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Article
Significance of Surface Formate Coverage on the Reaction Kinetics of Methanol Synthesis from CO2 Hydrogenation over Cu Panpan Wu, and Bo Yang ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b01910 • Publication Date (Web): 15 Sep 2017 Downloaded from http://pubs.acs.org on September 15, 2017
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ACS Catalysis
1
Significance of Surface Formate Coverage on the Reaction Kinetics of Methanol
2
Synthesis from CO2 Hydrogenation over Cu
3
Panpan Wu,1,2,3 Bo Yang1,4,*
4 5 6
1
7
Huaxia Road, Shanghai 201210, China
8
2
9
China
School of Physical Science and Technology, ShanghaiTech University, 393 Middle
Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050,
10
3
University of Chinese Academy of Sciences, Beijing, 101407, China
11
4
Key Laboratory of Low-Carbon Conversion Science & Engineering, Shanghai
12
Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
13
*Email address:
[email protected] 14 15 16
Abstract
17
The hydrogenation of CO2 to methanol over copper-based catalysts has attracted
18
considerable attentions recently. Among all the proposed reaction mechanisms, a large
19
number of experimental and theoretical studies have focused on the one via HCOO
20
intermediate due to the fact that a high coverage of formate over catalyst surfaces
21
were observed experimentally. In order to systematically understand the influence of
22
formate species coverage on the reaction kinetics of methanol synthesis, energetics of
23
the CO2 hydrogenation pathway over clean and one/two formate pre-adsorbed Cu(211)
24
are obtained using density functional theory (DFT) calculations, and these energetics
25
are further employed for the microkinetic modeling. We find that the adsorption
26
energies of the intermediates and transition-states involved in the reaction pathway
27
are changed in the presence of spectating formate species, and consequently the
28
potential energy diagrams are varied. Microkinetic analysis shows that the turn-over
29
frequencies (TOFs) over different formate pre-adsorbed surfaces vary under the same 1 ACS Paragon Plus Environment
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reaction condition. Particularly, the reaction rates obtained over clean Cu(211) are
2
generally the lowest, while those over one/two formate pre-adsorbed surfaces are
3
depending on the reaction temperatures and pressures. Meanwhile, we find that, only
4
when the formate coverage effect is considered, some of the TOFs obtained from
5
microkinetic modeling are in fair agreement with previous experimental results under
6
similar conditions. After the degree of rate control analysis, it is found that the
7
combination of HCOO and HCOOH hydrogenation steps can be treated as the
8
‘effective rate-determining step’, which can be written as HCOO* + 2H* →
9
H2COOH* + 2*. Therefore, the formation of methanol is mainly controlled by the
10
surface coverage of formate and hydrogen at steady state, as well as the free energy
11
barriers of the effective rate-determining step, i.e. effective free energy barriers.
12 13
Key words:
14
Density functional theory; formate coverage effect; CO2 hydrogenation; methanol
15
synthesis; degree of rate control; BEEF-vdW.
16 17
1. Introduction
18
Methanol synthesis from CO2 hydrogenation over copper-based catalysts has attracted
19
considerable interests owing to its industrial applications and environmental
20
significance. In industry, methanol is produced from synthesis gas, a mixture of CO,
21
CO2 and H2, at temperatures of 473~573 K and pressures of 50~100 bar over the
22
Cu/ZnO/Al2O3 catalyst.1,2 Several experimental studies have shown that CO2 in
23
synthesis gas is the main carbon source of methanol synthesis.3-5 For example,
24
Chinchen et al. previously found that, while adding 14C labelled 14CO or 14CO2 to the
25
reactant mixtures of CO2/CO/H2, the fraction of methanol made from carbon dioxide
26
rises with the increase of p C O 2 / p C O ratio, thus the authors concluded that methanol
27
is mainly produced from CO2 in the feedstock.4 The most puzzling questions in this
28
field till now are lying on the reaction mechanism and the nature of catalytic active
29
sites. 2 ACS Paragon Plus Environment
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Given the fact that the most abundant adsorbate on the catalyst surface within the
2
limit of detection is formate, it is easy to understand that a large number of
3
experimental and theoretical studies focused on the reaction pathway via HCOO
4
intermediate.6-13 For example, Rasmussen et al. developed a model to understand the
5
kinetics of methanol synthesis over Cu and found that formate is a stable
6
intermediate.9 Theoretically, Grabow and Mavrikakis revealed that the hydrogenation
7
of CO2 to methanol on Cu(111) might follow the formate mechanism, in which the
8
surface adsorbed HCOO, HCOOH, CH2OOH, CH2O and CH3O are involved, and it
9
was found that the formation of COOH, the precursor for CO formation, is much
10
more difficult than that of HCOO over Cu.10 Moreover, the hydrogenation of CO2,
11
following the formate mechanism, is found more favorable than CO hydrogenation
12
over Cu.11 Recently, Kattel and co-workers also suggested that methanol synthesis via
13
HCOO intermediate on either Cu-Zn alloy or Cu-ZnO interface is energetically
14
favored compared with the reverse water-gas shift (RWGS) pathway through COOH
15
and CO intermediates.12 Although the debate on whether the formate species is
16
participating the formation pathways of methanol over copper is still going on, its
17
spectating effect is widely recognized.14-16
18
The nature of the active site of copper-based catalysts for methanol synthesis is still
19
under debate. In situ X-ray photoelectron spectroscopy and surface X-ray diffraction
20
experiments suggested that metallic Cu is the active site over copper-based
21
catalysts.17,18 While focusing on pristine Cu catalysts, experiments using Cu(100),9
22
Cu(110),19 and polycrystalline Cu films mainly composed of Cu(111) facet20 indicated
23
that CO2 hydrogenation is structure-sensitive. Moreover, according to the
24
computational results reported by Behrens et al., the adsorption of intermediates
25
involved in CO2 hydrogenation over Cu(211) is much stronger than over Cu(111),21
26
which is consistent with the experimental phenomenon that the defects on the working
27
catalysts may act as the active site.
