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Microkinetic modeling of surface reactions
J.A. Dumesic et al. „The Microkinetics of Heterogeneous Catalysis“, ACS, Washington 1993.
One final thing I must now say
Of the light of knowledge a final ray
Reaction kinetics is in a mess
In spite of Eyring and Arrhenius
Alas, was it ever thus so
The more we learn, the less we know
John B. Butt
!
Is it true?
Reaction kinetics is in a mess
History of catalytic kinetics
1910’s 1940’s 1990’s
Michaelis-Menten
Langmuir-Hinschelwood
Hougen-Watson
Temkin- Snagovskii-Dumesic
ki is extracted from fitting particular kinetic equations
ki is either calculated or measured
7
Langmuir–Hinshelwood–Hougen–Watson approach
8
RDS
Chemical Engineering Physical Chemistry
LHHW approach
Reactor models
Theory of elementary acts (on surfaces)
Kinetics on real surfaces
Theory of complex reactions
Mass transfer
Langmuir Hinshelwood
Hougen
Eyring Polanyi
Horiuti Temkin
Frank-Kamenetskii
Mathematics
Optimization
Statistical analysis of parameters
Yu. Snagovsky, G. Ostrovsky
Modelling of kinetics of heterogeneous
catalytic processes, 1976
Ostrovsky Froment
11
: stoichiometric number
: stoichiometric coefficient
*: active center
N(1)
N(2)
1. O2 + 2* 2O* 1 1
2. H2 + 2* 2H* 2 0
3. H* + O* OH* + * 2 0
4. OH* + H* H2O + 2* 2 0
5. H2 + O* H2O + * 0 2
2H2 + O2 2H2O
N(i): routes
Alternative: theory of complex reactions, Horiuti-Temkin
3 CO + 2 H2O = 2 CO2 + CH3OH
How to derive kinetic equation?
Can it be done by computer?
Should explicit vs implicit rate expressions be used?
How to incorporate surface nonuniformity?
What about lateral interactions?
What is physical meaning of rate constants?
Can they be calculated from theory?
How to do numerical data fitting?
How to do statistical analysis?
1 1
1
0
1f
a p
a pln
Temkin isotherm
Edge Corner
Face
edgesG facesG
Difference in activities of different surface atoms
D.Yu. Murzin, Journal of Catalysis, 2010, 276, 85
clusterdekdk
1
11 )(
RT
GG terracesadsedgesads )( ,,
Surf
ace
ato
ms
(%)
Dispersion
R. van Hardeveld, F. Hartog, Surface Science 15 (1969) 189.
Surface Structure
Surface Sites
Planar atoms
Edge atoms
Corner atoms
Adatoms
Kinks
Defect
terrace step
What about gas phase non-catalytic reactions?
Transition state theory
A + B ↔ AB‡ → C + D
when C and D emerge, the reaction has to go through the lowest energy barrier (represented by the transition state)
K‡ k
For molecules ei= ei + vi + ri + ti
electronic vibrational rotational translational
q=qe qv qr qt
A molecule of n atoms has 3 n degrees of freedom
Translation – 3
Vibration – nonlinear : 3n-6
linear : 3n-5
n=1 : 3 translation
n=2 : 3 translation, 1 vibration, 2 –rotation
n=3 : 3 translation
linear : 4 vibration, 2–rotation
nonlinear : 3 vibration, 3–rotation
Degrees of freedom
AC : 3n-1 (instead of one vibrational - one along reaction coordinate)
Translation mass
Rotation moment of inertia, thus structure of a molecule should be known
For activated complexes -? Vibration usually harmonic oscillator
- IR spectra
Electronic usually qe 1
Symmetrical
stretching
Antisymmetrical
stretching Scissoring
Rocking
Wagging
Twisting
Vibrations of atoms in the -CH2 group
Vibrational partition functions are calculated quantum
mechanically within the framework of the harmonic
approximation. The harmonic oscillator partition function
is given by:
where is the vibrational frequency in for mode
i . The product is over all vibrational modes.
