This document presents a study examining the catalytic activity of stepped ruthenium and rhenium surfaces for steam reforming of methane. It develops a microkinetic model to predict the turnover frequency (TOF) as a function of key catalyst descriptors. Scaling laws are established using atomic oxygen and carbon binding energies as descriptors to predict intermediate species energies. A free energy diagram shows reactions 4 and 8 have high activation barriers, so the model assumes one is rate limiting. TOF volcano plots are created and show good agreement with rates calculated directly from catalyst data, correctly predicting Ru and Rh have high activity.

1. Nicholas Montes
05950018
CHEMENG 242: Final Project
Explanation for the Catalytic Activity of Stepped Ruthenium
and Rhenium Surfaces During Steam Reforming of Methane
Introduction
Steam reforming of methane is an important step in producing hydrocarbon fuels and is
also widely used in hydrogen production. The conversion of methane and water to hydrogen and
carbon monoxide (given by the reaction below) must occur on a catalytic surfaces to be
practically useful because of prohibitively slow reaction rates in the purely gas phase reaction.
H2O(g) + CH4(g) ↔ 3H2(g) + CO(g)
Ruthenium and Rhenium (hereafter referred to as Ru and Rh, respectively) are known to be
among two of the best catalysts for this process.[1] There are several characteristics that any
catalytic surface chosen for this reaction must possess: The surface must be able to adsorb water
and methane and desorb hydrogen and carbon monoxide at a reasonable rate, the reaction should
not have any intermediate activation barriers that make the overall reaction rate prohibitively
slow, and finally the surface must yield the desired products.
The purpose of this report is to provide an explanation for the observed catalytic activity
of Ru and Rh on stepped (211) surfaces. This will be accomplished by using several catalysts
with well-documented energetics to develop a predictive model that estimates the number of
times a reaction occurs per second, also known as the turn over frequency (TOF), as a function
of several key catalyst descriptors. It will then be shown how the results of this model can be
explained in terms of reaction activation barriers and rate limiting steps, and how this same
explanation can be applied to the observed catalytic activity of Ru and Rh.
Methods
The reaction mechanism outlined in Table 1, proposed by Jones, et al. [2], was utilized in
this study. Using this mechanism, elementary reaction energies and activation energies for
Ru(211), Rh(211), Pt(211), Pd(211), Cu(211), Ag(211), Au(211) were obtained using the
CatApp tool [3].
1. H2O(g) + * ↔ H2O* 6. CH2 + * ↔ CH* + H*
2. H2O* + * ↔ OH* + H* 7. CH + * ↔ C* + H*
3. OH* + * ↔ O* + H* 8. C* + O* ↔ CO*
4. CH4(g) + 2* ↔ CH3* + H* 9. CO* ↔ CO(g) + *
5. CH3 + * ↔ CH2* + H* 10. 2H* ↔ H2(g) + 2*
Table 1: Steam Reforming mechanism used in this work
The atomic oxygen binding energy and the atomic carbon binding energy were chosen as
“descriptors” for this reaction. Based on the knowledge of these two binding energies for a given
catalyst, a series of linear scaling laws were established to predict all other intermediate species
and transition state binding energies using a multivariable regression. These scaling laws allow
one to “simulate” a catalyst by choosing values for the two descriptors and predicting the

2. CHEMENG 242: Final Project Nicholas Montes
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energies of all other intermediate species. While this approach assumes a relationship between
the descriptors and all other binding energies exists, the Discussion section will highlight why
this is a reasonable assumption.
Once the energies of each intermediate species were know (from CatApp or scaling
laws), the change in free energy for each elementary step was found by the following expression:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!∆!!,! =!∆! − !∆!
