The d-band model and Heterogeneous Catalysis – Part 1

The d-band model
and
Heterogeneous Catalysis – Part 1
Thomas Bligaard
Center for Atomic-scale Materials Design
Department of Physics
Technical University of Denmark
Chemical Surface Physics School, Stockholm
May 19, 2010
Harvesting sunlight
Global annual energy
consumption supplied by
the sun in one hour
Sustainable but
- Low intensity
- Weather, season and
time dependent
Chemical storage
- High energy density
- Storable/moveable
- Bridges temporal cycles of
production & consumption
- Exploits existing
infrastructure
Part of the solution: Chemical storage
However...
The Catalyst Challenge
High catalytic efficiency
- Large surface area – nanoparticles
More
efficient
A catalyst
is
a catalysts
material and
-•Optimal
surface
composition
that speeds
up a chemical reaction
structure
– design
• Stable catalysts
• Catalysts made from
Earth-abundant materials
~80 years ago:
Where is the hope ?
- for using calculations in solving atomic-scale problems
P.A.M. Dirac
(Nobel Prize
Physics, 1933)
“The general theory of quantum
mechanics is now almost complete. The
underlying physical laws necessary for the
mathematical theory of a large part of
physics and the whole of chemistry are
thus completely known, and the difficulty
is only that the exact application of these
laws leads to equations much too
complicated to be soluble.”
(Dirac, 1929)
~40 years ago: Here it is !
“In conclusion, I would like to
emphasize strongly my belief that the
era of computing chemists, when
hundreds if not thousands of
chemists will go to the computing
machine instead of the laboratory for
increasingly many facets of chemical
information, is already at hand.”
(Mulliken, Nobel Lecture, 1966)
R.S. Mulliken
Nobel Prize,
Chemistry, 1966
~Today: The revolution is to come
New possibilities – eScience:
“The next 10 to 20 years will see computational
science firmly embedded in the fabric of science
– the most profound development in the scientific
method in over three centuries.”
A SCIENCE-BASED CASE FOR LARGE-SCALE SIMULATION
Office of Science
U.S. Department of Energy, 2003
Æ The big revolution is still to come !
Computational
Traditional
design
simulation
at theflow
atomic scale
Nørskov, Bligaard
Rossmeisl, Christensen
Nature Chemistry
1, 37-46 (2009)
Outline of today’s lecture
Material design strategies
- Surface activity:
• The d-band model (briefly)
• Linear energy correlations/Scaling relations
• Brønsted-Evans-Polanyi relations
• Volcano-relations
• Understanding the experimental trends for
the steam reforming reaction
- Catalyst design
• Methanation
• Selective hydrogenation
• Hydrogen evolution
Outline of tomorrow’s lecture
The d-band model and its implications in more detail
• The Newns-Anderson model
• Effective medium theory
• Electronic structure effects in alloying
• Structure sensitivity of catalytic reactions
• The electronic and geometrical effects in
heterogeneous catalysis
Three flavors of systematic
“Computational Design”
A. Direct computational search
B. Data base screening
C. Descriptor-based search
Bligaard, Andersson, Skriver, Jacobsen, Christensen, Nørskov
Materials Research Society Bulletin 31, 986 (2006)
Three flavors of systematic
“Computational Design”
A. Direct computational search
B. Data base screening
C. Descriptor-based search
Bligaard, Andersson, Skriver, Jacobsen, Christensen, Nørskov
Materials Research Society Bulletin 31, 986 (2006)
Direct Computational Search
Pick a set of
structures/compositions
Calculate their properties
Good enough ?
No !
Yes!