Partition functions
TS Theory
Molecular partition function for a gas-phase species is
a product of contributions from translational,
rotational and vibrational degrees of freedom
vibirotitransii qqqQ ,,,
3
2/3
,
)2(
h
Tkmq bi
transi
)(8
2
2
, moleculelinearh
TkIq
r
biroti
j
b
ij
vibi
Tk
hq
exp1
1,
vibrationof
normalofsfrequencie...ij
numbersymmetryrotational...r
inertiaofmoment...iI
modes
Where do we need (micro)kinetic modelling in heterogeneous catalysis?
HC-SCR
Elegant solution attractive for car
manufacturers
Passive control = unburned hydrocarbons from the
engine are used for reduction of NOx over a catalyst
HC-SCR
Engine
Air
Fuel
DPF SCR
HC-SCR
Active control = unburned hydrocarbons + added
fuel (diesel) is used for NOx reduction
HC-SCR
Engine
Air
Fuel
DPF SCR
Fuel
Eränen, Klingstedt, Arve, Lindfors, Murzin, J. Cat. 227 (2004) 328-343
NO (g) + O 2 (g) + C x H y (g)
NO x (ads) C x H y O z (ads)
R - NO (g or ads)
R - CN (g or ads)
R - NCO (g or ads)
R - NO 2 (g or ads)
R - NH 2 (g or ads)
NH 3 (g or ads) Activated
NO x (g or ads)
N 2 (g)
(1) (2)
(3)
(6)
(5)
(7)
(8)
(4)
a)
a)
a)
Mechanism
5 bricks
Engine: 6.4 ltr common rail turbo diesel
off road
Manufacturer: Sisu Diesel Oy
Fuel: < 10 ppm sulphur, 25-30 % aromatics
Full-scale vehicle tests with off-road engine
2 on-line Horiba analysers
for NOx and HC.
Smoke analyser
Full-scale vehicle tests with off-road engine
Fully automated engine control system.
Full-scale vehicle tests with off-road engine
4-layers of Ag/alumina vs. single layer. Total mass of catalyst = 0.4 g and HC1/NO = 6 (octane).
-60
-40
-20
0
20
40
60
80
100
150 200 250 300 350 400 450 500 550 600
Temperature (°C)
Con
ver
sion
(%
)
NOx to N2 conversion
CO conversion
Q uartz w oolA g/alum ina
G as in
1.5 cm 0.175 cm
Gas in
Ag/alumina
0.7 cm
Segmentation of Ag/alumina
heterogeneous-homogeneous reaction network
Ag/Al2O3 Cu-ZSM-5
empty space
NO
C8H18
CO
CO2
H2O
O2 Amines and oxygenates
70 % N2
at 200 °C
Arve, Klingstedt, Eränen, Lindfors, Murzin, Cat. Lett. 105 (2005) 133
Cascade concept
world patent application; inventors ÅA/Volvo
Full-scale Ag/alumina cascade
NOx [g/km]
0
0.1
0.2
0.3
0.4
0.5
0.6
Euro
3
cold
warm
warm
HC
NOx [g/km]
0
0.1
0.2
0.3
0.4
0.5
0.6
Euro
3
cold
warm
warm
HC
Euro
4
From conceptual design to full scale vehicle tests
Not enough!
Klingstedt et al. Top. Cat. 30/31 (2004) 27-30
0
10
20
30
40
50
60
70
80
90
100
150 200 250 300 350 400 450 500 550 600
Temperature (°C)
NO
x t
o N
2 c
on
ver
sion
(%
)
Octane + H2
H2
Octane
Hydrogen as co-reductant?
Low T activity should be improved
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
150 250 350 450 550
Octane concentration (ppm)
NO
x t
o N
2 c
on
versi
on
(%
)
0.25 vol.% H2
0.5 vol.% H2
1 vol.% H2
H2
In the presence of H2, NO reduction is predominantly dependent
on H2 concentration and also on C8H18 concentration!
