c-Al2O3 or SiO2 were prepared by incipient
wetness impregnation with aqueous solutions of hexachloroplatinic
acid (H2PtCl6, Aldrich, CAS #16941-12-1, 8 wt.% solution) or rho-
dium(III) nitrate (Rh(NO3)3, Aldrich, CAS #13139-58-9, 10 wt.%
Gradient-corrected plane-wave density functional theory calcu-
lations were carried out to determine the optimized structures and
energies of reactants, transition states, and products for reactions
of adsorbed CH4 and CO with isolated chemisorbed oxygen atoms
(Oꢀ) on a Pt(1 1 1) surface and on different surface sites of cubo-
octahedral Pt clusters with 201 atoms (Pt201, Ntotal = 201, 1.8 nm
diameter, Scheme 1). The Pt(1 1 1) surface was described using
periodic 3 ꢂ 3 unit cells comprised of four layers of Pt atoms (9
Pt atoms in each layer) and a 1.5 nm vacuum region to separate
the metal surfaces. Pt201 cubo-octahedral clusters are low-energy
optimized structures and expose eight (1 1 1) (Scheme 1b) and
six (1 0 0) (Scheme 1c) edge-shared facets [13]. The (1 1 1) and
(1 0 0) terraces on Pt201 cluster contain 19 and 9 Pt atoms, respec-
tively; the number of these exposed atoms (NS), together with the
total number of Pt atoms (Ntotal = 201), results in a fractional dis-
persion (NS/Ntotal) of 0.61. These surface Pt atoms are denoted as
sites 1–4 based on their coordination numbers, and oxygen adsorp-
tion sites are denoted as sites I–V, as shown in Scheme 1b and c.
Simulations were carried out by placing the Pt201 cluster at the
center of a 3 ꢂ 3 ꢂ 3 nm cubic unit cell and at least 0.8 nm from all
cell edges to prevent electronic interactions among clusters. Subse-
quent simulations with larger 4 ꢂ 4 ꢂ 4 nm unit cells gave adsorp-
tion energies that differ by <2 kJ molꢁ1 from those in the
3 ꢂ 3 ꢂ 3 nm cell, consistent with the absence of inter-cluster
solution), respectively.
c ,
-Al2O3 (Sasol, Lot #C1643, 193 m2 gꢁ1
0.57 cm3 gꢁ1 pore volume) was treated in flowing dry air (Praxair,
zero grade, 0.8 cm3 gꢁ1 sꢁ1) by heating (at 0.083 K sꢁ1) to 998 K or
1123 K (for Pt and Rh catalyst preparation, respectively) and holding
for 3 h. X-ray diffractograms of treated Al2O3 samples showed the
exclusive presence of
c-phase Al2O3. SiO2 (Grace Davison, Grade
62, Lot #995, 280 m2 gꢁ1) was treated in flowing dry air (Praxair,
zero grade, 0.8 cm3 gꢁ1 sꢁ1) by heating to 923 K at 0.083 K sꢁ1 and
holding for 3 h. These supports were impregnated to incipient wet-
ness with the respective metal precursors and treated in ambient air
at 383 Kꢁf1or 8 h and in flowing dry air (Praxair, zero grade,
0.8 cm3 g sꢁ1) by heating to 998 K (for Pt) or 1123 K (for Rh) at
0.083 K sꢁ1 and holding for 3 h. Samples were cooled to ambient
temperature and then treated in a flowing H2/Ar mixture (9% H2/
Ar, Praxair, Certified Standard) by heating to 923 K (0.083 K sꢁ1
,
0.8 cm3 gꢁ1 sꢁ1) and holding for 2 h and then cooling to 573 K. A
He stream (Praxair, UHP grade, 0.8 cm3 gꢁ1 sꢁ1) was introduced to
the sample at 573 K before cooling to ambient temperature when
this stream was then replaced by an O2/He mixture (0.5% O2/He,
Praxair, Certified Standard, 0.8 cm3 gꢁ1 sꢁ1) for 2 h to prevent exten-
sive oxidation of metal clusters upon contact with ambient air.

12
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
(a)
(b)
(111)
II
IV
V
(100)
(100)
(111)
4
2
3
1
(111)
(c)
(111)
I
III
(100)
Scheme 1. (a) Model of a cubo-octahedral Pt cluster (1.8 nm cluster size) consists of 201 Pt atoms with: (b) eight (1 1 1) and (c) six (1 0 0) planes. There are four distinct types
of surface Pt atom (labeled sites 1–4) depending on their coordination numbers. Oxygen atoms bind on threefold fcc sites (location II, IV, and V) on the (1 1 1) surfaces (b) and
on the bridge sites (location I and III) on the (1 0 0) surfaces (c).
ECH
are the energies for the respective optimized gas-phase
interactions. All calculations were carried out using the Perdew
Wang 91 (PW91) [14] form of the generalized gradient approxima-
tion (GGA) in the Vienna Ab-initio Simulation Package (VASP)
[15–17]. The wavefunctions were generated using a periodic
expansion of plane waves up to a 396 eV kinetic energy cutoff.
The interactions between valence and core electrons were de-
scribed by Vanderbilt ultrasoft pseudopotentials (US-PP) [18].
The electronic state energy of the system was converged to within
9.65 ꢂ 10ꢁ3 kJ molꢁ1 (10ꢁ4 eV), whereas the forces on each of the
atoms were converged to within 48.2 kJ (mol nm)ꢁ1 (0.5 eV nmꢁ1).
The first Brillouin zone was sampled using (1 ꢂ 1 ꢂ 1) and
(3 ꢂ 3 ꢂ 1) Monkhorst–Pack k-point meshes for the Pt201 clusters
and Pt(1 1 1) surfaces, respectively [19]. In the Pt201 cluster calcu-
lations, all Pt atoms and all adsorbate atoms were fully relaxed. On
Pt(1 1 1) surfaces, Pt atoms in the top two layers and adsorbed spe-
cies were fully relaxed, while Pt atoms in the bottom two layers
were held fixed at their bulk distances.
4ðgÞ
molecules.
Transition state complexes and reaction barriers for C–H bond
dissociation and for CO adsorption and oxidation were calculated
using the climbing-image nudged elastic band (CI-NEB) method
[20]. Four equally spaced images were chosen between the reac-
tant and product states to represent the reaction coordinate. The
forces perpendicular to the reaction coordinate for each of these
images were optimized using 50 structural optimization steps to
establish the highest energy state along the reaction trajectory.
The climbing algorithm was then turned on and used to drive the
image that exhibits the highest energy up along the reaction coor-
dinate by maximizing the energy along the tangent to the potential
energy surface to within
a
force of 48.2 kJ (mol nm)ꢁ1
(0.5 eV nmꢁ1). This is used to isolate a stationary point which is a
maximum along the minimum energy path and to calculate the
activation energy. Full frequency calculations would be required
to ensure that this was the transition state. The significant CPU ef-
fort necessary to calculate second derivatives made it prohibitive
to carry out full frequency calculations.
The heat of atomic oxygen adsorption (QO, with respect to
O2(g)) is defined here as the negative of the energy for:
0:5O2ðgÞ þ Pt ! Oꢀ—Pt
ð1Þ
in which Pt atoms are present on either Pt201 clusters or Pt(1 1 1)
surfaces. QO is therefore given by the total DFT-optimized energies
for a chemisorbed oxygen atom (Oꢀ) on Pt201 clusters (or Pt(1 1 1)
surfaces), for bare Pt201 clusters (or bare Pt(1 1 1) surfaces), and
2.4. Ensemble-averaged rate constants
The relative rates of CO and CH4 oxidation were calculated on
Pt201 clusters (Scheme 1) using statistical and transition state the-
ory methods, DFT estimates of activation barriers on different sites
at Pt201 cluster surfaces, and measured activation entropies. These
reactions can proceed on metal–metal (ꢀ–ꢀ) and metal–oxygen
(ꢀ–Oꢀ) site pairs with different barriers depending on the coordina-
tion of metal sites or the heat of atomic oxygen adsorption (Eq.
(2)); therefore, their barriers were averaged over all possible site
pairs on Pt201 clusters and taken together with the activation
entropies to obtain the ensemble-averaged CO and CH4 oxidation
rate constants. We have examined in detail the reactivity of five
distinct oxygen adsorption sites (sites I–V) and four types of Pt
sites (sites 1–4), including corner, edge, and terrace locations on
(1 1 1) and (1 0 0) surfaces (Scheme 1). We considered clusters
with one Oꢀ atom, because such low Oꢀ coverages prevail during
CH4–O2 reactions at conditions leading to near complete O2 con-
sumption would favor COꢀ desorption before subsequent oxidation
to CO2. Both (1 1 1) and (1 0 0) facets were treated as Langmuirian
for O2(g), denoted here as EPt–O, EPt, and EO ðgÞ, respectively:
2
QO ¼ ꢁðEPt—O ꢁ EPt ꢁ 0:5EO ðgÞÞ
ð2Þ
2
We assume here that the zero-point energy contributions and any
changes in heat capacity between 0 K and 298 K are small compared
with overall reaction energies. The heats of non-dissociative
adsorption for CO (QCO) and CH4 (QCH ) are taken as the negative
4
values of the calculated reaction energies for CO and CH4 molecular
adsorption (denoted as
DECO,ads and DECH ;ads, respectively) on Pt201
4
clusters (or Pt(1 1 1) surfaces):
QCO ¼ ꢁ ECO;ads ¼ ꢁðEPt—CO ꢁ EPt ꢁ ECOðgÞÞ
D
ð3Þ
ð4Þ
QCH ¼ ꢁ
D
ECH ¼ ꢁðEPt—CH ꢁ EPt ꢁ ECH ðgÞÞ
4;ads
4
4
4
where EPt–CO and EPt—CH are the energies for chemisorbed CO and
4
CH4 on Pt201 clusters (or Pt(1 1 1) surfaces), EPt is the energy of
the bare Pt201 clusters (or bare Pt(1 1 1) surfaces), and ECO(g) and

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
13
surfaces, on which site pairs involved in CO and CH4 reactions were
treated as non-interacting ensembles.
covered surfaces), which activate C–H bonds more effectively than
Oꢀ–Oꢀ or ꢀ–ꢀ site pairs prevalent at larger or smaller O2/CH4 ratios,
respectively; these ꢀ–Oꢀ site pairs lead to the sharp maximum
observed in turnover rates at intermediate O2/CH4 ratios (Fig. 1a
and b) [23]. CO was only detected (CO/CO2 < 0.02) at O2/CH4 ratios
below 0.04, indicating that CH4 combustion, instead of partial oxi-
dation, is the predominant catalytic reaction, even at very low O2/
CH4 ratios (Section 3.2).
Any effects of gradients in temperature and concentration within
catalyst pellets and across the film boundaries of gas and solid
phases on CH4 turnover rates (873 K) were ruled out by varying
intrapellet dilution ratios (k; 100–300) at constant bed dilution ra-
We consider two limiting cases for the distribution of Oꢀ on
Pt201 clusters: (i) random Oꢀ occupation at all surface Pt sites irre-
spective of coordination and (ii) site occupancy prescribed by oxy-
gen adsorption thermodynamics (QO; Eq. (2)). In the first case, the
occupation probability (Pj,random) is given by the fraction of Oꢀ
atoms of type j among all Oꢀ atoms, where j is a roman numeral
from I to V, as shown in Scheme 1. In the second case, Pj,weighted
is determined by the number of each type of Oꢀ adsorption site (de-
noted here as mj or mk, where j and k refer to the specific sites I–V
in Scheme 1, thus j, k = 1–5 and 1 = I, 2 = II, 3 = III, 4 = IV, 5 = V) and
weighted by their heats of atomic oxygen adsorption (QO,j, QO,k):
tios (v; 4700). The smallest intrapellet dilution ratios (100) gave
ꢀ
ꢁ
higher turnover rates than larger ratios (>200), because of small
residual temperature gradients even after such significant dilutions
(Fig. 1a). Turnover rates did not depend on intrapellet dilution for k
values above 200, which rendered intrapellet temperature and con-
centration gradients kinetically undetectable. These results also rule
out the gradients across the gas and solid boundaries, because such
gradients would lead to rates that depend on the density of active
sites within pellets. CH4 oxidation rates strictly proportional to the
number of surface Pt atoms within such pellets and turnover rates
independent of intrapellet site densities have rigorously confirmed
the removal of these gradients (Fig. 1a).
QO;j
RT
mj exp
ꢀ
ꢁ
Pj;weighted
¼
ð5Þ
P
QO;k
5
k¼1mkexp
RT
3. Results and discussion
3.1. Detection and removal of transport corruptions in measured rates
Rigorous kinetic measurements require the absence of transport
restrictions within catalyst pellets and reactors in order to ensure
that local temperatures and reactant and product concentrations
at active sites reflect those measured in the contacting gas phase.