28
In addition to the analyses on the energetics of methanol formation pathways,
29
microkinetic models were also proposed. van Rensburg and co-workers performed 3 ACS Paragon Plus Environment
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microkinetic analyses on the relationship between formate saturation coverage and the
2
turn-over rate of methanol synthesis based on the energetic data reported before,11 and
3
they found that the rate of methanol formation is sensitive to the coverage of formate
4
at steady-state.22 The approach the authors used was controlling the sites that formate
5
could occupy during the reaction, and therefore varying the limits of formate
6
saturation coverage, to find out the change of reaction rate. However, it should be
7
pointed out that the effect of formate coverage on the adsorption energies of surface
8
intermediates were not considered in their work. More recently, Studt et al. undertook
9
a microkinetic study on methanol synthesis from syngas over copper-based catalysts
10
combining experimental and theoretical methods, and they concluded that the catalyst
11
mixture optimizes the reaction kinetics, whereas the feed gas optimizes the
12
equilibrium thermodynamics of the system.23
13
In the current work, we present a systematic study regarding the influence of formate
14
coverage on the reaction rate of methanol synthesis with the coverage-dependent
15
adsorbate-adsorbate interactions included. We are using clean and one/two formate
16
pre-adsorbed Cu(211) surfaces to model the reaction pathway at different formate
17
coverages. The same approach has been proved effective in the literature for the
18
analysis of coverage effects in surface reaction studies.24,25 Such approach is also able
19
to reflect different reaction kinetics along with the process of formate build-up over
20
the catalyst at the initial stage of CO2 hydrogenation. An alternative approach is to
21
determine the relations between all the adsorption/activation energies and coverages,
22
which may be linear or non-linear, and then run the self-consistent iterative
23
simulations.26,27 However, this approach is quite time-consuming considering the
24
complex reaction network of methanol synthesis, and the results obtained are strongly
25
dependent on the relations obtained, and therefore is not taken here. The adsorption
26
energies of HCOO at different coverages are calculated and compared. Meanwhile,
27
the energetics of all elementary reactions involved in the mechanism are calculated at
28
incremental formate coverages. We then carry out a microkinetic modeling based on
29
the energies obtained from density functional theory (DFT) calculations to gain more 4 ACS Paragon Plus Environment
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insight into the effect of formate coverage on the reaction rate and the identification of
2
rate-determining steps in the whole pathway.
3 4
2. Computational details
5
2.1 DFT calculation methods
6
The
7
projector-augmented wave (PAW) method31,32 was used to perform all the density
8
functional calculations. The generalized gradient approximation (GGA) with the
9
BEEF-vdW exchange-correlation functional,33 which explicitly takes long-range
10
dispersion force into consideration and has been widely used to model surface
11
catalysis reactions,11,34-36 was employed to set the plane-wave basis. The BEEF-vdW
12
functional was used here because it was found that the inclusion of van der Waals
13
interactions gives a better description on the energetics of CO2 hydrogenation
14
compared to RPBE.11 The bulk lattice constant of copper was optimized yielding a
15
value of 3.658 Å, which is close to the experimental bulk lattice constant of 3.615 Å.
16
Twelve-layer and 3×4 slabs with the upmost six Cu layers relaxed during optimization
17
were used to model the adsorption and reaction processes over Cu(211) surfaces.