It was assumed the !∆!term was very small therefore ∆! ≈ ∆!. Furthermore, the entropy of all
gas phase species was taken to be 2 meV/K and that of all surface adsorbed species was taken to
be 0 eV/K. Varying the gas phase entropy to account for partial pressure had a negligible impact
due to the small magnitude of the Boltzmann constant (!! = 0.086 meV/K). The adsorbed
species assumption is well justified since the majority of a molecule’s entropy is a result of its
translational motion, which can be largely be neglected when it is adsorbed on a surface. While
characterizing the free energies, the change in free energy of the overall reaction was taken to be
a constant, ∆!!"#$% =!-1.23 eV. In order to hold ∆!!"#$%!constant, the reaction energy of reaction
10 was adjusted accordingly. The actual energetics of reaction 10 were studied for several
catalysts. Reaction 10 was found to be exothermic and to have a small activation energy, making
it highly unlikely it is rate limiting. During the analysis the following reaction conditions were
held constant: T = 1000 K, PH2O = 0.4 bar, PH2 = 0.1 bar, PCO = 0.1 bar, PCH4 = 0.4 bar.
A microkinetic model was developed to estimate the overall reaction rate, or TOF. In this
model it was assumed only reaction 4 or reaction 8 was rate limiting and that all other reactions
were in quasi-equilibrium. This assumption will be addressed using a free energy diagram in the
Results section. The TOF was taken to be the minimum reaction rate found by separately
considering reaction 4 and 8 to be rate limiting. The following expressions were used to calculate
the equilibrium constants and the reaction rate constant of the rate limiting step.
!!! =!!
!∆!!
!!! !, !!,!"#$%#& =!
!!!
ℎ
!
!∆!!,!,!"#$%#&
!!! , !!!!!!!!!,!"#$%"&' =!
!!!
ℎ
!
!∆!!,!,!"#$%"&'
!!!
Finally a “volcano” plot of the log10(TOF) as a function of the two descriptors was
created by considering a range of values for the descriptors, using the scaling laws to estimate
free energies of all intermediate species, and using the microkinetic model to predict the TOF.
This simplified model treats reaction conditions such as temperature, pressure, and
surface coverage as constant, and therefore only represents what is happening locally. Much
more detailed energy and mass balances would be required to predict the catalytic activity when
designing of a reactor, for instance. Additional factors, such as the catalyst support and varying
surface geometries were not considered in this study. Despite this, the model is still useful for
directly comparing transition metal catalysts to one another under constant reaction conditions.
Results
Using the reaction energies obtained from CatApp and the assumptions outlined above,
free energy diagrams for each catalyst were created as shown in Figure 1. The free energy
diagram reveals reaction 4 and reaction 8 both have high activation barriers. For that reason, in
the microkinetic model, one of these two reactions was assumed to be rate limiting.

3. CHEMENG 242: Final Project Nicholas Montes
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Figure 1: Free energy diagram of steam reforming reaction. Reactions 4 and 8 (marked with *) are potentially rate
limiting due to their high activation energies. Reaction 10 occurs three times per overall reaction.
Scaling laws were created using !!∗ and !!∗ as descriptors. These laws were of the form:
!!∗ = !!!!∗ + !!!!∗ + !!, where i is any intermediate species.
The values of these coefficients are given in Table 2. These descriptors were chosen because all
other intermediate species, with the exception of H*, bind to the surface through either an O and
C atom. The R2
values in Table 2 indicate the descriptors are a good choice for all but EH*. This
is acceptable because reaction 10 is unlikely to be rate limiting, meaning the value of EH* should
not influence to the results of the microkinetic model. Figure 2 shows that the energies calculated
using scaling relations were able to accurately reproduce the data obtained from CatApp.
EH2O* EOH* ECH3* ECH2* ECH* ECO* EH* EC-O* ECH3-H*
α -.0245 -0.055 0.169 0.536 0.700 0.376 0.089 0.901 0.314
β 0.183 0.638 0.166 -0.084 0.111 0.121 0.129 0.886 0.077
γ -2.580 -1.477 0.460 -0.104 0.262 -1.949 -0.178 1.165 0.498
R2
0.74 0.98 0.86 0.90 0.97 0.89 0.69 .99 0.87
$10!
$8!
$6!
$4!
$2!
0!
2!
4!
6!