Measured rates and selectivities that do not depend on the extent
of catalyst dilution provide the sole unequivocal evidence for strict
kinetic control and for the rigorous absence of transport corrup-
tions of measured chemical reaction rates [21,22].
Bed temperature gradients were probed using physical mix-
tures of diluent and catalyst particles at bed dilution ratios (v) of
1000–4700 and constant intraparticle dilution ratios (k; 200). Bed
dilution ratios of 1000 gave higher turnover rates than at higher
values (
that give the highest reaction and heat generation rates (Fig. 1b).
Turnover rates became insensitive to bed dilution for values
v P 2000) at the intermediate O2/CH4 ratios (0.06–0.18)
v
Fig. 1a and b shows CH4 turnover rates (873 K) at various dilu-
tion ratios within the pellets (k) (100–300 diluent-to-catalyst ratio)
or the catalyst bed (v) (1000–4700 diluent-to-catalyst ratio) at
above 2000, for which turnover rates no longer depended on the
number of sites within the catalyst bed. These extensive dilution
levels (k P 200 and
v P 2000) were required for strict kinetic con-
0.02–0.33 O2/CH4 reactant ratios on Pt/Al2O3 (0.2 wt.% Pt; 8.5 nm
mean Pt cluster diameter). For these O2/CH4 values, the O2/CH4
ratios determine Oꢀ coverages on cluster surfaces because of the ki-
netic coupling between irreversible C–H bond and O2 dissociation
steps that form and remove the Oꢀ atoms [23]. Turnover rates
trol and for identical temperatures and concentrations at active
sites and in the contacting gas phase; these dilution requirements,
which have been seldom (if at all) met in previously reported rate
data and correspond to reactor heat loads smaller than
0.35 W cmꢁ3 for the dimensions of the reactor and pellets
(8.1 mm and 0.180 mm, respectively) used here, are required to
eliminate transport artifacts to obtain the rate data and associated
mechanistic interpretations.
reached their highest values (>900 mol CH4 (g-atom Ptsurface-s)ꢁ1
,
hereinafter denoted as sꢁ1) on Pt surfaces covered partially with
chemisorbed oxygen atoms (Oꢀ), which prevail at intermediate
O2/CH4 ratios (0.07–0.12). These Oꢀ species form ꢀ–Oꢀ site pairs
with vicinal Pt atoms (ꢀ, also denoted as oxygen vacancies on Oꢀ
CH4–O2 turnover rates were also measured on Rh/Al2O3
(0.2 wt.% Rh; 3.3 nm mean cluster diameter) at similar bed and
1400
1200
(a)
(b)
1200
1000
800
600
400
200
0
1000
800
600
400
200
0
0
0.1
0.2
O2/CH4
0.3
0.4
0
0.1
0.2
O2/CH4
0.3
0.4
Fig. 1. (a) Effects of intrapellet diluent-to-catalyst ratio (k) {100 (d), 200 (N), 300 (j)} on CH4 turnover rates (per exposed Pt atom; 873 K) on 0.2 wt.% Pt/Al2O3 (8.5 nm mean
cluster diameter), plotted here as a function of O2/CH4 ratio (4700 diluent/catalyst interpellet dilution ratio (
), 0.15 mg cat., 2.08 cm3 (STP) sꢁ1, 4.9 kPa CH4). (b) Effects of
interpellet diluent-to-catalyst ratio ( ) {1000 (d), 2000 (N), 4700 (j)} on CH4 turnover rates (per exposed Pt atom; 873 K) on 0.2 wt.% Pt/Al2O3 (8.5 nm mean cluster
diameter), plotted here as a function of O2/CH4 ratio (200 diluent/catalyst intrapellet dilution ratio (k), 0.15 mg cat., 2.08 cm3 (STP) sꢁ1, 4.9 kPa CH4).
v
v

14
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
intrapellet dilutions (k = 100–300;
v
= 1900–2800; Table 1). Turn-
co-reactants were depleted and O2/CH4 ratios concurrently de-
creased. Similar effects were observed when inlet O2/CH4 ratios
(instead of residence times) were changed while keeping the resi-
dence time constant (Fig. 1a and b). These trends were also found
on 0.2 wt.% Rh/Al2O3 (Fig. 2b). These kinetic effects of O2/CH4 ratios
reflect changes in the identities of the most abundant surface inter-
mediates (MASI) and of the kinetically relevant steps [23]. As the
Oꢀ coverage on Pt clusters decreases with decreasing O2/CH4 ratio,
the kinetically relevant step shifts from C–H bond activation on
oxygen–oxygen (Oꢀ–Oꢀ) site pairs to on metal–oxygen (ꢀ–Oꢀ) site
pairs, and ultimately to O2 activation on metal–metal (ꢀ–ꢀ) site
pairs [23]. When O2 is no longer present, CH4 reforming becomes
the prevalent reaction and C–H bond activation occurs on metal–
metal (ꢀ–ꢀ) site pairs, which forms carbonaceous intermediates
that are removed by Oꢀ species derived from H2O or CO2 [24].
H2 was not detected before O2 depletion on any of the catalysts
used, apparently because if formed, it reacted very rapidly with Oꢀ
to form H2O before the reactor exit at all residence times required
for practical CH4 conversions. CO2 and H2O were the only products
detected even at residence times that led to nearly complete O2
conversion (1.2 ꢂ 10ꢁ4 (g-atom Ptsurface-s)(mol CH4)ꢁ1 and
1.4 ꢂ 10ꢁ3 (g-atom Rhsurface-s)(mol CH4)ꢁ1)). Even at the smallest
O2/CH4 ratios (<0.04 for Pt; <0.03 for Rh), CO/CO2 ratios were near
CO detection limits (<0.013 for Pt; ꢄ0.005 for Rh) at all residence
times that led to detectable O2 effluent concentrations. These data
are consistent with those measured by varying the O2/CH4 ratios at
a constant residence time (Fig. 1a and b), for which CO was de-
tected (CO/CO2 < 0.02) only at O2/CH4 ratios below 0.04. These ef-
fects of residence time and O2/CH4 ratio on outlet CO/CO2 ratios
over rates were smaller on Rh than on Pt at all O2/CH4 ratios {max-
imum rates were ꢃ70 sꢁ1 for Rh (Table 1 and Fig. 2) vs. ꢃ900 sꢁ1
for Pt (Fig. 1a and b); Section 3.2}; these reaction rates led to a
maximum volumetric heat generation rate of 5.4 ꢂ 10ꢁ2 W cmꢁ3
,
which was much smaller than that on the Pt catalysts
(0.35 W cmꢁ3). Therefore, CH4–O2 reactions on Rh are less likely
to cause temperature gradients, as confirmed from turnover rates
that are independent of the values of k and
These data show that extensive dilutions at the scales of pellets
(k P 200; 0.180 mm pellet diameter) and reactor beds ( P 2000;
8.1 mm reactor diameter) are required to obtain CH4–O2 rate data
under conditions of strict kinetic control and to eliminate transport
artifacts ubiquitous in these highly exothermic reactions. All rates
and selectivities reported herein were measured using these dilu-
tion ratios and volumetric heat generation rates much smaller than
those causing transport corruptions of chemical rates
(60.35 W cmꢁ3).
v (Table 1).
v
3.2. Residence time effects on turnover rates and CO/CO2 selectivities
Fig. 2a and b show CH4 turnover rates, CO/CO2 selectivity ratios,
and outlet O2 pressures as a function of residence time on Pt/Al2O3
(0.2 wt.%; 8.5 nm mean cluster diameter) and Rh/Al2O3 (0.2 wt.%;
3.3 nm mean cluster diameter) for inlet O2/CH4 ratios of 0.125
and 0.13, respectively, which make O2 the limiting reactant.
On Pt, turnover rates initially increased (from 270 to 370 sꢁ1) as
the residence time increased (from 0.4 ꢂ 10ꢁ4 to 1.2 ꢂ 10ꢁ4
(g-atom Ptsurface-s)(mol CH4)ꢁ1), but ultimately decreased as O2
Table 1
Effects of intraparticle (k) and interparticle (v) diluent-to-catalyst ratios on CH4 turnover rates on 0.2 wt.% Rh/Al2O3 (3.3 nm mean cluster diameter) catalyst at 873 K.
Turnover rate (mol CH4 (g-atom Rhsurface-s)ꢁ1
)
Heat load (10ꢁ2 W cmꢁ3
)
Intraparticle (k) diluent-to-catalyst ratio
Interparticle (v) diluent-to-catalyst ratio
65.3
68.1
62.0
71.9
5.4
3.8
3.5
4.1
300
300
200
100
1900
2800
2800
2800
(0.37 mg cat., 0.583 cm3 (STP) sꢁ1, 0.13 inlet O2/CH4 ratio).
×102
× 102
O2 /CH4
O2 /CH4
(a)
(b)
4.0 2.3
3
0
9.9
0.0
10
7
1.8
1.6
1.4
1.2
1
70
60
50
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
400
350
300
250
200
150
100
50
(a)
(b)
CH4
turnover rate
CH4
turnover
rate
40
30
20
10
0
CO selectivity
0.8
0.6
0.4
0.2
0
CO selectivity
O2 pressure
O2 pressure
0
0
1
2
3
4
5
0
1
2
3
Residence time ×104
Residence time ×103
[g-atom Ptsurface-s-(mol CH4)-1]
[g-atom Rhsurface-s-(mol CH4)-1]
Fig. 2. (a) CH4 turnover rate (d), outlet O2 pressure (j), and CO selectivity (N) during CH4–O2 reactions on 0.2 wt.% Pt/Al2O3 (8.5 nm mean cluster diameter) as a function of
residence time for an inlet O2/CH4 feed ratio of 0.13 (873 K, 4.9 kPa CH4, k = 200, = 4700). O2/CH4 ratios at the effluent stream are indicated in the secondary x-axis. (b) CH4
turnover rate (d), outlet O2 pressure (j), and CO selectivity (N) during CH4–O2 reactions on 0.2 wt.% Rh/Al2O3 (3.3 nm average cluster diameter) as a function of residence
time for an inlet O2/CH4 feed ratio of 0.125 (873 K, 5.0 kPa CH4, k = 200, = 4700). O2/CH4 ratios at the effluent stream are indicated in the secondary x-axis.
v
v

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
15
KO2
indicate that CH4–O2 reactions form only CO2 and H2O at all prac-
tical O2/CH4 ratios and CH4 conversion levels.
O2 +*←⎯⎯→O2 *
(1)
These results were assessed at shorter residence times than pre-
vious studies [3,4] {ꢃ3.6 ꢂ 10ꢁ5 (cm3 catalyst)-s-(std cm3 total
flow)ꢁ1 in Fig. 1a and b vs. ꢃ10ꢁ2 (cm3 monolith volume)-s-(std
cm3 total flow)ꢁ1 reported in Refs. [3,4]}. Our results contradict
the previous findings [3,4] that CO selectively forms at short resi-
dence times. These previous conclusions [3,4] were based on data
acquired on catalysts wash-coated on monoliths, for which the me-
tal site densities and the volumetric heat generation rates were
estimated to be much larger than our samples (ꢃ135 W cmꢁ3
[25] vs. 60.35 W cmꢁ3 used herein). Rate and selectivity data on
those samples were influenced strongly by very severe tempera-
ture and concentration gradients with a reported temperature
difference between the inlet feed and catalyst surfaces exceeding
350 K [3,4]. The very small and typically undetectable CO/CO2 ra-
tios observed here before O2 depletion under conditions of strict
kinetic control at all residence times and inlet O2/CH4 ratios rigor-
ously show that CO and H2 do not form via direct reactions of CH4–
O2 mixtures on Pt or Rh catalysts. These results do not rule out COꢀ
desorption but they suggest that COꢀ, if desorbed unreacted, would
re-adsorb and react via subsequent reaction with Oꢀ along the cat-
alyst bed at all residence times required for detectable levels of CH4
conversion. CO (and H2) molecules form only via secondary reac-
tions of CH4 with combustion products (CO2 and H2O) after O2
depletion.