18
Therefore, one formate species on the surface would give rise to a coverage of 0.083
19
(1/12) monolayer (ML). The slab was set with a vacuum to be at least 11 Å to make
20
sure the reactions only take place on one side of the slabs. A 4×2×1 k-point grid
21
generated with the Monkhorst-Pack scheme was used. An energy cutoff of 500 eV and
22
convergence criteria of the force on each relaxed atoms below 0.05 eV/ Å were found
23
to give converged results in the current work. Transition-states were located with a
24
constrained minimization method.37-39 In this method, transition-states are identified
25
when (i) the force on the relaxed atoms vanish and (ii) the energy is a maximum along
26
the reaction coordinate, but a minimum with respect to all of the remaining degrees of
27
freedom.
28
Adsorption energies were defined as:
29
Vienna
Ab-initio
Simulation
Package
(VASP)
Ead = Etotal − Eslab − Eg 5 ACS Paragon Plus Environment
code28-30
with
the
(1)
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1
where Etotal is the energy of the system after adsorption, Eg is the energy of the
2
gas-phase molecule, and Eslab is the energy of slab. The correction to the energies of
3
gas phase molecules resulted from the systematic DFT errors in describing the
4
carbon-oxygen double bond with BEEF-vdW was used according to the values
5
reported in the literature,11,23,40,41 which are +0.41 and +0.09 eV for the gaseous CO2
6
and H2, respectively. In order to compare the adsorption of formate at different
7
coverages, the average and differential adsorption energies of formate were calculated,
8
where the average adsorption energies (∆Eavg) were calculated from the equation,
∆Eavg ( N ) =
9
Eslab+ N ⋅ads. − Eslab − N ⋅ Eads N
10
and the differential adsorption energies (∆Ediff) were calculated from the equation,
11
∆Ediff ( N ) = Eslab+N ⋅ads − Eslab+(N -1)⋅ads − Eads
(2)
(3)
12
where Eslab+N·ads is the energy of the system containing adsorbates with the number of
13
N, Eads is the energy of formate with respect to the energy of gaseous CO2+1/2H2.
14 15
2.2 Microkinetic model
16
Microkinetic analysis in the current work is manipulated using CatMAP module
17
introduced by Nørskov’s group,42,43 which has been used widely to obtain more
18
insight into surface catalytic reactions. In this module, elementary reactions
19
considered are the same with those reported in the literature10-12,21-23 and are listed as
20
follows:
21
H2(g) + 2* → 2H*
(R1)
22
CO2(g) + H* → HCOO*
(R2)
23
HCOO* + H* → HCOOH* + *
(R3)
24
HCOOH* + H* → CH2OOH* + *
(R4)
25
CH2OOH* + *→ CH2O* + OH*
(R5)
26
CH2O* + H* → CH3O* + *
(R6)
27
CH3O* + H*→ CH3OH(g) + 2*
(R7)
28
OH* + H* → H2O(g) + 2*
(R8) 6
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It should be mentioned that we also compared the activation energies of COOH
2
formation and CO2 direct decomposition at different formate coverages over Cu(211).
3
The corresponding transition-state configurations and activation energies are
4
presented in Figure S1 in the SI. We find that these two possible reactions are
5
experiencing much higher barriers than formate formation (as listed in Table 1).
6
Here, two different sites were considered: one for hydrogen atoms and the other for
7
the remaining adsorbates. In this approach, hydrogen is adsorbed at a special
8
“hydrogen reservoir” site,27,44 and does not compete with other adsorbates for a free
9
site. The free energies of adsorbates and transition-states at temperature T were
10
estimated according to the harmonic approximation, and the entropy is evaluated
11
using the following equation:
12
S (T ) = kB
harm DOF
∑ i
εi − ln 1 − e −ε i ε i kBT k T ( e − 1) B
(
kBT
) ,
13
where kB is Boltzmann constant; DOF is the number of harmonic energies (εi) used in
14
the summation denoted as degree of freedom, which is generally 3N, where N is the
15
number of atoms in the adsorbates or transition-states.
16
Meanwhile, the free energies of gas phase species are corrected as
17
G g (T ) = Eelec + E ZPE + ∫ C p d T − TS (T ) ,
18
where Cp is gas phase heat capacity as a function of temperature derived from
19
Shomate equations and the corresponding parameters in the equations were obtained
20
from
21
transition-state-theory. The temperature considered is from 373 to 573 K, consistent
22
with the typical industrial reaction conditions. The concentration of feed gases is CO2:
23
H2: CH3OH: H2O: inert gas = 0.10: 0.40: 0.01: 0.01: 0.48, which corresponds to a
24
CO2 conversion of around 10% and therefore the adsorption/desorption of methanol
25
and water are not considered in our kinetic model. The total pressure (ptotal) ranges
26
from 10 to 100 bar, corresponding to the reactant (CO2 + H2) partial pressure (preactant)
27
varying from 5 to 50 bar.