8!
FreeEnergy(eV)
Reaction Step
Ru(211)
Rh(211)
Pt(211)
Pd(211)
Cu(211)
Ag(211)
Au(211)
1 2 3 4* 5 6 7 8* 9 10 (x3)
$2!
0!
2!
4!
6!
$2! 0! 2! 4! 6!
Ei*(eV)Predicted
Ei* (eV) CatAPP
CH*!
C$O*!
Table 2 (top): Coefficeints for the scaling laws
established for each intermediate species. The R2
provides a measure of how well the regression fits the
actual data.
Figure 2 (left): Energies for CH* and C-O*
(transition state) obtained from CatApp versus the
calculated values using scaling laws. The solid line
corresponds to perfect agreement between observed
and calculated values.
!

4. CHEMENG 242: Final Project Nicholas Montes
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The microkinetic model assumed all but one reaction was in equilibrium at any one time.
It was therefore possible to obtain analytical expressions for each of the surface coverage terms.
Regardless of which step was taken to be rate limiting, the following expressions were obtained.
!!!!
!∗
= !!!!!!, !
!!!
!∗
=
!!!
!!"
,
!!"
!∗
=
!!!! !!"!!!!
!!!
,
!!
!∗
=
!!!!!!!!"!!!!
!!!
,
!!"
!∗
=
!!"
!!
When reaction 4 was taken to be rate limiting the additional expressions were obtained:
!!
!∗
=!
!!"!!!
!!!!!!!!!!!!"!!!!
,
!!"
!∗
=!
!!"!!!
!/!
!!!!!!!!!!!!!!"
!/!
!!!!
,
!!"!
!∗
=!
!!"!!!
!
!!!!!!!!!!!!!!!!"
! !!!!
,
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!"!
!∗
=!
!!"!!!
!/!
!!!!!!!!!!!!!!!!!!"
!/!
!!!!
When reaction 8 was taken to be rate limiting the additional expressions were obtained:
!!
!∗
=!
!!!!!!!!!!"
!
!!"!
!!!
! ,
!!"
!∗
=!
!!!!!!!!"
!/!
!!"!
!!!
!/! ,!
!!"!
!∗
=!
!!!!!!"!!"!
!!!
,
!!"!
!∗
=!
!! !!"!!"!
!!!
The TOF was then found by taking the minimum value of R4 and R8, where
!! = !!!!"!!∗
!
− !!!!!"!!!, !! = !!!!!! − !!!!!"!∗
Using this model with the scaling laws, volcano plots (Fig. 3) were created. Table 3
shows the rates calculated using the scaling laws and microkinetic model were found to be in
fairly good agreement with the rates found using the catalyst data from CatApp. The scaling laws
were able to predict the reaction rate to within one order of magnitude for the Ru, Rh, Ag, and
Au catalysts and to within two orders of magnitude for the Pt, Pd and Cu catalysts.
Log10(TOF) Ru (211) Rh (211) Pt (211) Pd(211) Cu(211) Ag(211) Au(211)
CatApp -2.75 -0.74 -0.85 -5.69 -5.72 -14.28 -14.87
Scaling Laws -3.57 -1.27 -2.44 -3.99 -4.45 -13.53 -14.19
Table 3: Comparison of the predicted reaction rates using scaling laws and using the energetics obtained in CatApp.
Figure 3: “Volcano plots”. Contour lines represent the log10(TOF) of a reaction. The left plot considers only
reaction 4 to be rate limiting and the right plot considers only reaction 8 to be rate limiting. The middle plot shows
the overall reaction rate, which is taken as the minimum of the right and left plots.