The direct formation of CO (or H2) from CH4–O2 reactants
requires that COꢀ (or Hꢀ) desorbs from catalyst surfaces before sub-
sequent reactions with Oꢀ and that desorbed CO (or H2) does not
re-adsorb and react with Oꢀ at reactor residence times required
for practical CH4 conversion. The overall CO yields attainable in
CH4–O2 reactions depend on the selectivity of Oꢀ reactions with
CO and CH4. In what follows, we first address the mechanism for
CH4 and CO reactions with Oꢀ and then describe Oꢀ selectivities
in terms of kinetic and thermodynamic constants for the elemen-
tary steps that we propose to account for the kinetic dependence,
kinetic isotope effects, and ensemble-averaged rates obtained from
transition state and density functional theory. These quantitative
and molecular scale interpretations of Oꢀ selectivities provide a rig-
orous assessment on the maximum CO yield attainable from direct
CH4–O2 reactions (Section 3.7).
O2 *+ * ⎯k⎯O* → 2O*
(2)
(3)
(4)
KCH
4
CH4 +*←⎯⎯→CH4 *
CH4 *+* ⎯k⎯[⎯*−*] →CH3 *+H*
k[O*−*]
CH4 *+O* ⎯⎯⎯→CH3 *+OH*
(5)
kC*+O*
C* +O* ⎯⎯⎯→ CO* + *
(6)
(7)
(8)
*CO ⎯k⎯CO d⎯es ,k⎯CO⎯ads →CO + *
CO*+O* ⎯⎯kCO⎯oxi →CO2 *+ *
KCO
2
CO2 *←⎯⎯→CO2 + *
(9)
KH2
2H *←⎯⎯→H2 + 2*
(10)
KH*+O*
H *+O*←⎯⎯→OH*+ *
(11)
(12)
KH*+OH*
H *+OH *←⎯⎯⎯→H2O*+ *
KH2
O
H2O*←⎯⎯→H2O + *
(13)
(14)
kCH*
CHx *S +O*W ⎯⎯⎯→
Scheme 2. A proposed sequence of elementary steps for CH4–O2 reactions on Pt
clusters uncovered of chemisorbed oxygen atoms. ? and M denote irreversible and
quasi-equilibrated steps, respectively.
k is the rate coefficient and K is the
equilibrium constant for the respective elementary step.
pressure and unaffected by either the CH4 pressure or isotope iden-
tity (CH4/CD4 kinetic isotope effects = 1.01) and from the small
measured activation barriers (<3 kJ molꢁ1) [23].
O2 chemisorbs molecularly as O2ꢀ on unoccupied Pt sites (ꢀ, Step
1, refer to Scheme 2 herein for the identity of elementary steps)
[26] and subsequently dissociates on vicinal ꢀ sites to form Oꢀ (Step
2). CH4 adsorbs weakly on vacant ꢀsites (ꢀ, Step 3) and then reacts
ꢀ
ꢀ
with vicinal species to form CH3 and Hꢀ (Step 4). CH4 can also
react with vicinal Oꢀ species to form CH3 and OHꢀ (Step 5). In
ꢀ
ꢀ
3.3. Oxygen selectivities from competitive reactions of 12CO and 13CH4
with O2 on Pt clusters
either case, the CH3 subsequently decomposes via successive H-
abstractions and Oꢀ insertions (Step 6) to form COꢀ. COꢀ can desorb
(Step 7) or react with another Oꢀ to form CO2 (Steps 8 and 9). Sim-
ilarly, Hꢀ can recombine with another Hꢀ to form H2 (Step 10) or re-
act with Oꢀ and then Hꢀ (or OHꢀ) to form H2O (Steps 11–13). These
steps also include the possible readsorption of CO and H2 (reverse
of Steps 7 and 10) to re-form COꢀ and Hꢀ, which can react with Oꢀ
to form CO2 and H2O and complete a combustion turnover.
CO oxidation turnover rates are proportional to O2 pressure and
unaffected by CO pressure [23], consistent with kinetically relevant
O2 dissociation steps on bare Pt clusters. In fact, CH4 [23], C2H6
[27], and CO [23] oxidation rates on uncovered Pt clusters were
all independent of the identity, concentration, or reactivity of the
reductant and limited solely by O2 activation steps. Thus, these
Here, we consider Oꢀ selectivities on Pt clusters essentially
uncovered by reactive intermediates, because such surfaces are
most likely to desorb COꢀ (or Hꢀ) before subsequent reactions of
these species with vicinal Oꢀ to form CO2 (or H2O). Oꢀ selectivities
(SOꢀ) on uncovered Pt surfaces reflect the ratio of reactive collision
probabilities of desorbed CO and CH4 reactant with Oꢀ, which are
given by the first-order rate constants of CO (kO —CO) and CH4
2
(kO
) oxidation, respectively:
2—CH4
k
¼
O2—CO
ꢀ
SO
ð6Þ
k
O2—CH4
rates are related to the O2 consumption rates (rO ) by their respec-
2
These Oꢀ selectivities can be rigorously measured by introducing
12CO into a 13CH4–O2 mixture. The evidence for the low coverage
of intermediates on Pt clusters at these low O2/CH4 ratios (<0.08
for 8.5 nm Pt clusters) and for the sequence of elementary steps
(Scheme 2) involved in CH4 and CO oxidation via reactions with
Oꢀ species are consistent with the rate dependencies and kinetic
isotope effects reported elsewhere [23]. At these O2/CH4 ratios,
CH4 conversion rates are limited by O2 dissociation steps on uncov-
ered Pt surfaces, as confirmed from rates that are proportional to O2
tive reaction stoichiometries. O2 consumption rates are propor-
tional to O2 pressures with an effective rate constant given by
ꢀ
the product of O2 adsorption equilibrium constant (KO ) and O2
2
ꢀ
dissociation rate constant (kO ), as defined in Steps 1 and 2, respec-
tively, and derived elsewhere [23,27]. O2 consumption rates were
identical (Table 2; Entries 1–2, 0.2 wt.% Pt/SiO2, 33 nm mean clus-
ter diameter), and CO (rCO) and CH4 (rCH ) turnover rates for CO–O2
4
and CH4–O2 reactants are related to each other and to the O2 con-
sumption rates by reaction stoichiometry:

16
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
Table 2
O2 turnover rates during 13CH4–12CO–O2, 12CH4–O2, and 12CO–O2 reactions and ratios of O2 turnover rates in 13CH4–12CO–O2 and CO–O2 mixtures (b, Eq. (17)) on supported Pt
clusters of 1.8 nm and 33 nm mean cluster diameters (0.2 wt.% Pt supported on Al2O3 and SiO2, respectively) at 873 K.
O2 turnover rates (mol O2 (g-atom Ptsurface-s)ꢁ1
)
b
ðO2
Þ
ðO2
Þ
Entry
Pt cluster size (nm)
Reactant mixture
O2 pressure (kPa)
ðCOÞ
ðCH4
Þ
1
2
3
4
5
6
33
33
33
1.8
1.8
1.8
12CH4–O2
0.036
0.036
0.036
0.009
0.009
0.009
–
0.022 [52]
–
0.022
–
0.008
0.0033
500.1
512.4
496.0
9.0
7.5
7.1
–
–
0.99
–
0.83
0.79
12CO–O2
0.23
0.23
0.024
0.024
0.024
13CH4–12CO–O2
12CO–O2
13CH4–12CO–O2
13CH4–12CO–O2
(k = 200,
v
= 4700, 0.15 mg cat., 2.08 cm3 (STP) sꢁ1).
ꢀ
rO ¼ 2rCH ¼ 0:5rCO ¼ KO kO ðO2Þ
ð7Þ
70
60
50
40
30
20
10
0
2
4
2
In CH4–CO–O2 mixtures, O2 consumption rates are also limited by O2
activation and are given by the combined rates of O2 reactions with
CH4 and CO (and H2) weighed by their respective conversion stoichi-
ometries. O2 consumption rates in CH4–CO–O2 mixtures (Table 2,
Entry 3) are similar to those measured with CO–O2 or CH4–O2
mixtures (Entries 1–2) for a given O2 pressure, because CH4 and
CO oxidation share a common kinetically relevant O2 dissociation
step. O2 consumption rates in CH4–CO–O2 mixtures are given by:
33 nm Pt
(Pt/SiO2)
rO ¼ 2
m
1rCH ;1 þ 0:5
m
2rCH ;2 þ 0:5rCO þ 0:5rH
ð8Þ
2
4
4
2
1.8 nm Pt
(Pt/Al2O3)
in which rCH and rCH are the rates of CH4 conversion to CO2 and
H2O and to CO and H2, respectively, rH is the rate of sequential H2
reactions with O2, and m1 and m2 are the selectivity ratios. Although
4;1
4;2
2
CO forms only in trace concentrations from CH4–O2 reactants before
O2 depletion (Section 3.2), CO may form more readily from CH4
when additional CO is added to the CH4–O2 reactants, because CO
effectively scavenges Oꢀ (as shown later in this section) and de-
creases the Oꢀ coverages. At the low Oꢀ coverages prevalent in
CH4–CO–O2 mixtures, rates of initial C–H bond activation are lar-
gely unaffected by Oꢀ concentrations and thus remain similar to
those in CH4–O2 mixtures, because Oꢀ atoms are not involved in
the kinetically relevant C–H bond activation step (Sections 3.3
and 3.5–3.6). The sequential oxidation of the COꢀ intermediates
formed from CH4, however, becomes much less effective at the
low Oꢀ coverages, because this step requires an Oꢀ atom vicinal to
the COꢀ (Section 3.6). This decrease in COꢀ oxidation rates leads to
incomplete CH4 oxidation and thus to CO formation from CH4 in
CH4–CO–O2 mixtures. The first-order rate constants for O2 reactions
0
0.02
0.04
0.06
0.08
0.1
0.12
O2/CO ratio
Fig. 3. Oꢀ selectivity (SO
,
873 K) during competitive 13CH4–12CO oxidation
ꢀ
reactions on 1.8 nm and 33 nm Pt clusters as a function of O2/CO ratio (0.3 mg
0.2 wt.% Pt/Al2O3 or Pt/SiO2, respectively; 1.2 kPa (4), 2.0 kPa (h, ꢂ), 2.8 kPa (e, ꢀ,
N, j), and 4.2 kPa (d) CH4; 0.008 kPa (ꢀ, ꢂ), 0.009 kPa (h, e, 4), 0.013 kPa (j), and
0.017 kPa (N, d) O2, 2.08 cm3 sꢁ1, k = 200,
v = 4700).
mechanistic origins of these size effects are discussed in Section
3.4.
Oꢀ coverages reflect the kinetic coupling between steps that
scavenge Oꢀ using CO and CH4 and the step that forms Oꢀ via O2
dissociation. The fractional Oꢀ coverages during steady-state
with CH4 (k
) and CO (k —CO) on bare Pt surfaces are given by
13CH4–12CO–O2 reactions, denoted as ½ðOꢀÞ=ðLÞꢅCO—CH
where L
O2—CH4
O2
4—O2
their turnover rates divided by the respective reactant pressure:
is the total number of exposed Pt sites, are given by a pseudo stea-
dy-state treatment for Oꢀ intermediates with unoccupied sites (ꢀ)
as the most abundant surface intermediates (MASI). This treat-
2
m
1rCH ;1 þ 0:5
m
2rCH ;2 þ 0:5rH
4
4
2
kO
¼
ð9Þ
2—CH4
2—CO
ðCH4Þ
ꢀ
ment, together with the assumption that the concentration of
equals L, leads the Oꢀ coverages to become proportional to O2/CO
0:5rCO
ðCOÞ
kO
¼
ð10Þ
ratios with a coefficient that contains the equilibrium constant
for O2 adsorption (KO ) and the rate constants for Oꢀ2 dissociation
2
Their ratios give the Oꢀ selectivities (SO ) upon substitution into Eq.
ꢀ
(kO ) and CO adsorption (kCO ads) (defined in Scheme 2), as derived
in Appendix (Supplementary material):
ꢀ
(6).
Oꢀ selectivities were measured from 12CO2, 13CO2, and 13CO for-
mation rates using 13CH4–12CO–O2 mixtures (O2/CO = 0.02–0.23;
O2/CH4 = 0.0027–0.017) on Pt clusters (1.8 nm and 33 nm mean
diameters, 0.2 wt.% Pt) at 873 K. O2 turnover rates (also the total
CO and CH4 rates) were proportional to O2 pressure, consistent
with O2 dissociation on essentially uncovered Pt cluster surfaces
as the kinetically relevant step during catalysis. Oꢀ selectivities
(Eq. (6)) are shown in Fig. 3 as a function of O2/CO inlet ratios.
These selectivities were much greater than unity (10–60), indicat-
ing that Oꢀ atoms react preferentially with COꢀ instead of CH4 on Pt
clusters. Oꢀ selectivities increased with O2/CO ratios on both large
and small Pt clusters, but were higher on larger Pt clusters. The
ꢂ
ꢃ
ꢂ
ꢃ
ðOꢀÞ
ðLÞ
2KO kO O2
ꢀ
2
¼
ð11Þ
kCO ads CO
CO—CH4—O2
The kinetic relevance of the molecular CO adsorption step in CO oxi-
dation reactions and the presence of its rate constant (kCO ads) in Eq.