Kinetics
Arve, Backman, Klingstedt, Eränen, Murzin, Applied Catalysis A. Gen , 2006, 303, 96-102
Reactions 1-4 are
accelerated by H2
NO (g) + O 2 (g) + C x H y (g)
NO x (ads) C x H y O z (ads)
R - NO (g or ads)
R - CN (g or ads)
R - NCO (g or ads)
R - NO 2 (g or ads)
R - NH 2 (g or ads)
NH 3 (g or ads) Activated
NO x (g or ads)
N 2 (g)
(1) (2)
(3)
(6)
(5)
(7)
(8)
(4)
a)
a)
a)
Effect of hydrogen: mechanism
0
10
20
30
40
50
60
70
80
90
100
150 200 250 300 350 400 450 500 550 600
Temperature (°C)
NO
x t
o N
2 c
on
ver
sion
(%
)
Quartz woolAg/alumina
Gas in
1.5 cm 0.175 cm
Gas in
Ag/alumina
0.7 cm
Effect of hydrogen: gas phase reactions?
Kinetic modelling
Backman, Arve, Klingstedt, Murzin, Applied Catalysis A. General, 2006, 304, 86-92
0.0000
0.0010
0.0020
0.0030
0.0040
0.0050
0.0000 0.0010 0.0020 0.0030 0.0040 0.0050
experimental rate (10-4
mol/g s)
esti
mate
d r
ate
(10-4
mo
l/g
s)
Kinetic modelling
Backman, Arve, Klingstedt, Murzin, Applied Catalysis A. General, 2006, 304, 86-92
History of catalytic kinetics
1910’s 1940’s 1990’s
Michaelis-Menten
Langmuir-Hinschelwood
Hougen-Watson
Temkin- Snagovsky-Dumesic
ki is extracted from fitting particular kinetic equations
ki is either calculated or measured
What is microkinetics about?
Definition of microkinetic analysis examination of catalytic reactions in terms of elementary chemical reactions that occur on the catalytic surface and their relation with each other and with the surface during a catalytic cycle
J. A. Dumesic et al., Ind. Eng. Chem. Res. 1987, 26 (1399)
It means that the subject of investigation is not the overall reaction but each particular elementary reaction.
Surface reaction
Metal
1. Adsorption 2. (Diffusion on the surface) 3. Surface reaction 4. Desorption
Elementary reactions
elementary reaction is such a reaction in which one or more of the species react directly to form products
molecularity is the number of colliding molecules in a single reaction step
different types
Dissociation AB = A + B
Combination A + B = AB
Disproportionation AB + C = A + BC
Kinetic variables in MK
Preexponential factor Collision theory
Transition State theory
Activation energy Unity Bond Index – Quadratic Exponential
Potential (UBI-QEP)
DFT
Collision theory
is used to determine rate constants for adsorption processes in terms of number of gas-phase molecules colliding with a surface per unit are per unit time
demanded inputs
sticking coefficient (as a function of temperature)
pressure
- Bimolecular rate constant
- Preexponential factor
- Example: with Ps 1 and estimate of AB
upper limit for preexponential factor
Collision Theory
Tk
ETkPk
b
a
AB
bABsAB exp
82
AB
bABsAB
TkPA
82
CT- Bimolecular surface reaction
Modification to represent bimolecular reactions between mobile species on surfaces
BA
b
a
AB
bABsAB
Tk
ETkPr
exp
22
ionsconcentratsurface
velocityrelativeaverage ldimensionatwoTk
BA
AB
b
...
...2
,
TS – Adsorption processes
A(g) A# A*
Rate of reaction for an activated complex of complete surface mobility
A
bgA
AbA n
Tk
E
q
q
h
Tkr
#0
exp#
TS Theory
Molecular partition function for a gas-phase species is
a product of contributions from translational,
rotational and vibrational degrees of freedom
vibirotitransii qqqQ ,,,
3
2/3
,
)2(
h
Tkmq bi
transi
)(8
2
2
, moleculelinearh
TkIq
r
biroti
j
b
ij
vibi
Tk
hq
exp1
1,
vibrationof
normalofsfrequencie...ij
numbersymmetryrotational...r
inertiaofmoment...iI
modes
TS Theory
Order-of-magnitude estimates
kBT/h = 1013 s-1
qi,trans = 5*108 cm-1 (per degree of translational freedom)
qi,rot = 10 (per degree of rotational freedom)
qi,vib = 1 (per degree of vibrational freedom)
BA
bBA
ABbAB nn
Tk
E
Q
h
Tkr
#0
exp#
TS – Desorption processes
A* A# A(g)
Rate of desorption
surfacetheonAspecies
ofionconcentratA ...
