Reaction Kinetics Workshop, Part I Outline

Transcription

Catalysis Center for Energy Innovation
Reaction Kinetics Workshop, Part I
June 12, 2016
University of Delaware
Department of Chemical and Biomolecular Engineering Center for Catalytic Science and Technology (CCST)
Catalysis Center for Energy Innovation (CCEI), an Energy Frontier Research Center
CCEI is an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Sciences
Outline
Types of catalytic kinetic models and microkinetic modeling
Overview of parameter estimation methods and scales
Accuracy
Lateral interactions
Semi‐empirical methods
Thermodynamic consistency
MKM uses
Reactor design, analysis, catalyst discovery
Kinetic Monte Carlo
1
Outline
Accuracy
MKM uses
Kinetic Monte Carlo
Surface Reaction Rate Calculation Paradigm
• Hierarchy of calculation of surface reaction rates
Empirical ratelaw; typically
fitted to
experimental data
LangmuirHinshelwood ratelaw; developed
using rate
determining step
(RDS) and MF
theory
Microkinetic
analysis;
No assumptions
on RDS (Dumesic,
1993)
Complexity/Reliability/Accuracy
2
Global reaction rate models
Reaction A+B  Products
Typical power‐low expression
 E / RT
a
b
r=k eff C A C B ; k eff =A eff e
eff
The parameters have no physical significance
Exponents unrelated to stoichiometry
Apparent activation energies can be negative
Prediction is reliable within the given experimental space
Can describe overall rate and heat effects
Simple interpolation models
Not good for process optimization
Can typically describe only one set of data
An example of scatter in literature rate expressions for CH4
catalytic combustion on Pt
Investigator
Yao (Ind. Eng. Chem. Prod. Res. Dev., 1980)
Lam & Trimm (Chem. Eng. Sci., 1980)
Ea(kcal/mol)
aCH4
bO2
21
1.0
-0.6
1.0/0.75
18/40
1.0
Aube & Sapoundijev (CCE, 2000)
13
1.0
Firth & Holland (Trans. Faraday Soc., 1969)
48
1.0
Niwa et al. (App. Cat, 1983)
29
0.9
0.0
Aryafar & Zaera (Cat. Lett, 1997)
32
1.1
-0.1
Song et al. (Combust. Flame, 1991)
33
1.0
0.5
Literature rate expressions (mostly under ‘fuel‐rich’ conditions) indicate scatter in activation energies and rxn orders
Is the scatter a result of (1) different operating conditions and surface area, (2) catalyst preparation, (3) fitting procedure/inadequacy of power‐law kinetics?
3
Summary of LH rate expressions
LH expressions are based on a priori assumptions and intuition They are usually fitted using a limited number of data
Multiple rate expressions can describe the same data
Multiple parameters even for the same rate expression may exist
Even if data is well‐fitted, parameters may be physically unreasonable
LH expressions, even if correct, are limited to one regime and cannot describe changes in RDS, MARI, etc. with operating conditions
LH Rates on Rh
CH4 total oxidation (combustion)
CH4 + 2O2= CO2 + 2H2O
Steam reforming of CH4
CO2-reforming of CH4
RWGS
= effectiveness factor
4
Comparison of model to data: Conversion
Process is away from equilibrium
Model fits data fairly well
Reactions in series is proposed
Combustion of syngas is important dashed lines=model w/o
consecutive combustion of CO
and H2;
solid lines=model with
consecutive CO and H2
combustion
Are the parameters/model reasonable?
Estimated parameters
Hads
[kcal/mol]
13.9
39.5
6.2
Models may fit but most
often than not include
unrealistic parameters
5
Microkinetic Modeling
An example
• All relevant elementary reactions
– Written by hand or computer generated1
• No simplifying assumptions
• Rate determining step (RDS), partial equilibrium (PE), quasi‐steady state (QSS), and most abundant reaction intermediate (MARI) are all computed
• Reactor + Catalyst model needed
– Use computer software, such as surface CHEMKIN3, Cantera2, or Matlab
H 2( g )  12 O2( g )  H 2O( g )
Elementary Re actions
H 2( g )  2*  2 H *
O2( g )  2*  2O *
H * O*  HO *  *
HO *  H *  H 2O *  *
H 2O*  H 2O( g )
1Ring:
Rangarajan et al., Computers & Chemical Engineering 45, 114 (2012).
(Matlab Chem Kinetics Package): Goodwin et al., Cantera: An Object-oriented Software Toolkit for
Chemical Kinetics, Thermodynamics, and Transport Processes. 2014.
3Chemkin (Fortran Chem Kinetics Package): Coltrin; Kee and Rupley, Int. J. Chem. Kinet. 23, 1111 (1991).
Coltrin; Kee and Rupley Surface CHEMKIN (Version 4. 0): A Fortran package for analyzing heterogeneous
chemical kinetics at a solid-surface---gas-phase interface; SAND-90-8003B; 1991.