(11) are shown in Section 3.6. The linear relationships between Oꢀ
coverage and O2/CO ratios (Eq. (11)) and between Oꢀ selectivity
and O2/CO ratios (for ratios below 0.06 on 33 nm Pt clusters,
Fig. 3) provide evidence for a concomitant relationship between
the Oꢀ coverage and selectivity; this relation indicates, in turn, that
reactive collision probabilities for CO oxidation (the numerator

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
17
term in Eq. (6)) relative to those of CH4 increase with increasing Oꢀ
coverage.
increasing the overall reactive collision probabilities of CH4 with
Oꢀ (kO , Eq. (9)) and decreasing the Oꢀ selectivities.
2—CH4
A Langmuir treatment for CO oxidation reactions requires
immobile Oꢀ atoms adjacent to CO. The observed linear increase
in Oꢀ selectivity with increasing O2/CO ratio, which defines the
Oꢀ coverage (Eq. (11)), for O2/CO ratios below 0.06 (on 33 nm Pt
clusters, Fig. 3) indicates that the reactive CH4 collision probabili-
ties appeared in the denominator of the Oꢀ selectivity expression
(Eq. (6)) are insensitive to Oꢀ coverages. This suggests that kineti-
cally relevant C–H bond activation occurs on exposed metal atom
site pairs (ꢀ–ꢀ) with Oꢀ atoms involved only in latter steps that re-
3.4. Site occupation by carbonaceous intermediates produced from the
initial C–H bond activation steps and their effects on oxygen
selectivities
Next, we examine the dependence of reactive collision probabil-
ities for 13CH4 reactions (also the effective rate consꢀtants, kO
,
2—CH4
Eq. (9)) on 13CH4 pressure and show that the CHx species, pro-
duced from the C–H bond activation steps, bind reversibly on a
portion of the Pt sites at the low Oꢀ coverages prevalent in
move the carbonaceous CHx (x = 1–3) and Hꢀ produced from the
ꢀ
13CH4–12CO–O2 mixtures. We propose that the binding of CHx on
ꢀ
C–H bond activation steps. These kinetic treatments, together with
the assumption that the selectivity ratios for CH4 to form CO2 and
CO in CH4–CO–O2 mixtures (m1 and m2) are equal [28], lead to the
these sites at low O2/CO ratios and their gradual removal as the
O2/CO ratio increases cause the deviation in Oꢀ selectivity from
the predicted linear trend with the O2/CO ratio (Eq. (12)) in
Fig. 3. We consider Pt atoms with high coordination (denoted as
selectivity expression:
ꢂ
½Oꢀꢅ
½Lꢅ
ꢃ
ꢂ
ꢃ
ꢀ
ꢀ
kCOads
kO KO
O2
W) to remain accessible for the kinetically relevant initial C–H
2
ꢀ
SO
¼
KCH
¼
ð12Þ
4
ꢀ—ꢀꢅ
½ — ꢅ
ꢀ
ꢀ
7k
½
3:5k
KCH CO
bond activation in CH4 (Step 4). On these sites, elementary steps
4
for the sequential C–H bond dissociation and CHxꢀ (x = 1–3) oxida-
which depends on the CH4 (KCH ) and O2 (KO ) adsorption equilib-
tion are kinetically irrelevant. In contrast, coordinatively unsatu-
4
2
ꢀ
ꢀ
ꢀ
rium constants, the C–H bond activation (k ꢅ) and O2 dissociation
rated Pt atoms (denoted as
)
bind the carbonaceous
½
—
S
ꢀ
(kO ) rate constants, as defined in Scheme 2, and O2/CO ratios. This
expression was derived by substituting Eq. (11) into Eqs. (6), (9),
and (10), the details of which are shown in Appendix (Supplemen-
tary material). The linear increase in SOꢀ with O2/CO ratio (Eq. (12))
was confirmed from the selectivity data measured on 33 nm Pt clus-
ters for O2/CO ratios below 0.06 (Fig. 3). In contrast, the alternate
route in which kinetically relevant C–H bond activation occurs on
intermediates produced from the initial C–H bond activation steps
ꢀ
ꢀ
(CHx S) strongly. On these coordinatively unsaturated sites, ini-
S
tial C–H bondꢀactivation becomes kinetically irrelevant and the re-
moval of CHx S species via oxidation by vicinal reactive oxygen
intermediates (Step 14, elementary rate constantꢀ kCHꢀ, Scheme 2)
limits the CH4 turnover rates. The rates of CHx S reactions with
Oꢀ increase as Oꢀ coverage (set by O2/CO ratio) increases. The
ꢀ–Oꢀ site pairs (Step 5) would cause the SO values to be unaffected
ꢀ
ꢀ
coordinꢀatively unsaturated sites are surrounded predominantly
S
by O2/CO ratios because these ratios determine the Oꢀ concentra-
tions required for both the CO and CH4 oxidation steps and affect
both rates to the same extent (derivation in Appendix (Supplemen-
tary material)):
ꢀ
by the
sites, thus CH4 turnover rates (rCH ;S) on these
sites
S
W
4
are given by:
ðOꢀWÞ
ꢀ
ꢀ
rCH ¼ kCH ðCHx SÞ
ð14Þ
4;S
L
ꢀ
where Oꢀ refers to the chemisorbed oxygen atom binds on the
kCO ads
W
W
ꢀ
SO
¼
ð13Þ
site vicinal of the ꢀS site. A pseudo steady-state approximation of the
ꢀ
ꢀ
7k
KCH
½O — ꢅ
4
ꢀ
carbonaceous intermediates (CHx S) and the assumption of Oꢀ as
S
The coordination of exposed Pt atoms influences Oꢀ selectivities be-
cause of its consequences for O2 dissociation and C–H bond activa-
tion rate constants. O2 dissociation is non-activated and its rate
ꢀ
ꢀ
minority surface species (relative to
and CHx S) give the first-
order CH4 reaction rate constant for the sites (kCH ;S), as derived
S
ꢀ
S
4
in Appendix (Supplementary material):
ꢀ
constant (kO KO , Eq. (7)) is insensitive to Pt coordination [23]. Rate
2
ꢀ
ꢀ
rCH
ðCH4Þ
k
½ — ꢅ;S
4;S
ꢀ
ꢀ
ꢀ
ꢀ
KCH ), how-
— ꢅ
constants for C–H bond activation on – site pairs (k
ꢀ
ꢀ
ꢁꢁ
kCH
¼
¼
ð15Þ
½
4;S
4
k
ꢀ ꢀ
— ꢅ;S
kCO ads
½
CO
O2
1 þ
ðCH4Þ
ever, depend strongly on Pt coordination [24]. The rate constant for
C–H bond activation increases as surface atoms become more
coordinatively unsaturated with decreasing cluster size (Pt [24],
Rh [29], Ru [30], Pd [31]), consistent with the lower C–H bond acti-
vation barriers resulting from more effective stabilization of reac-
kCHꢀ
2KO2 kOꢀ
ꢀ
ꢀ
—
where k ꢅ;S is the elementary rate constant for the initial C–H bond
½
ꢀ
ꢀ
W
activation on the
–
site pairs (Step 4, Scheme 2). The overall
S
first-order CH4 reaction rate constant (kCH , related to kO
via
2—CH4
4
tion products (CH3 and Hꢀ) on the corner and edge sites
ꢀ
the reaction stoichiometry) is simply the sum of the respective rate
constants for ꢀS (kCH ;S) and ꢀW (kCH ;W) sites, weighted by the relative
prevalent on small clusters (as described in Section 3.5). These ef-
fects of surface Pt coordination on C–H bond activation rate con-
stants are responsible for the lower Oꢀ selectivities observed on
smaller clusters at all O2/CO ratios (0.02–0.05; Fig. 3).
4
4
site abundance, which is given here in terms of the fraction of sur-
ꢀ
face atoms acting as
sites (C):
W
k
CH4
¼
¼
C
C
kCH þ ð1 ꢁ
C
ÞkCH
4;W
4;S
SOꢀ values become smaller than expected from the predicted
linear trend with O2/CO ratios (Eq. (12)) at higher O2/CO ratios
(>0.06) on the 33 nm Pt clusters and for the entire range of O2/
CO ratios (0.02–0.05) on the 1.8 nm clusters. The deviation in SOꢀ
is a result of an apparent increase in its denominator, the reactive
ꢀ
½ —ꢀꢅ;S
k
ꢀ
ꢀ
ꢁꢁ
ꢀ
ꢀ
k
½
— ꢅ;W þ ð1 ꢁ
C
Þ
ð16Þ
k
ꢀ ꢀ
— ꢅ;S
kCO ads
½
CO
O2
1 þ
ðCH4Þ
kCH
ꢀ
2KO2 kOꢀ
This equation is used to describe the rate data in Fig. 4, which shows
collision probabilities of CH4 with Oꢀ (kO
, Eq. (9)), with increas-
the effective rate constants for 13CH4 reactions (kO
, Eq. (9)) on a
2—CH4
2—CH4
ing O2/CO ratio and Oꢀ coverage. In the next section, we show that
0.2 wt.% Pt/Al2O3 catalyst (1.8 nm mean cluster diameter) as a func-
tion of O2/CO ratio and different 13CH4 pressures (1.2–2.8 kPa) in
13CH4–12CO–O2 mixtures at 873 K. The effective rate constants for
13CH4 reactions increased slightly with increasing O2/CO ratio
(which determines the Oꢀ coverage; Eq. (11)) and were larger at
1.2 kPa 13CH4 than at 2.0 kPa and 2.8 kPa 13CH4 pressures for each
O2/CO ratio. A non-linear regression of these data using Eq. (16)
ꢀ
the kO
increase is resulted from the removal of CHx species
2—CH4
chemisorbed on coordinatively unsaturated corner and edge sites
of Pt clusters via reactions with Oꢀ to form CO or CO2. As a conse-
quence, these under-coordinated surface atoms that are more reac-
tive than terrace sites [24] become accessible for C–H bond
activation and participate in catalytic turnovers (Step 4), thus

18
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
2.5
2
3.5. Theoretical assessment of the initial C–H bond dissociation in CH4
on metal atom site pairs of Pt201 clusters
Density functional theory calculations were carried out to
determine reaction and activation energies for the initial C–H bond
activation of CH4 over the various Pt sites on model Pt201 cubo-
octahedral cluster surfaces (1.8 nm diameter, refers to Scheme 1
herein), previously examined on single crystal extended surfaces
[32–34]. The structure of the bare Pt201 cluster was fully optimized,
resulting in an average Pt–Pt distance within the inner core of the
cluster (0.282 nm) similar to the value reported for bulk Pt
(0.277 nm [35]). The Pt–Pt bond lengths at the corner and edge
sites were slightly shorter (0.272 nm) as a result of the lower coor-
dination numbers of these sites (CNcorner = 6 and CNedge = 7 for sites
1 and 2, respectively) relative to those of the terrace sites (CN100,ter-
race = 8 and CN111,terrace = 9 for sites 3 and 4, respectively), which
leads to stronger Pt–Pt bonds and to a slight reconstruction at
these sites, as also observed experimentally [36]. This bond con-
traction becomes even more evident on smaller clusters (55 atoms)
than on larger clusters, as observed for Pt, Rh, and Pd clusters, be-
cause of larger fractions of coordinatively unsaturated atoms resid-
ing on the corner and edge sites [37]. The bond contraction at these
sites partially compensates for their lower degrees of coordinative
saturation and lowers the overall surface free energy. These effects
and their catalytic consequences cannot be appropriately captured
in periodic calculations on extended and ordered single crystal sur-
faces because relaxation and reconstruction on such surfaces are
constrained by actual structural differences between planar and
curved surfaces as well as the computational limitations imposed
by periodic cell boundaries. Clusters that are large enough (>100
atoms) such as the Pt201 capture the various sites (e.g., terrace, cor-
ner, edge, Scheme 1) of working catalytic particles and therefore
provide a more reliable theoretical representation than extended
flat or stepped surfaces, thus allowing for the systematic studies
of the coordination and cluster size effects on catalytic rates.