A
bA
Abd
Tk
E
q
q
h
Tkr
#0
exp*
#
1*
#
A
A
q
q
A
b
bd
Tk
E
h
Tkr
#0
exp sh
Tkb /1013
TS – Preexponential Factors Estimates
TS – Preexponential Factors Estimates
Kinetic variables in MK
Preexponential factor Collision theory
Transition State theory
Activation energy Unity Bond Index – Quadratic Exponential
Potential (UBI-QEP)
DFT
Estimates for Activation Energies
Rate constant = f (A ; EA)
EA estimation difficult
1) Empirical correlations for EA from heats of reaction
Bond-order conservation (BOC) by Shustorovich
A2 A* + A*
nMetalAAA QDE
2
32 atomsmetalnwith
siteonAofstrengthadsorptionE
bondAAofstrengthD
adsorptiondissforenergyactE
nMetalA
A
A
*...
...
.....
2
ABads Aads+Bads
)(2
1int,
BA
BAABads
QQHE
Enthalpy of dissociation
Atom Cu Ag Au Ni Pd Pt
H 33.6 31.2 27.6 37.8 37.2 36.6
O 61.8 48.0 45.0 69.0 52.3 51.0
N 69.0 60.0 58.2 81.0 78.0 69.6
C 72.0 66.2 65.0 102.6 96.0 90.0
Recommended values of Q0A (kcal/mol) for atoms adsorbed on single fcc metal surfaces
UBI-QEP
allows us to enumerate
adsorption heats (atomic, di-, polyatomic molecules)
activation energy of the reaction
more phenomenological than empirical approach
usually good accuracy (≈ 1-3 kcal/mol)
there is some information which one has to know
geometry of adsorption
total bond energy in gas phase of each adsorbed compound
the number of bonds between catalyst and admolecule
E. Shustorovich and A. V. Zeigarnik, Surf. Sci. 2003, 527, 137
Estimates for Activation Energies
2) Conversion of elementary steps into families of reactions
- especially for large mechanisms where limited experimental data are available
- example: reaction of a paraffin over a metal surface including hydrogenation and dehydrogenation steps
BrØnsted-Evans-Polanyi correlation
.)1(
.
0
0
endothHEE
exothHEE
iiA
iiA
stepelementaryi
formationofheatH
family the for
constantsPolanyiEvansE
i
...
...
...,0
• v
J. Catal. 209 (2002) 275.
This linear BEP correlation in a
number of cases leads directly to
volcano curves where the
fundamental parameter is the
dissociative chemisorption energy of
the key reactant.
BrØnsted-Evans-Polanyi
Logatottir, Rod, Nørskov, Hammer, Dahl, Jacobsen, J. Catal. 197, 229 (2001)
Brønsted-Evans-Polanyi relation
88
Rate is determined by adsorption of nitrogen
89
Theoretical volcano for the production of methane from syngas, CO, and H2.
Nørskov J K et al. PNAS 2011;108:937-943 ©2011 by National Academy of Sciences
More complex cases
A bit of DFT
Schrödinger Equation
H is the quantum mechanical Hamiltonian for the system (an operator containing derivatives)
E is the energy of the system
is the wavefunction (contains everything we are allowed to know about the system)
||2 is the probability distribution of the particles
Schrodinger Equation in 1-D:
EH
2 2
2( ) ( ) ( )
2
dV x x E x
m dx
Atomic Orbitals: How do electrons move
around the nucleus? Density of shading represents the probability of finding an electron at any point. The graph shows how probability varies with distance.
Since electrons are particles that have wavelike properties, we cannot expect them to behave like point-like objects moving along precise trajectories. Erwin Schrödinger: Replace the precise trajectory of particles by a wavefunction (ψ), a mathematical function that varies with position Max Born: physical interpretation of wavefunctions. Probability of finding a particle in a region is proportional to ψ2.