NIST.45
The
pre-exponential
factors
were
28
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determined
using
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3. Results and Discussion
2
3.1 Formate adsorption energies as a function of coverage
3
As mentioned above, it was reported in the literature that the reaction rate of methanol
4
synthesis is sensitive to HCOO saturation coverage.22 Meanwhile, the coverage of
5
adsorbates is relevant to the corresponding adsorption energies, i.e. stronger
6
adsorption of formate would increase its coverage, but higher coverage would in turn
7
weaken the adsorption strength to some extent due to the lateral interactions between
8
adsorbates.
9
different coverages are calculated and the trend is shown in Figure 1. One can see that
10
the adsorption of formate becomes weaker with the increase of coverage, and the
11
average (differential) adsorption energy varies from -1.34 (-1.34) eV to -1.06 (-0.78)
12
eV corresponding to the formate coverage from 0.083 to 0.250 ML, respectively.
13
Coverage-dependent adsorbate-adsorbate interactions have been studied previously
14
for the systems of CO methanation and NO oxidation,27,52 and it was found that the
15
reaction rates might change by several orders of magnitude with coverage variation.
16
Considering that formate is the most abundant species on the surface, it is of essence
17
to take the interactions between formate and the surface intermediates into
18
consideration while investigating the reaction kinetics of methanol synthesis.
19
In the reaction pathways investigated, it is postulated that only one formate species in
20
the slab participates in methanol synthesis reaction and the residual adsorbed HCOO
21
act as spectators during the process at different coverages. Therefore, we define θDFT
22
as the coverage of all the surface species while performing the DFT calculations, and
23
pre-ads , where θIM is the coverage of surface intermediates during the θ DFT = θ IM + θ HCOO
24
pre-ads reaction, which is 0.083 ML, and θ HCOO is the coverage of formate pre-adsorbed on
25
Cu(211), which is 0, 0.083 and 0.167 ML for the surfaces with zero, one and two
26
pre-adsorbed formate species, respectively.
2,46-51
Here, the average/differential adsorption energies of formate at
27 28
3.2 CO2 hydrogenation over clean Cu(211)
29
The reaction energetics over clean Cu(211), where θDFT is 0.083 ML and the 8 ACS Paragon Plus Environment
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adsorbate-adsorbate interactions can be neglected, are calculated and listed in Table 1.
2
The configurations of corresponding adsorption and transition states are presented in
3
Figure 2. It should be mentioned that we tried different possible adsorption and
4
transition state structures in the current work and those shown in the figures are with
5
the lowest energies. One can see that the transition-state structures of HCOO-H,
6
H-CHOOH, CH3O-H and H-OH are those with hydrogen atoms binding to the Cu
7
atoms at the lower terrace of Cu(211), in accordance with the structures reported
8
previously in the literature.11 As listed in Table 1, the hydrogenation of HCOO has the
9
highest activation energy of 1.27 eV in the reaction pathway, and the corresponding
10
reaction energy is calculated to be endothermic by 0.55 eV, indicating that the
11
hydrogenation of HCOO is relatively difficult and formate species may get
12
accumulated over clean Cu(211).
13 14
3.3 CO2 hydrogenation over one and two formate pre-adsorbed Cu(211)
15
We study the coverage effect by employing a model with one and two fomate species
16
pre-adsorbed on the catalyst surfaces with a bridging bi-dentate structure, leading to
17
θDFT values of 0.167 and 0.250 ML, respectively. The relevant adsorption and
18
transition state structures are presented in Figure 3.
19
When θDFT = 0.167 ML, corresponding to the situation of one formate and one
20
reaction intermediate on the surface, the spectating formate species adsorbs on the
21
surface through two oxygen atoms binding with two copper atoms at the step-edge
22
site. The adsorption configurations of the intermediates involved in the reactions are
23
quite similar to those over clean Cu(211), whereas the geometries of transition-states
24
are slightly different for CH2O-OH and H-CH2O. As shown in Figure 3, at the θDFT of
25
0.167 ML, both CH2OOH dissociation and CH2O hydrogenation occurs with CH2O
26
binding at the step-edge site whilst the hydroxyl/hydrogen moiety staying at the
27
terrace Cu atoms.
28
Further increase of the number of pre-adsorbed formate changes θDFT to 0.250 ML
29
over Cu(211). Under such situation, the two spectating formate species tend to get 9 ACS Paragon Plus Environment
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stabilized through adjusting their adsorption configurations. As we can see from
2
Figure 3, one of the formate species binds at the step-bridge site with two oxygen
3
atoms, while the other formate turns into the structure with two oxygen atoms
4
bonding to the step and terrace copper atoms, respectively. It should be noted that we
5
have examined the barriers of the formation and hydrogenation of all three formate
6
species, the structures of which are shown in Figure S2 in the Supporting Information
7
(SI), and those shown in Figure 3 are the most stable ones.