CH4 activation on the Pt201 cluster proceeds by the initial
adsorption of CH4 (Step 3) on a Pt site, which can be one of the four
1.5
1
0.5
0
0
0.02
O2/CO ratio
0.04
0.06
Fig. 4. Effective rate constants (also the reactive collision probabilities) for 13CH4
oxidation reactions (kO
Eq. (9), 873 K) in 13CH4–12CO–O2 mixtures as
function of O2/CO ratio on 0.2 wt.% Pt/Al2O3 (1.8 nm mean Pt cluster diameter); the
lines are derived from regression of rate data with Eq. (16) (0.3 mg cat.; 1.2 kPa (j),
2.0 kPa (d), and 2.8 kPa (N) CH4, 0.0093 kPa (j, d, N) O2; 2.08 cm3 sꢁ1, k = 200,
;
a
2 —CH4
v
= 4700).
with minimization of residuals and steepest descent algorithms for
parameter estimations give the predicted reactive 13CH4 collision
probabilities, which are plotted together with the measured values
ꢀ
k
½
ꢀ
ꢀ
ꢀ
in Fig. 4, and the derived kinetic parameters (
C
ꢅ;W, (1 ꢁ
C
)k
,
—
½
—
ꢅ;S
ꢅ;SkCO adsð2k KO kO
ꢁ1) in Table A.1 in Appendix (Supplemen-
ꢀ
ꢀ
ꢀ
ꢀ
k
½
Þ
—
CH
2
tary material). Eq. (16) accurately describes the effects of CH4 pres-
sure. As the oxygen coverage (OꢀW, set by O2/CO ratio) increases, the
CHx S coverage decreases and ꢀS sites become available for catalytic
ꢀ
turnovers. The ꢀS sites are more reactive than the ꢀW sites for the ini-
tial C–H bond activation because of their lower coordinations and
ꢀ
concomitantly stronger binding to CH3 (Section 3.5), leading to
higher first-order CH4 reaction rate constant (kCH , Eq. (16)) and to
4
different Pt sites identified in Scheme 1. The adsorption energy for
lower Oꢀ selectivities than the predicted linear trend according to
Eq. (12) (Fig. 3) at higher oxygen coverages.
CH4 precursors (3 kJ molꢁ1
) from the gradient-corrected ex-
ꢀ
change–correlation functionals in plane-wave DFT (e.g., PW91) is
underpredicted because these functionals do not accurately cap-
ture weak attractive van der Waal interactions [38,39]. On both
the (1 1 1) and (1 0 0) facets, the dissociation of one of the C–H
The total number of unoccupied sites is smaller during reactions
in 13CH4–12CO–O2 than in CO–O2 mixtures, because CHx species
ꢀ
are not present during CO–O2 reactions. O2 turnover rates in
13CH4–12CO–O2 (rO
) and CO–O2 (rO
13CH4ꢁ12COꢁO2
) mixtures
ꢀ
2;COꢁO2
;
bonds in CH4 (Step 4) occurs via an oxidative insertion of the Pt
are both limited by2O2 dissociation. Their ratio (b) reflects ꢀthe frac-
tion of exposed Pt atoms that are not covered by CHx during
13CH4–12CO–O2 reactions on which the O2 predominantly reacts
with CO:
atom into the C–H bond (Fig. A.1b), followed by the transfer of
the resulting H to a vicinal Pt–Pt bridge site (Fig. A.1c). The metal
site pair (ꢀ–ꢀ) discussed herein refers to the specific sites where
the CH3 and Hꢀ products reside rather than the total number of
ꢀ
Pt atoms involved in the C–H bond dissociation step. Alternatively,
the C–H bond dissociation step can proceed on a metal–oxygen site
pair via a concerted step involving the oxidative insertion of a Pt
atom into the C–H bond and a hydrogen abstraction by a vicinal
Oꢀ (Step 5, Fig. A.2), which will be discussed in Section 3.6. The
2
ꢀ
ꢀ
r
13CH4
ꢁ
12CO—O2
K
O2
kO ðO2Þ½ð Þ ꢁ ðCHxꢀÞꢅ
O2
;
b ¼
ꢆ
2
ꢀ
rO
2;CO—O2
ꢀ
KO kO ðO2Þð Þ
2
2
½ðꢀÞ ꢁ ðCHxꢀÞꢅ
ꢆ
ð17Þ
2
structures of reactant, transition, anꢀd product states for the CH4
ðLÞ
ꢀ
activation at each of the different
–
and ꢀ–Oꢀ site pairs (Steps 4
and 5, respectively) on the Pt201 cluster are given in Figs. A.1 and
A.2 and Tables A.2 and A.3 in Appendix (Supplementary material).
The reaction energy diagrams and the structures of the intermedi-
ates and transition states for the two distinct CH4 activation paths
where L is the total number of exposed Pt atoms. The b values were
0.83 and 0.79 for CH4 pressures of 1.13 and 2.73 kPa (O2/
CH4 = 0.008 and 0.0033), respectively, at an O2/CO ratio of 0.024
on the smaller Pt clusters (1.8 nm mean diameter; Table 2, Entries
5–6). In contrast, the b values are identical within experimental
accuracy on the larger Pt clusters (33 nm; b > 0.99, O2/
CH4 = 0.022, Table 2, Entry 3) and at a higher O2/CO ratio (0.23),
on –ꢀ and –Oꢀ site pairs, respectively, are summarized in Fig. 5a.
C–H bond activation on the various ꢀ–ꢀ site pairs on (1 1 1) and
(1 0 0) facets of the Pt201 cluster proceeds via mechanistically sim-
ilar steps in which one of the Pt atoms undergoes oxidative addi-
tion into the C–H bond. Here, we first discuss the specific details
of this step by using a representative case in which the site pairs
consist of two terrace Pt atoms on the (1 1 1) facet (site 4, Scheme
ꢀ
ꢀ
ꢀ
suggesting that almost all exposed Pt atoms are uncovered by CHx
species produced from the C–H bond activation steps in
13CH4–12CO–O2 mixtures under those conditions.

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
19
Step 5
(CH3*--OH*)
(a)
81-115
Step 4
(CH3*--H*)
(CH3*--OH*
)
(CH3*--H*)
47-79
CH3*+OH*
CH4(g)
*
CH4
3
2-6
2-35
CH4* +O*
*
CH3 +H*
CH3 +OH*
*
CH3*+H*
*
CH4
Reaction coordinate
(b)
(CO--*)
1
(CO*--O*)
CO(g)
68-91
(CO*--O*)
212-233
(CO--*)
150-198
CO*
CO2(g)
CO2(g)
CO*+O*
Reaction coordinate
Fig. 5. (a) Reaction energy diagram for initial C–H bond dissociation of CH4 on the various Pt metal–metal (ꢀ–ꢀ) (Step 4, Scheme 2) and metal–oxygen (ꢀ–Oꢀ) site pairs (Step 5,
Scheme 2) on Pt201 clusters. The energy ranges of intermediates, transition states, and products are given with respect to the reactant energy. (b) Reaction energy diagram for
CO oxidation reaction on the various Pt metal–oxygen (ꢀ–Oꢀ) site pairs on Pt201 clusters. The energy ranges of intermediates, transition states, and products are given with
respect to the reactant energy. See Appendix (Supplementary material) for the structural details of these steps.
1b) and then the connections between the barriers for this step and
the coordination numbers of the different Pt sites on the cluster.
The oxidative insertion of Pt into the C–H bond proceeds by the di-
rect interaction of an exposed Pt atom with the C–H bond. This
interaction weakens the C–H bond thus resulting in its elongation
from 0.109 nm in the CH4(g) to 0.152 nm in the transition state.
The Pt atom (labeled Pt1 in Fig. A.1b) interacts with both the C
(0.222 nm) and H (0.162 nm) atoms to form a three-centered car-
bon–metal–hydrogen (H3Cꢀ–Hꢀ)à activated complex, similar to that
involved in C–H bond activation by organometallic complexes [40].
The H–Pt distances between the H-atom and the two vicinal Pt
sites (labeled Pt2 and Pt3 in Fig. A.1b) in the transition state are
0.245 nm and 0.261 nm, respectively. These distances are much
longer than the Pt–H bond lengths in the product state of
0.174 nm and 0.178 nm (Fig. A.1c), indicating that the vicinal Pt
sites do not assist the C–H bond activation steps, but instead pro-
mote the H transfer later along the reaction coordinate. The calcu-
lated transition state for the C–H bond activation is rather late
along the reaction coordinate as there is a significant stretch in
the C–H bond (>0.4 nm) and direct occupation of the rꢀ C–H bond-
ing state with electron density as was suggested previously for al-
kane activation over transition metal surfaces [41,42]. The
transition state structure suggests strong interactions between
the Pt atom that carries out the oxidative insertion step and both
the C and H atoms. These interactions indicate the formation of
an immobilized (H3Cꢀ–Hꢀ)à transition state complex from a gas-
phase CH4 molecule with a significant loss in entropy. The C–H
bond activation step is completed by transferring the H-atom in
ꢀ
the C–H bond to a vicinal Pt–Pt bridge site to form the CH3 and
Hꢀ products. In contrast to Pt(1 1 1) surfaces, C–H bond dissocia-

20
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
(b) 1
140
120
100
80
440
(a)
(a)
(b)
1120
1100
880
60
660
40
440
20
20
0
0
4
6
8
10
190
195
200
205
210
2215
CH3* binding energy (kJ mol-1)
Pt coordination number
Fig. 6. (a) Effects of Pt coordination number on the DFT-calculated C–H bond activation barriers of CH4 on Pt metal–metal (ꢀ–ꢀ) site pairs (j) and on Pt metal–oxygen atom (ꢀ–
Oꢀ) site pairs (d) on the various Pt sites (type i = 1–4, Scheme 1) of a Pt201 cluster. C–H bond activation barriers on Pt metal–metal (ꢀ–ꢀ) site pairs at Pt(1 1 1) (ꢀ) and Pt(1 0 0)
(N) surfaces and on Pt metal–oxygen atom (ꢀ–Oꢀ) site pairs at Pt(1 1 1) (ꢂ) surfaces are included for comparison. (b) Effects of CH3ꢀ binding energy at the various Pt sites on
the C–H bond activation barriers of CH4 on Pt metal–metal ꢀ(ꢀ–ꢀ) (j) and Pt metal–oxygen atom (ꢀ–Oꢀ) (d) site pairs on the surfaces of a Pt201 cluster. The data points
correspond to sites 4, 3, 2, 1 (Scheme 1) with increasing CH3 binding energy (see Table 4).
tion on Pt clusters was found to be slightly exothermic rather than
endothermic. The small increase in reaction exothermicity is likely
resulted from small perturbations in the Pt bond order on cluster
surfaces caused by the presence of coordinatively unsaturated me-
tal atoms located at the neighbor and next-nearest neighbor sites
that increase the Pt–C interactions slightly.
tion energies) suggests a direct relationship between the C–H bond
ꢀ
activation barriers and the CH3 binding energies (given by the
heats of CH3ꢀ adsorption in Table 4), as plotted in Fig. 6b. The bar-
rier for the site giving a methyl binding energy of 207 kJ molꢁ1 is
slightly higher than predicted from the linear correlation. This
ꢀ
structure is the only one for which CH3 groups reside at (1 0 0)
ꢀ
ꢀ
The barriers for the C–H bond activation on
–
site pairs are
surfaces, while all other points reflect events on (1 1 1) facets. Scat-
ters are expected in such linear relationships upon changing the
surface geometries involved in the binding because such a change
leads to steps that are no longer belong to the same reaction family
[43].
correlated directly with the coordination number of the Pt atom
that carries out the oxidative insertion step on both the (1 1 1)
and (1 0 0) facets, as shown in Fig. 6a. The barriers for reactions
carried out at the Pt terrace sites (79 kJ molꢁ1 for site 4, Scheme 1)
are significantly higher than the more coordinatively unsaturated
corner, edge, and (1 0 0) sites (sites 1, 2, and 3, respectively, in
3.6. Theoretical assessment of the initial C–H bond dissociation in CH4
and CO oxidation assisted by metal–oxygen site pairs on Pt201 clusters
with a single chemisorbed oxygen atom
ꢀ
Scheme 1), as the terrace sites bind the CH3 in the product state
much more weakly than the coordinatively unsaturated sites. As
the Pt coordination number decreases from 9 to 6, the C–H bond
activation barriers decrease (from 79 to 47 kJ molꢁ1, Fig. 6a) and
the overall reaction becomes more exothermic as a result of the
stronger CH3ꢀ binding to the Pt site. Taken together with the nearly
fully formed Pt–CH3 bonds in the transition states (Pt–
CH3 = 0.222 nm at the transition state vs. Pt–CH3 = 0.207 nm at
the product state, Table A.2), the correlation between the C–H bond
activation barriers and the Pt coordination numbers (also the reac-
Next, we examine the C–H bond activation steps on the various
ꢀ–Oꢀ site pairs (Step 5, Scheme 2), each of which is formed from a
single chemisorbed Oꢀ atom and a vicinal ꢀ site on the Pt201 cluster.