Wavefunctions: ψ
s Orbitals
Boundary surface encloses surface with a > 90% probability of finding electron
Wavefunctions of s orbitals of higher energy have more complicated radial variation with nodes.
98
Hamiltonian for a Molecule
(Terms from left to right)
kinetic energy of the electrons
kinetic energy of the nuclei
electrostatic interaction between the electrons and the nuclei
electrostatic interaction between the electrons
electrostatic interaction between the nuclei
nuclei
BA AB
BAelectrons
ji ij
nuclei
A iA
Aelectrons
i
A
nuclei
A A
i
electrons
i e r
ZZe
r
e
r
Ze
mm
2222
22
2
22ˆ H
99
Solving the Schrödinger Equation
analytic solutions can be obtained only for very simple systems, like atoms with one electron.
particle in a box, harmonic oscillator, hydrogen atom can be solved exactly
need to make approximations so that molecules can be treated
approximations are a trade off between ease of computation and accuracy of the result
Cheaper than ab initio electronic structure methods, but not as accurate
101
102
The energy profile for the reaction
Microscopic level: DFT
A. Prestianni, F. Ferrante, O. A. Simakova, D. Duca,
D.Yu. Murzin, Chemistry. A European Journal , 2013, 19, 4577
APR of 1,2 propanediol
R. Cortese, L. Godina, D.Yu. Murzin, D. Duca
Is QC simple?
Complex molecules- conformation?
Size of cluster for modelling?
Cluster size dependence of the rates?
Solvent?
Deactivation
Surface Reaction
Schemes and Kinetic
Models
Adsorption
And Microcalorimetry
Heats, Coverages
Isotopic Studies
SSITKA and kinetics of
elementary steps
Detailed Kinetics
Activity, Selectivity,
Stability
XPS, XRD, Mössbauer
Alloy formation, oxidation
states, surface composition
IR
Surface species
Microscopy
Surface morphology
and composition
DFT
Electronic structure
of stable species,
intermediates and
transition states
Microkinetic Model Development
NH3 synthesis
Schlögl, FHI
MK model - example
3 CO + 2 H2O = 2 CO2 + CH3OH
rCO* = 3r1-r5-2r11
r* = -3r1-r2+2r3+r4+r5+r6
+r7+r8-2r9-2r10+2r11 rH2O* = 2r2-2r9
rCO2* = 2r3-2r11
rCH3OH* = -r4+r8
rH* = -r5-r6-r7-r8+2r9+2r10
rHCO* = r5-r6
rH2CO* = r6-r7
rH3CO* = r7-r8
rOH* = 2r9-2r10
rO* = 2r10-2r11
CO H2 CO2 H2O
a) T = 623K ptot = 2,1 MPa H2/CO = 3 b) T = 573K ptot = 1,1 MPa H2/CO = 3 c) T = 553K ptot = 2,1 MPa H2/CO = 3 d) T = 523K ptot = 2,1 MPa H2/CO = 3
Examples
G. Lozano-Blanco et al., Ind. Eng. Chem. Res. 2008, 47 (5879)
What to do if not all parameters are well identified or fitting is not good enough?
Solution to Dilemma?
Use MKM to specify all variables except few (one)
Use nonlinear regression to determine the unspecified parameter
Let us finish from where we started: HC SCR
Parameter tuning
Limitations for HC SCR: theory
Limitations for HC SCR:theory
Limitations for HC SCR: chemistry
Limitations for HC SCR: mass transfer
Conclusions
microkinetics is valuable tool
theoretical background is still rather undetermined
there is microkinetics and microkinetis
it has to be combined with experiments
Literature
R.D. Cortright, J.A. Dumesic
„Kinetics of Heterogeneous Catalytic Reactions: Analysis of Reaction Schemes“ in: Adv. Catal. 46 (2001) 161-264.
J.A. Dumesic, D.F. Rudd, L.M. Aparicio, J.E. Rekoske
„The Microkinetics of Heterogeneous Catalysis“
ACS, Washington 1993.
P. Stoltze
„Microkinetic simulation of catalytic reactions“
in: Progr. Surf. Sci. 65 (2000) 65-150.
E. Shustorovich et al., in: Surf. Sci. Rep. 31 (1998) 1