0 2 4 6
−3
−2
−1
0
1
2
3
Ru(211)
Rh(211)
Pt(211)
Pd(211)
Cu(211)
Ag(211)
Au(211)
E
C*
(eV)
E
O*
(eV)
−12
−10
−8
−6
−4
−2
0 2 4 6
−3
−2
−1
0
1
2
3
Ru(211)
Rh(211)
Pt(211)
Pd(211)
Cu(211)
Ag(211)
Au(211)
E
C*
(eV)
EO*
(eV)
−30
−25
−20
−15
−10
−5
0 2 4 6
−3
−2
−1
0
1
2
3
Ru(211)
Rh(211)
Pt(211)
Pd(211)
Cu(211)
Ag(211)
Au(211)
E
C*
(eV)
EO*
(eV)
−30
−25
−20
−15
−10
−5
0

5. CHEMENG 242: Final Project Nicholas Montes
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Discussion
The volcano plots provide some important insight into the nature of this reaction. By
comparing the plots on the left and the right, it can be seen that rate of the steam reforming
reaction on Ru and Rh is limited by the formation of CO* from C* and O* (reaction 8).
Therefore it is the activation free energy for the formation of CO* on Ru and Rh that determines
the reaction rate. Conversely, Pt and Pd are both limited by the adsorption and dissociation of
methane (reaction 4). In this case, it is the activation free energy to bind CH4 that is rate limiting.
These observations offer some valuable insight into why there is some inconsistency in the
literature as to whether Pt,Pd or Ru,Rh are the better catalysts. Since these sets of catalysts are
limited by different reaction mechanisms, one would expect the performance of one group versus
the other to be temperature dependent. This is because at high temperatures the reaction on Pt,Pd
is limited by a the adsorption of a gas phase species onto the surface. At high temperatures,
entropic effects (TΔS) can significantly increase the activation free energy of reaction 4, making
it more rate limiting. Therefore one would expect Ru,Rh to perform better at high temperatures
as they are limited by a free energy barrier that scales less with temperature.
Regardless of which reaction is rate limiting, Fig. 3 clearly shows that catalysts which
strongly bind O and C are predicted to have a higher TOF than those that don’t. Both Ru and Rh
meet this criteria. However, neither the plot not the microkinetic model offer an explanation as to
why Ru and Rh bind C and O the way they do. The physical phenomenon that causes this
behavior can be explained by electronic d-band theory. In transition metals, the high density of
atoms leads to the formation of a d-band, or closely packed set of electron energy states with a
particular “density of states” Molecular orbital theory predicts that when a species binds to the
surface, their electron states interact such that there is a creation of low energy “bonding” states
and high-energy “anti-bonding” states. This change is reflected in the d-band energy states. The
d band center roughly divides the d-band into “bonding” and “anti-bonding” states. When the d-
band center is close to the Fermi level strong binding occurs since many of the “bonding” states
are occupied while the “anti-bonding” states are unoccupied. It turns out that the strongest
bonding occurs when half of the d-band is filled such that the d-band center is closest to the
Fermi level. Molecular Ru has 6 out of 10 electrons in its d orbitals while Rh has 7 out 10
electrons in it orbitals. This explains why both Ru and Rh strongly bind C and O and why Ru
forms slightly stronger bonds with both species. This d-band behavior also provides an
explanation for why scaling laws are so effective. Since so much of the bonding process depends
on the d- band of the catalyst itself, a catalyst tends to exhibit the similar covalent bonding
behavior with a wide range of species. A final note, one should not assume that strong binding
always leads to better catalytic activity. As the free energy diagram shows, if a surface binds the
product species too strongly this can limit the overall reaction rate.
In summary it was shown that Ru and Rh possess qualities that make them good catalysts
for the steam methane reforming reaction. Due to their electronic structures, both catalysts bind
species in such a way that the absorption of reactants onto the surface, the intermediate reactions
between adsorbed species, and the desorption of products all occur in the absence of high free
energy barriers leading to high overall reaction rates.
References
1. J.R. Rostrup-Neilsen, J.HB, Hansen, J. Catal 144 (1993) 38.
2. G. Jones et al., J. Catal 259 (2008) 147-160.
3. Hummelshøj, J. S., Abild-Pedersen, F., Studt, F., Bligaard, T. and Nørskov, J. K. (2012). Angew.
Chem. Int. Ed. 51 (2012) 272–274.