Surfaces of the model Pt201 cluster with a single Oꢀ atom resemble
those encountered at low O2/CH4 ratios during CH4–O2 catalysis for
which COꢀ intermediates are most likely to desorb and direct par-
tial oxidation might become feasible. We first consider the Oꢀ
Table 3
Average Pt coordination numbers, heats of atomic oxygen adsorption, intrinsic and effective barriers for COꢀ and Oꢀ reactions on a cubo-octahedral Pt cluster (1.8 nm) consisting
of 201 Pt atoms and on a Pt(1 1 1) extended surface.
Oxygen adsorption Average Pt
Heat of Oꢀ adsorption, QO
Intrinsic barrier for COꢀ–Oꢀ reactions,
Effective barrier for COꢀ–Oꢀ reactions,
c
d
sitesa
coordination
(kJ molꢁ1
)
ðEjÞCOꢀ —O (kJ molꢁ1
)
ðEjÞCOꢀ—Oꢀ ;eff (kJ molꢁ1
)
ꢀ
I
II
III
IV
6.5
7.3
7.5
8.3
9
133
114
106
98
96
89
112
88
123
69
82
–
ꢁ72
ꢁ82
ꢁ69
ꢁ92
ꢁ87
–
V
Pt(1 1 1) surfaceb
9
a
b
c
Refer to Scheme 1 for the location of these sites.
Single crystal Pt(1 1 1) surface.
Calculated using Eq. (19).
d
Calculated using Eq. (20), averaging over all plausible reaction paths by considering the various types of Pt sites vicinal of the Oꢀ atom.

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
21
vation on ꢀ–ꢀ site pairs (Section 3.5; Fig. 6a) because both of the C–H
bond activation steps (on ꢀ–Oꢀ and ꢀ–ꢀ site pairs, Steps 4 and 5) pro-
ceed via an oxidative insertion mechanism. The barriers for C–H
binding energies at the various oxygen adsorption sites j (j = I–V,
Scheme 1) and then analyze the effects of these binding strengths
on the C–H bond activation barriers before extending the analysis
to CO oxidation reactions.
ꢀ
bond activation on –Oꢀ site pairs are also influenced by the extent
The Oꢀ atoms preferentially reside at threefold fcc sites (labeled
II, IV, V in Scheme 1b) on (1 1 1) surfaces and at bridge sites (labeled
I and III in Scheme 1c) on (1 0 0) surfaces. The binding energies of
isolated Oꢀ at these sites are reported as their respective heats of
oxygen adsorption (QO, Eq. (2)) in Table 3. The heat of oxygen
adsorption decreased from 133 to 96 kJ (mol Oꢀ)ꢁ1 as the average
coordination of the Pt atoms covalently bound to the Oꢀ increased
from 6.5 to 9. At the fcc terrace sites on the (1 1 1) surfaces (site
V, Scheme 1b) in which the average Pt coordination (hCNi) ap-
of O–H interactions at the transition state, which is related to the
Oꢀ reactivity and Pt–O bond strength. The correlation of the barriers
with the Pt–O bond strength, however, is much weaker than with the
Pt–CH3 bond strength [23], as expected from the weak interactions
between the O and H at the transition state (O–H bond length is
0.139–0.146 nm vs. 0.098 nm at the product state).
The calculated C–H bond activation barriers on ꢀ–Oꢀ site pairs
are, however, significantly larger (81–115 kJ molꢁ1, Step 5) than
similar barriers on ꢀ–ꢀ site pairs (4ꢀ7–79 kJ molꢁ1, Step 4) for each
of the Pt sites (the specific ꢀ in the –Oꢀ or ꢀ–ꢀ site pair that carries
out the oxidation addition step), as also found on Pt(1 1 1) surfaces
(122 kJ molꢁ1 vs. 89 kJ molꢁ1) and included in Fig. 6a. These larger
barriers are the result of repulsive interactions between the Oꢀ and
H-atom in the C–H bond that increase the transition state energies.
Both of the C–H bond activation routes are expected to exhibit sim-
ilar pre-exponential factors and entropy losses for the formation of
the respective transition states ((H3Cꢀ–Hꢀ)à or (H3Cꢀ–OHꢀ)à) from
CH4(g) reactants because of the similar extent of interactions be-
tween methyl groups and Pt sites in these transition states (the
Pt–CH3 bond lengths for a type 4 Pt site are 0.222–0.230 nm;
Tables A.2 and A.3). Taken ꢀtogether with the much lower C–H bond
proaches the value of 9, the heat of oxygen adsorption (96 kJ molꢁ1
)
becomes similar to those on the extended Pt(1 1 1) surfaces
(89 kJ molꢁ1), which exhibit the same avꢀerage coordination.
The presence of Oꢀ atoms near CH4 species may assist C–H
bond activation (Step 5) via concerted interactions reminiscent of
the three- and four-centered transition states involved in oxidative
addition [44],
r-bond metathesis [45], and oxidative hydrogen
migration [46], implicated in ligand-assisted C–H bond activation
that can occur in organometallic complexes [47]. Such Oꢀ-assisted
C–H activation routes have also been proposed for CH3OCH3 [48],
CH4 [23], and C2H6 [27] oxidation on Oꢀ-covered Pt clusters. In
the Oꢀ-assisted C–H bond activation step, a Pt atom inserts into
and elongates the C–H bond as the CH4 evolves into the (H3Cꢀ–
OHꢀ)à transition state complex (Fig. A.2, see Table A.3 for detailed
bond length information), similar to the oxidative insertion step
ꢀ
activation barriers on the –ꢀ than on the –Oꢀ sites for all Pt sites
(Fig. 6a), we conclude that C–H bond activation of CH4 occurs pre-
ꢀ
ꢀ
dominantly on
–
site-pairs at the low Oꢀ coverages prevalent at
ꢀ
ꢀ
–
site pairs (Section 3.5). The Oꢀ atom
the conditions used for rate measurements in Sections 3.3 and
3.4. Oꢀ insertion steps (into CHxꢀ or Cꢀ) are kinetically irrelevant be-
cause they occur later along the reaction path, except on a smalꢀl
fraction of coordinatively unsaturated Pt atoms that bind the CHx
described previously on
that is chemisorbed on the threefold fcc site (site II, IV, or V,
Scheme 1) shifts to the bridge site directly across from the Pt atom
that carries out the oxidative insertion as the reaction proceeds in
order to interact with the H-atom in the C–H bond. The Oꢀ atom
chemisorbed on the (1 0 0) surface (site I or III, Scheme 1) already
ꢀ
strongly and thus are occupied by CHx (Section 3.4). The kinetic
irrelevance of Oꢀ insertion steps for the majority of the Pt sites is
consistent with the increase in measured Oꢀ selectivity (SO ) with
ꢀ
ꢀ
resides at the bridge site vicinal to the CH4 and thus is appropri-
ately positioned to abstract the targeted H-atom. The Oꢀ and H
interaction results in O–H bond lengths of 0.139–0.146 nm in the
transition state (Table A.3). The C–H bond distance in the transition
state was calculated to be 0.130–0.134 nm, which is 0.021–
0.025 nm shorter than those found without the assistance of Oꢀ
O2/CO ratio (Eq. (12), Fig. 3).
We consider next the reactions of CO with a single Oꢀ atom
chemisorbed at the various sites on the Pt201 cluster. At such low
Oꢀ coverages, COꢀ intermediates that form are most likely to desorb
before encountering a second Oꢀ atom and undergoing further oxi-
dation to CO2, thus partial oxidation may become feasible. The
resulting CO, however, can re-adsorb and sequentially oxidize to
CO2. An Oꢀ atom at site j (j = I–V) can react with a COꢀ adsorbed
at any of the vicinal atop sites (i = 1–4; see Fig. A.3 in Appendix
(Supplementary material) for examples on plausible Oꢀ and COꢀ
reaction paths). The reaction energy diagram, which shows the
energies of the transition, intermediate, and product states with
respect to the gas-phase reactant state, is given in Fig. 5b; the
structural details for each of these states are provided in Fig. A.4
and Table A.4 in Appendix (Supplementary material). The calcu-
ꢀ
on –ꢀ site pairs (C–H bond distance = 0.152 nm, Section 3.5).
The C–H bond activation barriers on the various ꢀ–Oꢀ site pairs,
ꢀ
ðEiÞ
, are estimated by the energy difference between the (CH3
–
ꢀ—Oꢀ
OHꢀ)à transition state and the CH4 in the gas phase. The barrier is
reported for each type of Pt atom (i = 1–4, Scheme 1) in the ꢀ–Oꢀ
site pairs, calculated by averaging the individual rate constants
(each of which contains the individual barrier, EC–H,i,j) of all plausi-
ble reaction paths at that site resulting from using the different vic-
inal Oꢀ atoms (j = I–V, Scheme 1) to abstract the H, according to the
following equation:
0
1
5
P
EC—H;i;j
njexpðꢁ
Þ
kB
T
B
B
B
@
C
C
C
A
Table 4
j¼1
ꢀ
ðEiÞ
¼ ꢁk T ln
ð18Þ
ꢀ—Oꢀ
B
Pt coordination numbers, heats of CH3 and molecular COꢀ adsorption on a cubo-
5
P
octahedral Pt cluster (1.8 nm) consisting of 201 Pt atoms and on the Pt(1 1 1)
extended surface.
ðnjÞ
j¼1
i
Pt sitesa
Pt
Heat of CH3
Heat of molecular COꢀ
ꢀ
where nj is the number of vicinal Oꢀ atoms of type j (1 = I, 2 = II, 3 = III,
4 = IV, 5 = V) in Scheme 1. The C–H bond activation barrier increased
monotonically from 81 kJ molꢁ1 to 115 kJ molꢁ1 as the coordination
number of the Pt atom (ꢀ) in the ꢀ–Oꢀ site pairs increased from 6 to 9
on the Pt201 clusters (Fig. 6a), approaching the calculated value for
the similar step on extended Pt(1 1 1) surfaces (122 kJ molꢁ1, Pt
coordination number of 9). This trend reflects a direct relation of
C–H bond activation barriers on ꢀ–Oꢀ pairs with the extents of Pt–
coordination adsorption, QCH
adsorption, QCO,i
ꢀ;i
3
c
(kJ molꢁ1
)
(kJ molꢁ1
)
number
1
2
3
4
6
7
8
9
9
211
209
207
197
–
198
189
166
161
150
Pt(1 1 1) surfaceb
a
b
c
Refer to Scheme 1 for the location of these sites.
Single crystal Pt(1 1 1) surface.
Eq. (3).
ꢀ
CH3 interaction at the transition state and with the CH3 binding
strengths. Such a relation is similar to those found for C–H bond acti-

22
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
lated heats of non-dissociative adsorption for COꢀ at the different
Pt sites, QCO,i (Eq. (3)), increased from 161 to 198 kJ molꢁ1 as the
Pt surface atom coordination decreased from 9 to 6 (Table 4).
The activation barrier for the COꢀ and Oꢀ reaction (Step 8),
1000
100
10
1
, was calculated and reported for each type of Oꢀ atom
COꢀ—Oꢀ
ðEjÞ
(j = I–V, Scheme 1) using an expression that averages the rate con-
stants for the various reaction paths. The barrier is thus an average
of the exponential terms, each of which contains the individual
barrier depending on the identity of the neighboring COꢀ adsorp-
tion sites (type i = 1–4, Scheme 1):
.