8
One can see that most of the configurations of surface intermediates at the θDFT of
9
0.250 ML are similar to those at 0.167 ML, and therefore only the different ones are
10
discussed here. As shown in Figure 3, CH2OOH prefers to stay at the terrace hcp
11
hollow site when θDFT = 0.250 ML, whilst the bridge site at step edge is favored at
12
lower θDFT. Upon the dissociation of CH2OOH, the produced CH2O still binds to one
13
step copper atom but with the C=O bond more vertical to the step-edge site.
14
Meanwhile, the hydroxyl moiety tends to stay at the terrace hcp hollow site when θDFT
15
is higher. These subtle structure changes imply that the self-adjustment of
16
intermediates are experiencing a steric effect caused by the increase of formate
17
coverage. The corresponding transition-state structures are presented in Figure 3,
18
which are similar to those at θDFT = 0.167 ML.
19 20
3.4 Potential energy diagrams at different θDFT
21
Based on the energies obtained above, the potential energy diagrams of CO2
22
hydrogenation to methanol at different θDFT are presented in Figure 4. It can be found
23
from the figure that the activation of CO2 is insensitive to surface formate coverage
24
variation, whilst the barriers of formate further hydrogenation to formic acid are
25
decreasing with the increase of formate coverage.
26
It is interesting to see that the adsorption of formic acid at the θDFT of 0.167 ML is the
27
strongest among the three studied coverages, and the trend is different from that
28
observed for the adsorption of formate. To explain this, charge density differences
29
induced by the adsorption of HCOOH is studied. The charge density difference (∆ρ) 10 ACS Paragon Plus Environment
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is defined as
∆ ρ = ρ HCOOH+slab − ρ slab − ρ HCOOH
2
ρHCOOH+slab
(4)
3
where
is the charge density distribution of formic acid adsorbed on
4
slabs with different fomate species pre-adsorbed as shown in Figure 5, and
5
ρHCOOH
6
pre-adsorbed formate species and HCOOH only, respectively. The yellow contours
7
represent charge accumulations, and the blue contours denote charge depressions. The
8
scales of the charge densities are identical. It can be clearly seen that the charge
9
distribution of the copper atom that HCOOH adsorbs on differs from each other at
10
different formate coverages. In Figure 5b, the copper atom binding with HCOOH
11
transfers the most charge, corresponding to the θDFT of 0.167 ML. This is consistent
12
with the trend obtained for the adsorption of HCOOH and indicating that the presence
13
of spectating formate would influence the charge distribution of copper atoms.
14
In contrast to the formation of HCOOH, both the barriers and reaction energies for
15
CH2OOH generation and dissociation at different coverages are similar, therefore,
16
stronger HCOOH adsorption would give rise to more stable transition-states for
17
formic acid hydrogenation, as shown in Figure 4. It will be revealed later that the
18
transition-state of CH2OOH generation is in fact rate-determining in the reaction
19
pathway of methanol synthesis under the industrial reaction conditions, and the trend
20
of HCOOH adsorption energies revealed above is crucial to understanding the activity
21
trend of methanol synthesis. Subsequent hydrogenation of CH2O and OH lead to the
22
desired products CH3OH and H2O, respectively, and the corresponding barriers and
23
reaction energies are listed in Table 1. Based on the analyses of the energy diagrams
24
in Figure 4, it is obvious that the energetics of CO2 hydrogenation are indeed strongly
25
influenced by the number of pre-adsorbed formate.
ρslab
and
are the charge density distributions of Cu (211) with different numbers of
26 27
3.5 Reaction kinetics at different θDFT
28
The kinetics of methanol synthesis are explored based on the energetics obtained 11 ACS Paragon Plus Environment
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above at different reaction conditions. In our study, the coverage of most
2
intermediates obtained are essentially zero at the steady state and only surface HCOO
3
are found. Figure 6a-c shows the trend of the obtained formate coverages from kinetic
4
k , ss analyses at steady state ( θ HCOO ), in which the coverage of pre-adsorbed formate is
5
included, and the corresponding calculated turn-over frequency (TOF) as a function of
6
temperature (373 - 573 K) and pressure (preactant = 5, 25 and 50 bar) are presented in
7
Figure 6d-f. The trend of the obtained TOFs at all the temperatures and pressures
8
studied are shown in Figure S3 in the SI. It is clear that the coverage of formate and
9
the TOF of methanol synthesis obtained from our microkinetic modeling at steady
10
state is strongly affected by the variation of θDFT.
11
k , ss When θDFT = 0.083 ML, as we can see from Figure 6a, θ HCOO behaves a minor
12
decrease from 1 to ~0.8 ML with the increase of temperature at low reactant pressure
13
(preactant = 5 bar). However, it remains almost 1 ML at higher pressures (preactant = 25
14
k , ss and 50 bar) as shown in Figure 6b and c. All of the θ HCOO s obtained are much higher
15
than the θDFT used, indicating that the energetics obtained from DFT calculations at
16
this low coverage cannot give rise to converged steady state information.
