Ab initio atomistic thermodynamics of
oxygen adsorption in graphene vacancies
Felix Hanke
Aug 26, 2009
Ab initio atomistic thermodynamics of
oxygen adsorption in graphene vacancies
Felix Hanke
Aug 26, 2009
Oxidative Dehydrogrenation of Ethylbenzene
2
+
2
+2
Most ethylbenzene
dehydrogenation catalysts are
based on iron(III) oxide,
promoted by several percent
potassium oxide or
potassium carbonate.
http://en.wikipedia.org/wiki/Styrene
Image: D. Su, AC-Dept. FHI
catalyst
all molecular images done with VMD, http://www.ks.uiuc.edu/Research/vmd
Oxidative Dehydrogrenation of Ethylbenzene
2
+
2
+2
Most ethylbenzene
dehydrogenation catalysts are
based on iron(III) oxide,
promoted by several percent
potassium oxide or
potassium carbonate???
Image: D. Su, AC-Dept. FHI
catalyst???
all molecular images done with VMD, http://www.ks.uiuc.edu/Research/vmd
Oxidative Dehydrogrenation of Ethylbenzene
2
+
100
80
60
40
20
0
+2
Carbon black
Graphite
CNT
80
Styrene yield (%)
Ethylbenzene conversion (%)
2
0
200
400
Time on stream (min)
600
60
40
20
0
0
200
400
Time on stream (min)
600
Experiments: Su et al. Catalysis Today 102 110 (2005) – FHI AC Department
Oxidative Dehydrogrenation of Ethylbenzene
2
+
100
80
60
40
20
0
+2
Carbon black
Graphite
CNT
80
Styrene yield (%)
Ethylbenzene conversion (%)
2
0
200
400
Time on stream (min)
600
60
40
20
0
0
200
400
Time on stream (min)
600
Where is the oxygen & what does it do???
Experiments: Su et al. Catalysis Today 102 110 (2005) – FHI AC Department
Density Functional Theory
Exchange Correlation functional: PBE
Geometry convergence: Fmax<0.01 eV/Å
all electron
numeric atomic orbitals
pseudopotentials
plane waves
FHI-aims*
Castep‡
FHI-aims Tier 2 basis set
Ultrasoft pseudopotentials
Ecut = 550 eV
molecules
* V. Blum et al. Comp. Phys. Comm. (2009)
periodic supercells
‡ Clark et al. Z. Krist. 220 567 (2005)
Lines of Oxygen
Li et al. PRL 96 176101 (2006)
ΔE = 1.2 eV
Lines of Oxygen
Li et al. PRL 96 176101 (2006)
ΔE = 1.2 eV
comment by Ajayan &Yacobson, Nature 441 818 (2006)
O=O
Oxidation Path
O
O
cycloaddition
O
O
Next-Nearest
Neighbour (NNN)
O
O
O
4th Neighbour (4N)
O
2O epoxy
O=O
Oxidation Path
O
O
cycloaddition
O
O
Next-Nearest
Neighbour (NNN)
O
O
O
4th Neighbour (4N)
O
2O epoxy
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
C20H12
C54H18
C96H24
Graphene
Finite size effect
2 Oepoxy
NNN
4N
2
Eads, O (eV)
2.0 cyclo
1.0
0.0
NNN
C20H12
C54H18
C96H24
graphene, 6x6
Mechanical
stabilization
4N
Nudged Elastic Band
images
springs for spatial
separation
own implementation for FHI-aims and CASTEP:
regular + climbing image NEB
Henkelman et al., J Chem Phys 113 9901 & 113 9978 (2000)
Adsorption barriers for O2
3.0
Energy (eV)
2.5
2.0
0.89eV
1.5
1.23eV
1.0
0.5
2.08eV
O2 gas
spin singlet
0.0
0
2
4
6
Path length (Å)
8
Hanke, Carlsson, Scheffler
to be published
Adsorption barriers for O2
3.0
Energy (eV)
2.5
2.0
0.89eV
underestimate!
1.5
1.23eV
1.0
0.5
2.08eV
O2 gas
spin singlet
0.0
0
2
4
6
Path length (Å)
8
Hanke, Carlsson, Scheffler
to be published
Adsorption barriers for O2
3.0
Energy (eV)
2.5
Improbable!