0
1
4
P
ECOꢁO;j;i
ni expðꢁ
Þ
B
B
B
@
C
C
C
A
kB
T
i¼1
ðEjÞCOꢀꢁOꢀ ¼ ꢁk T ln
ð19Þ
B
4
P
ðniÞ
0.1
i¼1
j
0.7
0.8
0.9
1
1.1
1.2
1000 K/ T
where ECO–O,j,i is the energy difference between the (COꢀ–Oꢀ)à tran-
sition state and the chemisorbed COꢀ at the reactant state and ni is
the number of vicinal Pt atoms of type i (i = 1–4). These barriers, as
shown in Table 3, were calculated to be between 69 and
123 kJ molꢁ1 depending on the specific Oꢀ atom used to oxidize
COꢀ. The site-specific heats of CO adsorption were subsequently
subtracted from the intrinsic CO oxidation barriers to determine
the effective barriers for the COꢀ–Oꢀ reactions, ðEjÞCOꢀ—Oꢀ;eff . The
effective barriers were evaluated for each type of Oꢀ atom (type
j = I–V) by averaging over the different barriers resulting from the
reactions of the Oꢀ with vicinal COꢀ bound on different types of Pt
sites (type i = 1–4, Scheme 1):
Fig. 7. Comparison of experimentally measured (d) and calculated (j, N) ratio of
KCH Þꢁ1) on 1.8 nm
ꢀ
ꢀ
ꢀ
rate constants for O2 and C–H bond activation (kO KO ð3:5k
½
—
ꢅ
2
4
(N) and 33 nm (d, j) Pt clusters. The experimental data (d) were measured in
13CH4–12CO–O2 mixtures on 0.2 wt.% Pt/SiO2 catalyst (0.3 mg cat., 33 nm average Pt
cluster diameter, 0.022 kPa O2, 0.16 kPa CO, 1.3 kPa 13CH4; 2.08 cm3 sꢁ1, k = 200,
v
= 4700). The calculated ensemble-averaged rate constant ratios (j: 33 nm Pt
cluster; N: 1.8 nm Pt cluster) were the same for the cases of random and energy-
weighted Oꢀ placements at each temperature.
on Pt/SiO2 (0.2 wt.%; 33 nm mean cluster diameter). The rate con-
KCH Þꢁ1), together with the O2/CO ra-
ꢀ
ꢀ
ꢀ
stant ratios (kO KO ð3:5k
½
— ꢅ
2
4
tios, determine Oꢀ selectivities (Eq. (12)) and, in turn, the
intrinsic limits of the maximum CO yields for direct CH4 and O2
reactions. The rate constant ratios for O2 to C–H bond activation
were larger than 200 in the 885–930 K range and decreased with
increasing temperature.
0
1
ꢂ
ꢃ
4
P
E
CO—O;j;iꢁQCO;i
ð
Þ
ni exp
ꢁ
4
B
B
B
@
C
C
C
A
kB
T
i¼1
ðEjÞCOꢀ—Oꢀ;eff ¼ ꢁk T ln
ð20Þ
P
B
i¼1ðniÞ
These rate constant ratios are interpreted using a transition
state theory formalism and the thermodynamic properties of reac-
tants and transition states for O2 and C–H bond activation:
j
where QCO,i, ECO–O,j,i, and ni are defined above. The effective barriers
for COꢀ–Oꢀ reactions are much less than zero (<ꢁ65 kJ molꢁ1, Ta-
ble 3) for all Oꢀ atoms because the intrinsic barriers for COꢀ–Oꢀ reac-
tions (Fig. 5b and Table 3) are much smaller than the heats of CO
adsorption (Table 4). The heats of CO adsorption are approximately
equal to the COꢀ desorption barriers because CO adsorption steps
are non-activated with barriers that are less than 5 kJ (mol CO)ꢁ1
at all surface sites. The difference in barriers between the COꢀ–Oꢀ
reaction and the COꢀ desorption provides an estimate of the ratio
of COꢀ oxidation to COꢀ desorption rates. This rate ratio, derived
by assuming similar activation entropy values for these steps, ex-
ceeds 2 ꢂ 104 for each type of Oꢀ atom. The much larger rates for
the COꢀ–Oꢀ reactions than for the COꢀ desorption indicate that the
initial CO adsorption step is essentially irreversible. CO oxidation,
as a result, is limited by the irreversible CO adsorption (reverse of
Step 7) where CO binds on a Pt site vicinal to an Oꢀ atom via the for-
mation of a (CO(g)–ꢀ)à complex (structures in Appendix Fig. A.6
(Supplementary material)). In the (CO(g)–ꢀ)à complex, the C@O
bond is slightly elongated (from 0.116 nm to 0.117 nm) and the
Pt–CO bond (0.185 nm) is formed. The ensemble-averaged barrier
for CO oxidation, calculated by averaging the CO adsorption barriers
over all the ꢀ–Oꢀ site pairs on the Pt201 cluster, is less than 5 kJ (mol
CO)ꢁ1, which is within the errors associated with DFT calculations
(<15 kJ (mol CO)ꢁ1). Thus, the CO oxidation is considered as a
non-activated step.
ꢀ
kO KO
1
3:5
2
¼
ꢀ
ꢀ
3:5k
KCH
½
— ꢅ
4
ꢂ
ꢃ
ꢂ
ꢃ
D
SOꢀ
ꢁ
D
SꢀCH
ð
D
HOꢀ
ꢁ
D
HꢀCH
4
Þ
2
4
2
ꢂ exp
exp
ꢁ
kB
kBT
ð21Þ
D
SꢀO (or
D
SꢀCH ) and
D
HꢀO (or
D
HꢀCH ) are the changes in entropy and
enthalpy, respectively, required to4form the (Oꢀ–Oꢀ)à (or (H3Cꢀ–Hꢀ)à)
transition states from gaseous O2 (or CH4) reactants. Linear regres-
sion analyses oꢀn the data in Fig. 7 usꢀing Eq. (21) led to estimates for
2
4
2
the (
D
SOꢀ
ꢁ
D
SCH ) and (
D
HOꢀ
ꢁ
D
HCH ) terms. The (
D
SOꢀ
ꢁ
D )
SꢀCH
4
2
2
4
2
term was found 4to be ꢁ31 J (mol-K)ꢁ1
;
D
SꢀCH reflects the entropy
4
loss of CH4(g) upon formation of the (H3Cꢀ–Hꢀ)à transition state in
ꢀ
ꢀ
the C–H bond activation step on
– site pairs and was previously
reported to be ꢁ99 J (mol-K)ꢁ1 and ꢁ108 J (mol-K)ꢁ1 for CH4–CO2
and CH4–H2O mixtures, respectively [24]. Substituting these values
into the (
D
SOꢀ
ꢁ
D
SꢀCH ) term of ꢁ31 J (mol-K)ꢁ1 give, in turn, an O2
activation ent2 ropy (
D
SꢀO ) of ꢃꢁ130 J (mol-K)ꢁ1, which is less nega-
4
2
tive than the value predicted for an immobile (Oꢀ–Oꢀ)à transition
state (ꢁ175 J (mol-K)ꢁ1). The measured enthalpy difference for
the O2 and CH4 reactants to form their respective transition states
(D
HOꢀ
ꢁ
D
HꢀCH ), is ꢁ81 kJ molꢁ1. This value, taken together with
2
4
non-activated O2 dissociation steps [23], gives a
D
HꢀCH value, which
4
is used to approximate the C–H bond dissociation barrier on ꢀ–ꢀ site
pairs (Step 4), of 81 kJ molꢁ1, consistent with the measured barriers
for this step during CH4 decomposition (78 kJ molꢁ1), CH4–CO2
(83 kJ molꢁ1), and CH4–H2O (75 kJ molꢁ1) reactions [24]. These
measured barriers are compared with the ensemble-averaged
3.7. Comparison of experimentally measured and calculated ensemble-
averaged oxygen selectivities in CH4–O2 mixtures
Fig. 7 shows the effects of temperature (885–935 K) on the ratio
of rate constants for O2 and C–H bond activation
barrier (ECH ), which is related to the calculated CH4 reaction rate
constant (kCH ), derived from DFT estimates of C–H bond activation
4
ꢀ
ꢀ
ꢀ
(kO KO ð3:5k
KCH Þꢁ1) measured from 13CH4–12CO–O2 reactions
½
— ꢅ
2
4
4

Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
23
barriers at various Pt sites i (ECꢁH;i, i = 1–4, Scheme 1, Fig. 6a)
weighed by their relative abundances on Pt201 clusters (Pi):
Pt clusters (1.8 nm mean cluster size), indicating that desorbed
CO may become detectable in effluent streams but at temperatures
unlikely to preserve their small size.
ꢂ
ꢃ
ꢂ
ꢃ
X
ꢁECH
ðꢁECꢁH;i
kB; T
Þ
4
Pt surface coordination and cluster size influence ensemble-
ꢀ
kCH ¼ A exp
¼
Ai;CH exp
Pi
ð22Þ
4
4
kBT
i¼1—4
ꢀ
ꢀ
— ꢅ
averaged rate constant ratios {kO KO ð3:5k
KCH Þꢁ1}, predomi-
½
2
4
nantly because of their concomitant effects on the C–H bond
A is the ensemble-averaged pre-exponential factor and ðAiÞ
is the
val-
CH4
ꢀ
ꢀ
activation rate constants (k
KCH ), since they do not affect the O2
½
—
ꢅ
4
pre-exponential factor for each Pt site (i). Assuming that ðAiÞ
CH4
ꢀ
dissociation rate constants (kO KO ) [23]. The ensemble-averaged
2
ues for all Pt sites remain the same, Eq. (22) can be rearranged to
give the ensemble-averaged barrier for C–H bond activation on
C–H bond activation barriers calculated using Eq. (23) decreased
from 76 kJ molꢁ1 to 64 kJ molꢁ1 (Fig. 8) as Pt clusters becamesmaller
(33–1.8 nm) and as the surface fraction of coordinatively unsatu-
rated metal atoms concomitantly increased. This decrease in barri-
ers with cluster size leads to an increase in the ensemble-averaged
CH4 reaction rate constants (Eq. (22)) and, in turn, to a decrease in
the calculated ensemble-averaged rate constant ratios (Fig. 7) and
smaller measured Oꢀ selectivities (Fig. 3) on the smaller clusters.
Oꢀ selectivities (Eq. (12)), determined from ensemble-averaged
ꢀ–ꢀ site-pairs (ECH ):
4
!
X
ðꢁECꢁH;i
Þ
ECH ¼ ꢁkBT ln
Pi exp
ð23Þ
4
kBT
i¼1—4
ECH was calculated to be 76 kJ molꢁ1 for 33 nm Pt clusters, consis-
4
tent with measured values (81 kJ molꢁ1).
The ensemble-averaged rate constant ratios for 1.8 nm and
33 nm cubo-octahedral Pt clusters were obtained from measured
ꢀ
ꢀ
ꢀ
rate constant ratios {kO KO ð3:5k
KCH Þꢁ1} and O2/CO ratios, were
½
— ꢅ
2
4
differences
in
O2
and
C–H
activation
entropies
used in a kinetic model that captures the CH4 oxidation to CO (and
H2) and their sequential oxidation to estimate the intrinsic limits of
the maximum CO yields. Solving the mole balances for CH4, CO,
and O2 in an isothermal–isobaric plug-flow reactor gives the max-
imum CO yields (Fig. A.7 in Appendix (Supplementary material)) as
a single-valued function of Oꢀ selectivities. These results suggest
that a small amount of CO, initially formed in the reactor, would
(D
SOꢀ
ꢁ
D
SꢀCH ¼ 31 J (mol-K)ꢁ1), DFT-derived C–H bond activation
2
barriers on t4he various Pt sites (EC–H,i, Fig. 6a and b) and their rel-
ative abundances (Pi), assuming that O2 dissociation is barrierless
(EO < 3 kJ molꢁ1 [23]) and that activation entropies are indepen-
2
dent of the specific activation site (
D
SOꢀ
ꢁ
D
SꢀCH ):
2
4
ꢀ
ꢁ
ꢁEO2
ꢂ
ꢃ
ꢀ
Sꢀ
ꢁ
D
S
exp
ꢀ
D
undergo rapid sequential oxidation because of the high
kO KO
3:5k
1
3:5
kBT
O2
CH4
2
ꢀ
ꢁ
¼
exp
ð24Þ
P
ꢀ
ꢁECꢁH;i
ꢀ
ꢀ
kO KO ð3:5k
KCH Þꢁ1 values and low O2/CO ratios.
ꢀ
ꢀ
½
—
ꢅ
KCH
kB
2
4
½ — ꢅ
4
i¼1—4Pi exp
kB
T
CO/CO2 ratios were much lower on Rh than on Pt clusters at all
conditions before the complete consumption of limiting O2 reac-
tants (Fig. 2a and b), suggesting that CO oxidation reactions are
more effective on Rh clusters. We were unable to measure the Oꢀ
selectivities in 13CH4–CO–O2 mixtures on Rh clusters at all O2/CO
ratios without completely depleting the limiting reactants, which
could be CO or O2 depending on the O2/CO ratio, because of the
high CO oxidation rates. These results suggest more reactive sur-
faces for CO oxidation and, in turn, higher Oꢀ selectivities toward
CO on Rh than on Pt, apparently caused by the stronger binding
of Oꢀ on Rh (DFT-calculated Oꢀ binding strengths are 469 kJ molꢁ1
and 354 kJ molꢁ1 for a single Oꢀ chemisorbed on Rh(1 1 1) and
Pt(1 1 1), respectively [49]), and the concomitantly larger Oꢀ con-
tents on Rh cluster surfaces. Catalytic effects of oxygen vacancies,
which have shown to increase the C–H bond activation rates, were
not detected at any amount of measurable O2 and O2/CH4 ratio on
Rh clusters. The C–H bond activation rate constants on Rh instead
increase solely with oxygen chemical potential, throughout the en-
tire O2/CH4 range (0.02–200; 873 K) [50]. The bulk of the Rh clus-
ters, as predicted from the phase equilibrium thermodynamics of
Rh and their oxides (Rh2O3, RhO2), remains in the oxide phase even
at an equilibrium O2 pressure of 0.01 kPa at 873 K [51]. In CH4–O2
mixtures, the Rh clusters are likely in their oxide phases in the
presence of O2 and surface oxygen atoms on the Rh oxide clusters
appear to selectively promote the CO oxidation, leading to the low-
er CO/CO2 ratios on Rh than on Pt. The low maximum CO yields on
Pt and the expected even lower yields on Rh led us to conclude that
direct CO (and H2) formation from CH4 and O2 reactions is unlikely
at CH4 conversions of practical interest on both the Pt and Rh clus-
ters, because these products are much more reactive than CH4.