17
k , ss As also shown in Figure 6a, when θDFT = 0.167 ML, θ HCOO decreases with the
18
increase of temperature, and converges around 0.167±0.050 ML from 513 to 543 K at
19
preactant = 5 bar and at 573 K and preactant = 25 bar, whilst at preactant = 50 bar, no
20
k , ss convergence between θDFT and θ HCOO is found in the temperature range studied in
21
the current work. However, one can see from Figure 6b and c that it is possible for
22
k , ss to approach 0.167 ML when the temperature is further increased. In the case of θ HCOO
23
k , ss θDFT = 0.250 ML, the coverages obtained ( θ HCOO ) converges at several different
24
conditions, e.g. 373 K with the value of 0.220 ML at preactant = 25 bar.
25
The TOFs of methanol synthesis are found increasing with temperature at all the
26
reactant pressures and coverages of surface species studied. We list the reaction
27
k , ss conditions, where the θ HCOO obtained converge with θDFT, and the corresponding
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TOFs in Table S1 in the SI. Considering that the formation rate of methanol obtained
2
over clean Cu(211) surface is 1.11 × 10-6 site-1 s-1 at the temperature of 513K and
3
reactant pressure of 5 bar, it is found from this table that the reaction rate obtained at
4
θDFT = 0.167 ML (4.17 × 10-4 site-1 s-1) is in fair agreement with that measured from
5
experiments, i.e. 1.2 × 10-3 site-1 s-1 under the same reaction conditions,53 whilst the
6
TOF obtained based on θDFT =0.083 ML energetics is not.
7 8
3.6 Degree of rate control analyses
9
In terms of the kinetic analyses of multistep reactions, identifying the
10
rate-determining steps (RDSs) is pivotal to making good predictions of the reaction
11
rates and to improving the TOFs by optimizing the structure of catalysts or reaction
12
conditions in practical terms.54 According to the relevant investigations reported, the
13
tool named degree of rate control (DRC) facilitates the analyses of reaction
14
mechanisms and kinetics, serving a quite similar purpose to determining the RDS.54-56
15
In this approach, Xi is defined as the value of DRC for the adsorption or transition
16
state i, and can be written as:
17
−∂ ln r Xi = ∂ ( Gio / RT ) o G j≠i
(5)
18
where Gio denotes the free energies of surface adsorbates or transition-states and the
19
partial derivative is taken holding constant the standard-state free energy of all other
20
species j (intermediates, transition-states, reactants and products). Specifically, the Xi
21
can be defined as XRC,i (degree of rate control for transition-states) or XTRC,i (degree of
22
thermodynamic rate control for adsorbates). We here investigate the Xi of the
23
methanol synthesis reactions at preactant = 50 bar to gain insight into the variation of
24
rate-determining step with temperature at different θDFT.
25
It is obvious from Figure 7 that XRC,i is positive and, in opposite, that XTRC,i is negative,
26
and the sum of XRC,i is 1 all the time.54-56 Taking the case of θDFT = 0.083 ML as an
27
example, as shown in Figure 7a, XRC,H-CHOOH increases from 0 to 1 with the 13 ACS Paragon Plus Environment
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1
temperature varying from 373 to 573K, while XRC,CH2O-OH decreases from 1 to 0
2
within the same temperature range. However, XRC,HCOO-H remains zero all the time,
3
indicating that the formation of formic acid is not rate-limiting under the conditions
4
studied. We note that the higher DRC of HCOOH hydrogenation than HCOO
5
hydrogenation is consistent with the computational results reported before.22
6
It was also reported in the literature that the degree of thermodynamic rate control of
7
the surface intermediate n is proportional to the coverage of such an intermediate (θn),
8
i.e. X TRC,n = −σ ⋅ θ n , where σ is the number of surface free site required by the
9
rate-determining elementary reactions identified.54-56 As we can see from Figure 7a,
10
the rate-determining transition state at θDFT = 0.083 ML is mainly the dissociation of
11
CH2OOH below 473K, which requires one more surface free sites to occur.
12
k , ss Meanwhile, the corresponding θ HCOO at low temperatures is almost 1 ML (see Figure
13
6c). However, as we can see from Figure S4 in the SI, with the increase of
14
temperature, the coverage of HCOO slightly decreases, and small amounts of free
15
sites released facilitate the dissociation of CH2OOH, resulting in the decrease of
16
XRC,CH2O-OH and increase of XRC,H-CHOOH. When the temperature is higher than 473 K,
17
the hydrogenation of HCOOH becomes the rate-determining transition-state.
18
Similar investigations are carried out at θDFT = 0.167 and 0.250 ML as well, the results
19
of which are shown in Figure 7b and c, respectively. It is clear that, at θDFT = 0.167
20
ML, the reaction rate is mainly sensitive to the free energy of H-CHOOH
21
transition-state above 423 K. With the increase of θDFT, the transition-state
22
determining the reaction rate of methanol synthesis is always H-CHOOH within the
23
whole temperature range.
