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

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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.

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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!

Free

Ene

rgy

(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

) Pre

dict

ed

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. !

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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)

EC* (eV)

E O* (e

V)

−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)

EC* (eV)

E O* (e

V)

−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)

EC* (eV)

E O* (e

V)

−30

−25

−20

−15

−10

−5

0

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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.