2.0
underestimate!
Alternatives:
Defects
Edges
1.5
1.0
0.5
0.89eV
1.23eV
2.08eV
O2 gas
spin singlet
0.0
0
2
4
6
Path length (Å)
8
Hanke, Carlsson, Scheffler
to be published
Adsorption barriers for O2
3.0
Energy (eV)
2.5
Improbable!
2.0
underestimate!
Alternatives:
Defects
Edges
1.5
1.0
0.5
0.89eV
1.23eV
2.08eV
O2 gas
spin singlet
0.0
0
2
4
6
Path length (Å)
8
Hanke, Carlsson, Scheffler
to be published
Our Approach
pure defects
Carlsson and Scheffler,
Phys. Rev. Lett 96, 046806 (2006)
CO/CO2
desorption dynamics
oxidized defects: which
ones actually exist?
How Vacancy Defects oxidize ...
= active site for initial oxidation
O2 Adsorption on Pentagons
ΔE (eV /O2)
2Otop
C-O-C+Obr
2Obr
2C=O
2C-O-C
2Otop
2C=O
C-O-C+Obr
2 C-O-C
Further oxidation of vacancies:
Coadsorption of O2
ΔE (eV/O2)
2Otop
O2 adsorption
O diffusion
C=O+Obr
C-O-C=O
2Otop
C=O+Obr
C-O-C=O (Lactone)
O2 Adsorption energy is less than elsehere on basal plane ...
YAO2 (Yet another O2)?
ΔE (eV/O2)
2Otop
2Otop
O2 adsorption
CO2
C=O+Obr
O diffusion
CO2 desorption
C-O-C=O
O=C-O-C=O
CO2
2Otop
C-O-C=O (Lactone)
V4:30
Lactone
-CO2
O=C-O-C=O (Anhydride)
+O2 = Anhydride
ab initio Atomistic Thermodynamics
Gsolid ≈ EDFT (T = 0) + Fvib (T ) − kB T ln gconf
Ggas (T, p) = EDFT (T = 0) + ∆µ(T, p0 ) + kB T ln(p/p0 )
Fvib (eV)
∆Gform (T, p) = ∆Gsolid (T, p) + ∆Ggas (T, p)
0
-0.5
-10
O=C-O-C=O
-O-(C=O)-OC=O
epoxy
C-O-C
C-O-(C=O)-C
500
1000
Temperature (K)
1500
4 Carbon vacancy: lowest ΔG wins
Gsolid (T ) = EDFT + Fvib (T ) + Fconf (T )
Ggas (T, pgas ) = EDFT + µgas (T, pgas )
∆Gform (T, p) = ∆Gsolid (T, p) + ∆Ggas (T, p)
ΔGform (eV)
10
5
0
-5
-15
10
3O
4O
10
-10
7O
-5
T = 700 K
11O
10
10
O2 pressure (atm)
0
10
5
Constrained Ab initio Atomistic
Thermodynamics
V4 phase
diagram
Carlsson, Hanke, Linic
and Scheffler,
PRL 102 166104 (2009)
V4 blank
V4:3O
V4:4O
V4:7O
V4:11O
Constrained Ab initio Atomistic
Thermodynamics
V4 phase
diagram
Carlsson, Hanke, Linic
and Scheffler,
PRL 102 166104 (2009)
V4 blank
V4:3O
V4:4O
V4:7O
V4:11O
Oxygen on the basal plane: kinetic
information
HOPG pit growth
Temperature-programmed
desorption
CO
ΔE =
2.8-3.6 eV
ΔEgrowth ≈1.75-1. 8 eV
Stevens et al J Phys Chem B 102, 10799 (1998)
CO2
ΔE =
1.2-2.6 eV
Marchon et al., Carbon 26, 507 (1988).
Dynamics: Introduction
STM of sputtered HOPG
oxidized at 530 C for 20 min
Temperature-Programmed
desorption: 1st principle peak
assignment
CO
CO2
Hoevel et al., J. Appl. Phys. 81, 154 (1997).
Marchon et al., Carbon 26, 507 (1988).