24
As discussed above, we find that it is reasonable to consider that the adsorption-state
25
of HCOO and the transition-state of HCOOH hydrogenation as the rate-determining
26
initial state and transition state of methanol synthesis, respectively, under the typical
27
industrial reaction conditions (> 500 K and preactant = 50 bar). Therefore, the
28
combination of HCOO and HCOOH hydrogenation steps can be treated as the
29
‘effective rate-determining step’, which is written as HCOO* + 2H* → H2COOH* + 14 ACS Paragon Plus Environment
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2*, for this process. The overall reaction rate of CO2 hydrogenation to methanol can
2
therefore be estimated using eff
3
r = k ⋅θHCOO ⋅θH2 = A ⋅ e−Ga
/ k BT
θHCOO ⋅θH2 ,
(6)
4
where Gaeff is the effective free energy barrier of the effective rate-determining step
5
and can be calculated with Ga , R 4 + ∆GR 3 , with Ga , R 4 and ∆GR 3 being the free
6
energy barrier of R4 and reaction free energy of R3, respectively. For example, at 503
7
K and preactant = 50 bar, the effective free energy barrier is 1.14 eV and the coverage of
8
HCOO and H over one formate pre-adsorbed Cu(211) surface is 0.796 and 0.026 ML,
9
respectively. Thus, the TOF estimated using equation (6) is 2.17 × 10-2 site-1 s-1, which
10
is identical to the rate obtained from microkinetic modeling at steady-state, as one can
11
see from Table S2 in the SI. The TOFs of methanol synthesis obtained from CatMAP
12
and those computed from equation (6) proposed in our work are shown in Figure 8 as
13
a function of temperature, and all the data used to plot this figure are listed in Table
14
S2 of the SI. We find that the TOFs fit well from the temperature where the XH-CHOOH
15
is approaching 1 and the transition state of HCOOH hydrogenation is rate determining
16
at different formate coverages, which strongly support the effective rate determining
17
step found in our work.
18
We further find that the hydrogenation of CO2 can be understood using the two-step
19
model developed before,2,49-51,57-59 in which the formation of methanol can be divided
20
into two processes, namely the ‘adsorption’ and ‘desorption’ of HCOO to/from the
21
catalyst surface. The ‘adsorption’ of HCOO is in fact the hydrogen-assisted adsorption
22
of CO2 onto the catalyst surface, whilst the ‘desorption’ process of HCOO from the
23
surface is a combination of a series of elementary steps including hydrogenation and
24
dissociation steps heading to the final formation of methanol. It is obvious from our
25
work that, over Cu(211), the ‘desorption’ of HCOO is rate-determining under reaction
26
conditions. However, the transition-state of HCOO hydrogenation is not necessarily
27
rate-determining, since the energy of this transition-state is lower than that of
28
HCOOH hydrogenation from the free energy landscape as shown in Figure S5 (T = 15 ACS Paragon Plus Environment
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1
503 K, pCO2 = 10 bar, pH2 = 40 bar and pCH3OH = pH2O = 1 bar) in the SI. While
2
increasing the values of θDFT, the corresponding adsorption strength of HCOO is
3
weakened to a larger extent than the destabilization of H-CHOOH on the surface,
4
leading to lower surface formate coverage at steady-state and smaller effective free
5
energy barriers. Considering that the coverage of hydrogen at the same temperature
6
and pressure over the surface are identical at different θDFT, the formation of methanol
7
is mainly controlled by the surface coverage of formate and the effective free energy
8
barriers as shown in equation (6) accordingly.
9 10
4. Conclusions
11
In summary, a systematic analysis of the effect of formate coverage on the reaction
12
kinetics of methanol synthesis over Cu(211) is carried out in the current work. The
13
following conclusions are obtained:
14
(i) Increasing formate coverage would destabilize the adsorption of most of the
15
reaction intermediates and transition states, except for the adsorption of formic acid at
16
θDFT = 0.167 ML. Further charge density difference analysis reveals that the copper
17
atom binding with HCOOH transfers the most charge under this situation;
18
(ii) TOFs at different coverages of surface species are also changed under the same
19
reaction condition, particularly, the reaction rates at θDFT = 0.083 ML are the lowest in
20
general. Meanwhile, we find that taking the coverage effect into account while
21
carrying out DFT calculations would give rise to more reasonable steady-state
22
information, compared with those from previous experimental studies.
23
(iii) The combination of HCOO and HCOOH hydrogenation steps can be treated as
24
the ‘effective rate-determining step’, which can be written as HCOO* + 2H* →
25
H2COOH* + 2* over Cu(211). As a result, the formation of methanol is mainly
26
controlled by the surface coverage of formate and the effective free energy barriers,
27
i.e. r = A ⋅ e
28
Our work shows that, in order to obtain better understandings on the kinetics of
29
surface reactions and to design more effective catalysts, it is essential to consider the
−Gaeff / kBT
θHCOO ⋅θH2 .