Experimental testing
Choose better
Structures/compositions
+ Adaptively improving
- Difficult to add
constraints after a run
Evolutionary
Algorithm
Johannessen, Bligaard, Ruban, Skriver,
Jacobsen, Nørskov, Phys. Rev. Lett. 88,
255506 (2002)
Evolutionary
Algorithm
The most stable 4component
ordered metal alloy
is found in the 11th
generation, and
the 20 most stable
have been
determined in 45
generations
Johannessen, Bligaard, Ruban,
Skriver, Jacobsen, Nørskov,
Phys. Rev. Lett. 88, 255506 (2002)
Evolutionary algorithm for 4-component alloys
EAs outperform random search by a factor of 50 – even for this simple example
Structural stability of ordered alloys
eV/atom
Formation energy
of the
L12 binary
alloy structures
with respect
to pure
metals
25 %
LMTO-GGA
calculations
75 %
Johannessen, Bligaard, Ruban, Skriver, Jacobsen, Nørskov,
Phys. Rev. Lett. 88, 255506 (2002)
Three flavors of systematic
“Computational Design”
A. Direct computational search
B. Data base screening
C. Descriptor-based search
Bligaard, Andersson, Skriver, Jacobsen, Christensen, Nørskov
Materials Research Society Bulletin 31, 986 (2006)
Screening of Computed Data
Calculate properties for a
large number of systems
Look for systems
having good qualities
Experimental testing
+ Ease of reusing data
- Difficult to include enough
interesting systems
Pareto
optimality
(as a method
for searching
databases)
The 82 alloys with
the most relevant
properties are
easily obtained
from the full
database of
> 64,000 alloys.
Bligaard, Johannessen, Ruban, Skriver, Jacobsen, Nørskov,
App. Phys. Lett. 83, 4527 (2003)
The Computational Materials
Data Repository
quaternary
ternary
Munter, Landis et al.
Æ International collaboration needed to reach relevant data base sizes
The vision
computation
experimental data
theory
The molecular engineering
workbench
understanding/concepts
new design tools
new experiments
Three flavors of systematic
“Computational Design”
A. Direct computational search
B. Data base screening
C. Descriptor-based search
Æ Developing the descriptors
Bligaard, Andersson, Skriver, Jacobsen, Christensen, Nørskov
Materials Research Society Bulletin 31, 986 (2006)
The origin of catalytic trends
Æ the d-band model
Hammer, Nørskov, Nature 376, 238 (1995)
Hammer, Nørskov, Adv. Catal. 45, 71 (2000)
Bligaard, Nørskov in Chemical bonding at surfaces, Elsevier (2008)
Corollary to the d-band model:
Æ adsorbate energies scale
The 0th order d-band model:
Adsorption energies on 3d, 4d,
and 5d metals is linear in the
d-band center location
Corollary to d-band model:
The adsorption energy of any
adsorbate scales with the
adsorption energy of any other
adsorbate on the d-metals
Nilsson, Pettersson, Hammer,
Bligaard, Christensen, Nørskov
Catal. Lett. 100, 111 (2005)
Scaling relations: CHx vs. C adsorption
Close-packed surfaces
CHx adsorption energies
CH3
CH2
Stepped surfaces
Abild-Pedersen, Greeley, Studt
Rossmeisl, Munter, Moses
Skulason, Bligaard, Nørskov
Phys. Rev. Lett. 99, 016105 (2007)
CH
Rationalization of scaling relations
d-band model
Hammer and Nørskov, Nature 376 (1995) 238
+
Effective Medium Theory (EMT)
Nørskov and Lang, Phys. Rev. B 21, 2131 (1980)
Nørskov, Rep. Prog. Phys. 53, 1253 (1990)