These partial oxidation products are formed from sequential reac-
tions of CO2 and H2O with residual CH4 at all practical tempera-
tures and O2/CH4 ratios.
The specific location of Oꢀ (random or energy-weighted, Eq. (5)) did
not influence ensemble-averaged rate constant ratios, because rate
ꢀ
constants for O2 dissociation ðkO KO Þ and C–H bond activation
2
KCH Þ were insensitive to Oꢀ binding energies. O2 dissociation
ꢀ
ðk
½
ꢀ
— ꢅ
4
rate constants depend only on entropy losses and are therefore
insensitive to Oꢀ location and surface coordination. C–H bond disso-
ciation rate constants depend on the activation entropy and enthal-
py for the formation of (H3Cꢀ–Hꢀ)à transition states from CH4(g). The
(H3Cꢀ–Hꢀ)à species do not involve Oꢀ (Sections 3.4–3.6) and, as a re-
sult, C–H activation rate constants also depend neither on the Oꢀ
location nor binding energy. The ensemble-averaged rate constant
ꢀ
ꢀ
ꢀ
ratios for O2 and C–H bond activation (kO KO ð3:5k
KCH Þꢁ1) were
½
— ꢅ
2
4
much larger than unity at all temperatures relevant to the practice
of catalytic CH4–O2 reactions (873–1273 K, Fig. 7) for the large Pt
clusters (33 nm mean cluster size). The ratios were smaller and
approached unity at higher temperatures (>1300 K) for the small
80
78
76
74
72
70
68
66
64
62
60
4. Conclusion
1
10
100
Pt cluster size (nm)
CO/CO2 ratios resulting from CH4 and O2 reactions on supported
Pt and Rh clusters were measured by varying the residence time
and O2/CH4 feed ratio independently in a regime of strict kinetic
Fig. 8. Effects of Pt cluster size on the calculated ensemble-averaged C–H bond
activation barriers of CH4 on Pt metal atom (ꢀ–ꢀ) site pairs using Eq. (23).

24
Y.-H. (Cathy) Chin et al. / Journal of Catalysis 283 (2011) 10–24
control, achieved by extensive dilutions of catalyst pellets and the
reactor bed. A small amount of CO was detected (CO/CO2 < 0.02)
only at very low O2/CH4 ratios (O2/CH4 < 0.004) as catalyst surfaces
were depleted of reactive oxygen intermediates.
References
[1] J.R. Rostrup-Nielsen, Catal. Today 71 (2002) 243.
[2] N. Dave, G.A. Foulds, Ind. Eng. Chem. Res. 34 (1995) 1037.
[3] D.A. Hickman, L.D. Schmidt, Science 259 (1993) 243.
[4] D.A. Hickman, E.A. Haupfear, L.D. Schmidt, Catal. Lett. 17 (1993) 223.
[5] D. Dissanayake, M.P. Rosynek, K.C.C. Kharas, J.H. Lunsford, J. Catal. 132 (1991)
117.
[6] W.J.M. Vermeiren, E. Blomsma, P.A. Jacobs, Catal. Today 13 (1992) 427.
[7] I. Tavazzi, M. Maestri, A. Beretta, G. Groppi, E. Tronconi, P. Forzatti, AIChE J. 52
(2006) 3234.
[8] A. Beretta, G. Groppi, M. Lualdi, I. Tavazzi, P. Forzatti, Ind. Eng. Chem. Res. 48
(2009) 3825.
[9] R. Horn, K.A. Williams, N.J. Degenstein, A. Bitsch-Larsen, D. Dalle Nogare, S.A.
Tupy, L.D. Schmidt, J. Catal. 249 (2007) 380.
Oxygen selectivities, defined by the ratios of reactive collision
probability (also the effective rate constant) of desorbed CO and
CH4 reactant, determine the CO/CO2 ratios in CH4–O2 reactions.
We have interpreted the oxygen selectivities rigorously in terms
of elementary rate and equilibrium constants and measured their
values by competitive 13CH4 and 12CO oxidation in 13CH4–12CO–
O2 mixtures. Reactive collision probabilities of CO with Oꢀ on
uncovered Pt clusters are much larger than those of CH4. The high-
er reactivity for CO than CH4 toward the Oꢀ limits the maximum
attainable CO yield from direct CH4 and O2 reactions.
[10] B.C. Enger, R. Lødeng, A. Holmen, Appl. Catal. A 364 (2009) 15.
[11] M.A. Vannice, J.E. Benson, M. Boudart, J. Catal. 16 (1970) 348.
[12] R.L. David, Handbook of Chemistry and Physics, 87th ed., CRC Press, Boca
Raton, FL, 2006. p. 4–26, p. 4–30.
Density functional theory (DFT) results are used within the
framework of transition state theory and ensemble-averaging
methods to calculate the oxygen selectivities. DFT calculations
were carried out on the corner, edge, and terrace sites of a model
cubo-octahedral Pt cluster (1.8 nm diameter) to probe the kineti-
cally relevant steps and the identity of active sites involved in
CH4 and CO oxidation. CH4 oxidation proceeds via kinetically rele-
vant C–H bond dissociation over Pt atom site pairs (ꢀ–ꢀ) in which
one of the Pt sites undergoes an oxidative insertion step into the
C–H bond. The barriers for this step are correlated to the Pt–CH3
bond strength and coordination number of the Pt atom that carries
out the oxidative insertion step. CO oxidation proceeds via a non-
activated molecular CO adsorption step; this step is irreversible be-
cause of the much larger barrier for its reverse step (COꢀ desorp-
tion) than for the sequential COꢀ and Oꢀ recombination. The
barriers for CO and CH4 oxidation were calculated from ensemble
averaging the individual barriers for the various types of surface
sites on the model Pt cluster. These barriers, together with the
measured activation entropies, give the calculated ensemble-aver-
aged Oꢀ selectivities. The Oꢀ selectivities are proportional to O2/CO
ratios and are estimated to be much larger than unity, especially
when a small amount of CO is formed initially, over the entire tem-
perature range typical for CH4–O2 catalysis. These results unequiv-
ocally show that oxidation of CO intermediate is much more rapid
than the activation of CH4 reactant. The marked reactivity differ-
ences between CO and CH4 lead to low intrinsic limits of the max-
imum CO yields from direct CH4 and O2 reactions at any practical
extent of CH4 conversion.
[13] R. Van Hardeveld, F. Hartog, Surf. Sci. 15 (1969) 189.
[14] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C.
Fiolhais, Phys. Rev. B 46 (1992) 6671.
[15] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251.
[16] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15.
[17] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169.
[18] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.
[19] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188.
[20] G. Henkelman, H. Jonsson, J. Chem. Phys. 113 (2000) 9978.
[21] R.M. Koros, E.J. Nowak, Chem. Eng. Sci. 22 (1967) 470.
[22] R. Madon, M. Boudart, Ind. Eng. Chem. Fund. 21 (1982) 438.
[23] Y.-H. Chin, C. Buda, M. Neurock, E. Iglesia, J. Am. Chem. Soc., in press.
[24] J. Wei, E. Iglesia, J. Phys. Chem. B 108 (2004) 4094.
[25] Estimated based on monolith volume of 2.5 cm3, 66.7 cm 3 sꢁ1 CH4/air feed
mixtures with an O2/CH4 ratio of 2, and 50% CH4 conversion.
[26] A. Eichler, J. Hafner, Phys. Rev. Lett. 79 (1997) 4481.
[27] M. García-Diéguez, Y.-H. Chin, E. Iglesia, J. Catal., submitted for publication.
ꢀ
[28] The exact
m1 and
m
2 values affect only the stoichiometry that appears in the SO
ꢀ
expression but not the functional dependence of SO on O2/CO ratios.
[29] J. Wei, E. Iglesia, J. Catal. 225 (2004) 116.
[30] J. Wei, E. Iglesia, J. Phys. Chem. B 108 (2004) 7253.
[31] A. Yamaguchi, E. Iglesia, J. Catal. 274 (2010) 52.
[32] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, Surf. Sci. 324 (1995) 345.
[33] I.M. Ciobica, F. Frechard, R.A. van Santen, A.W. Kleyn, J.A. Hafner, J. Phys. Chem.
B. 104 (2000) 3364.
[34] G. Jones, J.G. Jakobsen, S.S. Shim, J. Kleis, M.P. Andersson, J. Rossmeisl, F. Abild-
Pedersen, T. Bligaard, S. Helveg, B. Hinnemann, J.R. Rostrup-Nielsen, I.
Chorkendorff, J. Sehested, J.K. Norskov, J. Catal. 249 (2008) 147.
[35] N.N. Greenwood, A. Earnshaw, Chemistry of the Elements, second ed.,
Butterworth-Heinemann, 1997. p. 1148.
[36] S.I. Sanchez, L.D. Menard, A. Bram, J.H. Kang, M.W. Small, R.G. Nuzzo, A.I.
Frenkel, J. Am. Chem. Soc. 131 (2009) 7040.
[37] C. Buda, M. Neurock, unpublished results.
[38] Y. Zhao, D.G. Truhlar, Theor. Chem. Acc. 120 (2008) 215.
[39] G. Scuseria, V.N. Staroverov, in: C.E. Dykstra, G. Frenking, K.S. Kim, G.E.
Scuseria (Eds.), Theory and Applications of Computational Chemistry: The First
40 Years, Elsevier, Amsterdam, The Netherlands, 2005, p. 669.
[40] S. Sakaki, M. Ieki, J. Am. Chem. Soc. 115 (1993) 2373.
Acknowledgments
[41] P.S. Venkataraman, M. Neurock, V.S. Lusvardi, J.J. Lerou, D.D. Kragten, R.A. van
Santen, J. Phys. Chem. B 106 (2002) 1656.
This study was supported by BP as part of the Methane Conver-
sion Cooperative Research Program. We also gratefully acknowl-
edge the computational support from the Molecular Science
Computing Facility (MSCF) in the William R. Wiley Environmental
Molecular Sciences Laboratory, a national scientific user facility
sponsored by the US Department of Energy’s Office of Biological
and Environmental Research and located at the Pacific Northwest
National Laboratory. Pacific Northwest is operated by Battelle for
the Department of Energy.
[42] M. Neurock, Appl. Catal. 160 (1996) 169.
[43] R.A. van Santen, M. Neurock, S.G. Shetty, Chem. Rev. 110 (2010) 2005.
[44] W.D. Jones, Acc. Chem. Res. 36 (2003) 140.
[45] T.R. Cundari, J. Am. Chem. Soc. 116 (1994) 340.
[46] J. Oxgaard, R.P. Muller, W.A. Goddard III, R.A. Periana, J. Am. Chem. Soc. 126
(2004) 352.
[47] T.R. Cundari, T.V. Grimes, T.B. Gunnoe, J. Am. Chem. Soc. 129 (2007) 13172.
[48] A. Ishikawa, M. Neurock, E. Iglesia, J. Am. Chem. Soc. 129 (2007) 13201.
[49] R.A. van Santen, M. Neurock, Molecular Heterogeneous Catalysis: A Conceptual
and Computational Approach, Wiley-VCH, Weinheim, Cambridge, 2006.
[50] Y.-H. Chin, E. Iglesia, unpublished results.
[51] O. Muller, R. Roy, J. Less-Common Metals 16 (1968) 129.
[52] The Oꢀ coverages during steady-state catalysis depends on the operating O2/
CH4 ratios, the rate and thermodynamic constants for the O2 and C–H bond
activation elementary steps, which vary with Pt cluster size. For the 33 nm Pt
clusters, the surfaces are depleted of Oꢀ for O2/CH4 ratios below 0.08 at 873 K.
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.jcat.2011.06.011.