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coverage effect of surface abundant species while performing DFT calculations and
2
microkinetic studies.
3 4
Supporting Information
5
Turn-over frequencies, coverages and free energy barriers at different temperatures,
6
adsorption and transition state structures, free energy profiles
7 8
Acknowledgements
9
This work is financially supported by ShanghaiTech University, Shanghai Pujiang
10
Program (16PJ1406800), Shanghai Young Eastern Scholar Program (QD2016049)
11
and the Foundation of Key Laboratory of Low-Carbon Conversion Science &
12
Engineering, Shanghai Advanced Research Institute, Chinese Academy of Sciences.
13
We thank Shanghai Supercomputer Center for computing time.
14 15
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DOI:
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1
Table 1. Activation energies (Ea) and reaction energies (∆E) (in eV) of the elementary
2
reactions of methanol synthesis over Cu(211) at different covarges of surface spescies.
3
ZPE corrections are not included. 0.083 ML
0.167 ML
0.250 ML
Ea
∆E
Ea
∆E
Ea
∆E
CO2(g)+H*→HCOO*
0.20
-1.27
0.23
-0.99
0.29
-0.71
HCOO*+H*→HCOOH*+*
1.27
0.55
1.02
0.17
0.88
0.04
HCOOH*+H*→CH2OOH*+*
0.76
-0.11
0.79
0.03
0.82
0.05
CH2OOH*+*→CH2O*+OH*
0.42
0.35
0.49
0.34
0.30
0.31
CH2O*+H*→CH3O*+*
0.11
-1.09
0.21
-0.91
0.61
-0.53
CH3O*+H*→CH3OH(g)+2*
0.89
0.37
0.72
0.29
0.59
0.02
H*+OH*→H2O(g)+2*
1.01
0.32
0.87
0.20
0.83
-0.05
elementary reactions
4
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1 2
Figure 1. Differential adsorption energies (red square) and average adsorption
3
energies (black circle) of formate on Cu(211). All the adsorption energies are with
4
respect to the energy of CO2(g) + 1/2 H2(g).
5
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1 2
Figure 2. Adsorption structures (above) of HCOO, HCOOH, CH2OOH, CH2O, OH,
3
CH3O and H, and transition-state structures (below) of H-COO, HCOO-H,
4
H-CHOOH, CH2O-OH, H-CH2O, CH3O-H and H-OH on clean Cu(211). In this figure
5
and those hereafter, the Cu, C, H, and O atoms are represented in orange, gray, white
6
and red, respectively.
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Figure 3. Configurations of the adsorbed intermediates and corresponding
3
transition-states of the elementary steps of methanol synthesis on Cu(211) with one
4
and two pre-adsorbed formate. The spectating formate species are shown in stick type,
5
while the reaction intermediates are presented as ball-and-stick.
6
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Figure 4. Potential energy diagrams of the reaction pathway for methanol synthesis
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on Cu(211) with different coverages of surface species (θDFT) on the surface. The
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elementary reactions considered are listed in Table 1.
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Figure 5. Charge density difference plots for the adsorption of HCOOH over Cu(211)
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with different number of formate species pre-adsorbed. The yellow contours represent
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charge accumulations, and the blue contours denote charge depressions. The scales of
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the charge densities are identical.
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Figure 6. (a-c) The calculated coverages of HCOO as a function of temperature at
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preactant = 5, 25 and 50 bar, respectively. θDFT = 0.083, 0.167 and 0.250 ML are shown
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in yellow square, red circle and blue triangle, respectively. The corresponding
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calculated TOFs as a function of temperature are presented in (d-f). The feed
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composition is CO2(g) : H2(g) : CH3OH(g) : H2O(g) : inert gas = 0.10: 0.40 : 0.01 :
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0.01 : 0.48 at the steady-state in two tables and those hereafter.
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Figure 7. Degree of rate control for methanol synthesis from CO2 hydrogenation via
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HCOO intermediate for the rate-determining elementary steps versus temperature at
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industrial reaction conditions (preactant = 50 bar). a, b and c are corresponding to θDFT =
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0.083, 0.167 and 0.250 ML, respectively. Values for those transition-states and
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adsorbates close to zero are not shown here. The XHCOO-H, XH-CHOOH, XCH2O-OH and
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XHCOO are marked as black square, red circle, yellow triangle and blue invert-triangle,
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respectively.
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Figure 8. The TOFs of methanol synthesis as a function of temperature at preactant = 50
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bar obtained from CatMAP and equation (6) at θDFT = (a) 0.083, (b) 0.167 and (c)
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0.250 ML.
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