Æ Scaling slope
rationalization:
ΔE
AH x
= γ ( x) ΔE + ξ
A
γ ( x) = ( x max − x) / x max
Abild-Pedersen, Greeley, Studt, Rossmeisl, Munter, Moses, Skulason
Bligaard, Nørskov, Phys. Rev. Lett. 99, 016105 (2007)
Scaling relations: CHx vs. C
CHx adsorption energies
For AHx :
slope = (xmax-x)/xmax
Close-packed surfaces
CH3 : 1/4
Stepped surfaces
CH2 : 1/2
CH : 3/4
Abild-Pedersen, Greeley, Studt
Rossmeisl, Munter, Moses
Skulason, Bligaard, Nørskov
Phys. Rev. Lett. 99, 016105 (2007)
Scaling relations: NHx vs. N
Close-packed surfaces
NH2 : a=1/3
Stepped surfaces
NH : a=2/3
Abild-Pedersen, Greeley, Studt
Rossmeisl, Munter, Moses
Skulason, Bligaard, Nørskov
Phys. Rev. Lett. 99, 016105 (2007)
Scaling relations: OH vs. O
OH : a=1/2
Close-packed surfaces
Stepped surfaces
Abild-Pedersen, Greeley, Studt
Rossmeisl, Munter, Moses
Skulason, Bligaard, Nørskov
Phys. Rev. Lett. 99, 016105 (2007)
Scaling relations: SH vs. S
SH : a=1/2
Close-packed surfaces
Stepped surfaces
Abild-Pedersen, Greeley, Studt
Rossmeisl, Munter, Moses
Skulason, Bligaard, Nørskov
Phys. Rev. Lett. 99, 016105 (2007)
Predicting heats of reaction from scaling relations
Requires :
1. Atomic C, O, and
S adsorption
energies on all dmetals
2. Reaction
intermediates on
one metal (Pt)
Abild-Pedersen, Greeley, Studt
Rossmeisl, Munter, Moses
Skulason, Bligaard, Nørskov
Phys. Rev. Lett. 99, 016105 (2007)
Scaling: Methanation
Jones, Bligaard, Abild-Pedersen, Nørskov, J. Phys.: Cond. Mat. 20, 064239 (2008)
Scaling: Steam reforming
Scaling: Ammonia synthesis
Scaling: Water-gas-shift
Scaling: Methanol synthesis
Brønsted-Evans-Polanyi (BEP) relations:
Æ e.g. CO dissociation
Ediss (eV)
Andersson, Bligaard, Kustov, Larsen, Greeley, Johannessen, Christensen, Nørskov, J. Catal. 239, 501 (2006)
Volcano: The methanation reaction:
CO + 3H2 Æ CH4 + H2O
CO diss.
slow
C, O
poisoning
Ediss (eV)
Sabatier, Ber. Deutsch. Chem. Gesell. 44, 1984 (1911)
Bligaard, Nørskov, Dahl, Matthiesen, Christensen, Sehested, J. Catal. 224, 206 (2004)
Bligaard, Nørskov in “Chemical Bonding at Surfaces”, Elsevier (2008)
Universality of BEPs
BEPs exist for a number of
small molecules
– and happen to be identical
Æ
Omnipresence of volcanoes
– and very similar kinetics
Nørskov, Bligaard,
Logadottir, Bahn, Hansen,
Bollinger, Bengaard, Hammer,
Sljivancanin, Mavrikakis, Xu,
Dahl, Jacobsen
J. Catal. 209, 275 (2002)
Generalized kinetic models
“BEPs” + “Contracted energy diagrams”
Æ
“Generalized Kinetic Models”
Models simplified to the level where they only contain
the absolutely essential reaction steps
Bligaard, Nørskov, Dahl, Matthiesen, Christensen, Sehested,
J. Catal. 224, 206 (2004)
A generalized kinetic model: A2+2B Æ 2AB
A2 + 2* Æ 2A*
R1 = 2k1PA2Θ*2 - 2k-1ΘA2 (= r1 - r-1)
A* + B Æ AB + *
R2 = k2ΘAPB - k-2PABΘ* (= r2 - r-2)
Site conservation: 1 = ΘA + Θ*
Three equations with four unknowns (R1 , R2 , ΘA , and Θ*)
The missing equation is obtained from either:
Stationary coverage: dΘi/dt = 0: r1 + r-2 = r-1 + r2 (R1 = R2)
Rate-limitation:
E.g. reaction 1 is slow: r2 = r-2
(R2 = 0)
Stationary External Conditions
dPx/dt = 0
This reduces the differential equations to algebraic equations.
• Significantly reduces computation time.