Reaction Rates for TPD: strategy
image: W Ranke, FHI
Have: idea about the surface structure
Want: verifiable information for TPD interpretation
kB T
Desorption rates k(T ) =
h
vib
ZTS −∆E/kB T
e
vib
ZGS
Reaction Rates for TPD: strategy
image: W Ranke, FHI
Have: idea about the surface structure
Want: verifiable information for TPD interpretation
kB T
Desorption rates k(T ) =
h
vib
ZTS −∆E/kB T
e
vib
ZGS
Lactone group CO/CO2 desorption
2.05Å
1.52Å
∆E = 2.54eV
CO2
2
∆E = 2.93eV
CO
1
2
00
1
1Å
Å
8
.1
1.8
Energy (eV)
3
2
3
Path length (Å)
4
Temperature-programmed desorption
Desorption Rate (1/s)
Desorption rate*:
Rate equations for all
possible processes
(first order desorption)
1
10
10
-10
10
10
-5
-15
-20
CO2
CO
400
600
Temperature (K)
~ 1500-2000 DFT
single points per line
*
800
dPLact
= −kLact→CO2 PLact
dt
−kLact→CO PLact
T (t) = αt → Temperature
dependence
3×10
CO2
3×10
2×10
1×10
-2
-2
600
CO2
-2
2×10
1×10
-5
CO
-5
0
Desorption rate dP/dT
Desorption rate dP/dT
-2 spectrum
Lactone TPD
2×10
-2
700
1×10
2×10
2×10
1×10
5×10
-5
CO
-5
-2
α = 10 K/s
α = 0.1 K/s
α = 1 K/s
-5
-6
0
600
800
600
700
Temperature (K
700
800
Temperature (K)
High CO2 signal; CO signal is ~10-3 smaller
Complex desintegration: Anhydrides
two pathways with different intermediate states
2
O
-CO
-C
1.
12
eV
1.60
eV
1.43 eV
-CO
0.29 eV
-CO2
600
Anhydride desorption
spectrum
-2
3×10
700
300
4×10
2×10
-2
-2
0
-2
3×10
-2
2×10
-2
1×10
0
CO
Desorption rate dP/dT
Desorption rate [arb units]
CO2
-2
400
2×10
1×10
-2
-5
2×10
CO
-5
2×10
-2
α = 10 K/s
α = 0.1 K/s
α = 1 K/s
-5
1×10
5×10
300
500
CO2
-6
4000
Temperature (K)
500
600
700
Temperature (K
Desorption rate (arb units)
TPD spectra, α =
300
600
1
900
0.04
0.8
0.02
0.6
0
0.4
0.02
0.01
0 300
-1
1Ks
1200
CO2
carbonate
anhydride
lactone
carbonyl
CO
0.2
0
200
300
900
1200
600
Temperature (K)
400
Pressure gap: STM vs TPD
Desorption rate (arb units)
HOPG pit growth
300
1
600
0.04
0.8
0.02
0.6
0
0.4
0.02
900
1200
CO2
carbonate
anhydride
lactone
carbonyl
CO
0.2
0.01
0 300
0
200
300
400
900
1200
600
Temperature (K)
PTPD ! PSTM
500
600
∆Egrowth ≈ 1.75 − 1.8 eV
Stevens et al J Phys Chem B 102, 10799 (1998)
Desorption rate (arb units)
Summary
Phase diagram of
functional groups
300
1
600
0.04
0.8
0.02
0.6
0
0.4
0.02
900
1200
CO2
carbonate
anhydride
lactone
carbonyl
CO
0.2
0.01
0 300
0
200
300
400
900
1200
600
Temperature (K)
ab initio prediction of
desorption spectra
Thanks!!!
Matthias
Scheffler
Johan
Carlsson
Dirk Rosenthal
Inorganic
Chemistry
Mats Persson
U Liverpool
FHI theory as whole
Desorption rate (arb units)
Summary
Phase diagram of
functional groups
300
1
600
0.04
0.8
0.02
0.6
0
0.4
0.02
900
1200
CO2
carbonate
anhydride
lactone
carbonyl
CO
0.2
0.01
0 300
0
200
300
400
900
1200
600
Temperature (K)
ab initio prediction of
desorption spectra