A perfect local description of:
• Fixed bed reactors
• Fluidized bed reactors
• Trickle bed reactors
(But not applicable to Batch reactors)
Numerical problems
General micro-kinetic model:
• Singular differential equations
Stationary solution:
• Ill-conditioned algebraic equations
Therefore specialized numeric methods are required !?
Ill-conditioning of stationary state
5
Easy region
Log(TOF (1/s))
0
-4
-3
-2
-1
-5
0
1
-10
-15
r1 = r-1 , R2 << r1
-20
Eadsorption (eV)
r2 = r-2 , R1 << r2
2
The approach to equilibrium
- This simple model can be solved by Taylor-expanding
the equations in the limits where they are ill-defined.
R1 = 2k1PA2Θ*2 - 2k-1ΘA2 = 2k1PA2Θ*2(1-γ1),
γ1 = r-1/r1
R2 = k2ΘAPB - k-2PABΘ* = k2ΘAPB (1-γ2),
γ2 = r-2/r2
γ = γ1 γ22 = PAB2/(PA2PB2) . 1/Keq
This allows one to define the Kinetic Switching Parameter (KSP):
KSP = [ 3 + (2 Log(γ2) – Log(γ1))/Log(γ) ]/2
(which is 1 when step 1 is rate-determining and 2 when step 2 is)
Simplest generalized kinetics
A2+2B Æ 2AB
Ea
ΔE1
BEP + All entropy lost on surface
Dissociation is rate-limiting at optimum
Æ If the process follows the universal BEP-relations
TOF
KSP
Eads (eV)
The switching happens to the left of the maximum !
In other words: The optimal catalyst can not directly be
improved by lowering the barrier of the rate-determining step
Optimal catalysts
– dependence on the approach to equilibrium
1. A2 + 2* ↔ 2A*
2. A* + B ↔ AB + *
2
PAB
1
γ=
⋅
2
PA2 PB K eq
Very exothermic reactions take place at
small values of γ for a similar conversion
Optimal catalysts
– dependence on temperature and pressure
High temperature and low reactant pressure “moves”
the optimal catalyst towards more reactive surfaces.
Optimal catalysts
– dependence on precursor stability
1. A2 + * ↔ A2*
2. A2* ↔ 2A*
3. A* + B ↔ AB + *
1. A2 + 2* ↔ 2A*
2. B + * ↔ B*
3. A* + B* ↔ AB + 2*
Le Chatelier-like principle for optimal catalysts:
Æ coverage conservation laws
The coverage of a key reactant on the surface of the
optimal catalyst under given reaction conditions is
constant.
( in the simple case “coverage of A” = “1-BEPslope” )
The optimal catalyst is located where the coverage
switches – or where the adsorption free energy is
close to zero.
More product poisoning
Æ nobler surface required
1. A2 + 2* ↔ 2A*
2. A* + B ↔ AB + *
2
PAB
1
γ=
⋅
2
PA2 PB K eq
Very exothermic reactions take place at
small values of γ for a similar conversion
Lower temperature or high pressure
Æ Poisons surface
High temperature and low reactant pressure “moves”
the optimal catalyst towards more reactive surfaces.
Stronger precursor binding
Æ Precursor competes with key reactant
1. A2 + * ↔ A2*
2. A2* ↔ 2A*
3. A* + B ↔ AB + *
1. A2 + 2* ↔ 2A*
2. B + * ↔ B*
3. A* + B* ↔ AB + 2*
Le Chatelier-like principle for optimal catalysts:
Æ coverage conservation laws
The coverage of a key reactant on the surface of the
optimal catalyst under given reaction conditions is
constant.
( in the simple case “coverage of A” = “1-BEPslope” )
The optimal catalyst is located where the coverage
switches – or where the adsorption free energy is
close to zero
Æ ΔEads = -0.6eV at 300K or ΔEads = -1.8eV at 900K
Implications of ”Universality”
General insights into
”How to pick optimal catalysts”
Æ
Bligaard, Nørskov, Dahl, Matthiesen, Christensen, Sehested,
J. Catal. 224, 206 (2004)
Which is the best catalyst?
Ammonia synthesis :
N2+3H2 Æ 2NH3 (Ru, Fe, (Os))
Fischer Tropsch synthesis, methanation:
nCO+(2n+1)H2 Æ CnH2n+2+nH2O (Co, Ru, Rh, Ni)
NO reduction:
2NO+2H2 Æ N2+2H2O (Pt, Pd, Rh)
Oxidation:
O2+2XÆ 2XO (Pt, Pd, Ag)
……..
Understanding trends in catalytic activity
Nørskov, Bligaard,
Logadottir, Bahn,
Hansen, Bollinger,
Bengaard, Hammer,
Sljivancanin, Mavrikakis,
Xu, Dahl, Jacobsen
J.Catal. 209, 275 (2002)
Normalized TOF
Ea (eV)
Ea (eV)
-4
-3
-2
5
4
3
2
1
0
-1
Flat surface
4
3
2
1
0
-1
-2
Step sites
-1
0
1
2
3
4
CO
NO
O2
N2
1.0 Step kinetics
0.8
γ = 10-10, 10-5, 0.5
100 bar
673 K
H2:N2 = 3:1
0.6
0.4
0.2
0.0
-4
-3
-2
-1
0
1
ΔE (eV)
2
3
4
Understanding trends in catalytic activity
-4
Ea (eV)
Normalized TOF
N2+3H2 Æ 2NH3
Ea (eV)
Ammonia synthesis :
-3
-2
5
4
3
2
1
0
-1
Flat surface
4
3
2
1
0
-1
-2
Step sites
-1
0
1
2
3
4
CO
NO
O2
N2
Fe
Ru
CoMo
1.0 Step kinetics
0.8
γ = 10-10, 10-5, 0.5
100 bar
673 K
H2:N2 = 3:1
0.6
0.4
0.2
0.0
-4
-3
-2
-1
0
1
ΔE (eV)
2
3
4
Understanding trends in catalytic activity
Fischer Tropsch synthesis
and methanation:
Ea (eV)
-4
Normalized TOF
Ea (eV)
nCO+(2n+1)H2 Æ
CnH2n+2+nH2O
-3
-2
5
4
3
2
1
0
-1
Flat surface
4
3
2
1
0
-1
-2
Step sites
-1
0
1
2
3
4
CO
NO
O2
N2
Co
Ni
Ru
Fe
1.0 Step kinetics
0.8
γ = 10-10, 10-5, 0.5
100 bar
673 K
H2:N2 = 3:1
0.6
0.4
0.2
0.0
-4
-3
-2
-1
0
1
ΔE (eV)
2
3
4
Understanding trends in catalytic activity
-4
Ea (eV)
Normalized TOF
2NO+2H2 Æ N2+2H2O
Ea (eV)
NO reduction:
-3
-2
5
4
3
2
1
0
-1
Flat surface
4
3
2
1
0
-1
-2
Step sites
-1
0
1
2
3
4
CO
NO
O2
N2
PtRh
Pt
Pd
1.0 Step kinetics
0.8
γ = 10-10, 10-5, 0.5
100 bar
673 K
H2:N2 = 3:1
0.6
0.4
0.2
0.0
-4
-3
-2
-1
0
1
ΔE (eV)
2
3
4
Understanding trends in catalytic activity
-4
Ea (eV)
Normalized TOF
O2+2XÆ 2XO
Ea (eV)
Oxidation:
-3
-2
5
4
3
2
1
0
-1
Flat surface
4
3
2
1
0
-1
-2
Step sites
-1
0
1
2
3
4
CO
NO
O2
N2
Pt
Ag
1.0 Step kinetics
0.8
γ = 10-10, 10-5, 0.5
100 bar
673 K
H2:N2 = 3:1
0.6
0.4
0.2
0.0
-4
-3
-2
-1
0
1
ΔE (eV)
2
3
4