Reactor Design (commercial kinetics software)
2Cantera
Outline
Accuracy
MKM uses
Analysis
Catalyst discovery
6
Parameter Estimation of Microkinetic Models
 Parameters fitted to data
 Inability to simultaneously predict multiple experimental sets
 Parameters estimated with empirical methods (Bond-Order Conservation)
 Efficient, reasonable accuracy (2-4 kcal/mol)
 Limited to small adsorbates
 Density functional theory (DFT)-based semi-empirical methods
 Group additivity, Brønsted-Evans-Polanyi (BEP) relations
 Parameters obtained from DFT
 Fairly accurate (<5 kcal/mol)
 Hierarchical methods
 Empirical or semi-empirical to screen; DFT to refine (zero coverage limit)
 Include coverage effects
Hierarchy Enables Rapid Screening of
Chemistry, Fuels, and Catalysts
Accuracy, cost
Reactor scale:
Performance
Pseudo-homogeneous:
Ideal:
PFR, CSTR, etc. Transport correlations
Catalyst scale:
Reaction rate
Electronic scale:
Parameter estimation
Continuum:
MF-ODEs
Mesoscopic:
PDEs
Quantum-based
correlations:
BEPs, GA, LSRs
Discrete:
CG-KMC
Computational
Fluid Dynamics
(CFD)
Discrete:
KMC
Quantum:
ab initio, DFT, TST,
CPMD, QM/MM MD
7
Outline
Accuracy
MKM uses
Kinetic Monte Carlo
Accuracy of MKM
• Myth: A microkinetic (detailed) model [even with DFT input] can quantitatively describe experimental data
8
10
0
10
-1
10
-2
C2H6O2 Steam Reforming
Ea: 18 kcal mol-1
Ea: 15 kcal mol
1.8
1.9
2
1000 T
CO2 Rate / min-1
10
10
10
-1
2.1
2.2
-1
-1
2.3
Ea: 26 kcal mol-1
-2
1.8
Ea: 20 kcal mol-1
1.9
2
1000 T
1
10
0
10
-1
10
-2
Ea: 17 kcal mol-1
Ea: 15 kcal mol
1.8
1.9
/K
0
-4
10
2.1
2.2
-1
-1
/K
2.3
10
2
10
0
10
-1
10
-2
1.8
-1
2.1
1000 T -1 / K-1
1
0.5
2.2
2.3
Ea: 13 kcal mol-1
Ea: 16 kcal mol-1
1.9
2
1000 T
2.1
2.2
-1
-1
Normalized Sensitivity Coefficient
1
CO Rate / min-1
10
H2 Rate / min-1
H2 Rate / min-1
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
2.3
/K
1st (C-H) Thermal Dehydrogenation
2nd (C-H) Thermal Dehydrogenation
1st (O-H) Thermal Dehydrogenation
1st (C-H) Oxidative Dehydrogenation
1st (O-H) Oxidative Dehydrogenation
0.45
T = 483K
Excess Water
T = 483K
Stoichiometric
T = 543K
Excess Water
T = 543K
Stoichiometric
Feed Conditions
Model (♦) Experiments (■)
Good agreement with data*
No parameter fitting performed
*
Kandoi et al., J. Phys. Chem. C 115 (4) 961 (2011)
Thermal dehydrogenation steps are kinetically most important
OH*‐mediated steps inactive on Pt (due to low [OH*])
Christiansen and Vlachos, App. Cat. A: General 431–432, 18 (2012).
You Need to Ensure That MKM Captures Correctly Temperature effects
Reaction orders of reactants
Reaction orders of products (Effect of co‐feeding products)
Ideally the RDS is tested spectroscopically
Ideally the MASI is tested via IR
Salciccioli; Stamatakis; Caratzoulas and Vlachos, Chem. Eng. Sci. 66, 4319 (2011).
9
Outline
• Types of catalytic kinetic models and microkinetic modeling
• Overview of parameter estimation methods and scales
• Accuracy
• Lateral interactions
• Semi‐empirical methods
• Thermodynamic consistency
• MKM uses
– Reactor design, analysis, catalyst discovery
• Kinetic Monte Carlo
Lateral Interactions:
Estimation via Hierarchical Estimation Methodology
Myth: After parameterization of a microkinetic model via DFT (or semi‐empirical methods), the model is correct and no further refinement is needed
10
Lateral Interactions Are Typically Critical
Spatial Occupation Probability Map for CO*
1
1.5
y (nm)
0.8
1
0.6
0.4
0.5
0.2
0
0
0.5
1
x (nm)
1.5
0
Adsorbate heterogeneity arises due to coverage effects
Combinatorial problem in a priori estimating kinetic
parameters due to coverage effects
Review of Catalyst and Kinetic Modeling: Salciccioli et al., Chem. Eng. Sci. 66, 4319 (2011)
Hierarchical Multiscale Modeling Principle: Dealing with Size (No. of Reactions and Coverage)
Start with a sufficiently simple, physical model at each scale
Automatic mechanism generation
First‐principles based semi‐empirical parameter estimation
Link all models Identify important scale and parameter(s)
Sensitivity and flux analyses
Use higher level theory for this scale and parameter(s)
Kinetically relevant steps, inclusion of coverage effects, internal diffusion, etc.
Iterate First‐principles accuracy at orders of magnitude reduced cost
11
NH3 Decomposition on Ru: 2NH3 =N2+3H2
• NH3 as a storage medium
• ‘Pure’ H2 – No COx
• A microkinetic model is
build using BOC and TST
• Our microkinetic model
captures the trend
• High N* coverages
NH 3  *  NH 3 *
NH 3 * *  NH 2 *  H *
NH 2 * *  NH *  H *
NH * *  N *  H *
2N *  N 2  2 *
2H *  H 2  2 *
100
Exptl: Ganley
et al., AIChE
J. 2003
80
PFR model
60
40
20
0
et al.]
196 mExpts.
x 84 [Ganley
m x 1078
m
1
N*
0.8
0.6
0.4
0.2
E m pty sites (*)
0
650
850
1050
1250
T [K ]
Mhadeshwar et al., Cat. Letters 96, 13‐22 (2004)
DFT Estimates Lateral Interactions
• DACAPO (solid-state electronic
structure package by Hammer and
coworkers*)
130
• 3-Layer slab of Ru(0001)
120
• 2  2 unit cell
• All layers are relaxed
• Plane wave cutoff = 350eV
• 18 k-points for surface Brillouin zone
• Generalized gradient approximation
(PW-91)
DFT Calculations (this work)
Linear fit QN (at H*=0)=128.2-33.3N*
Linear fit QN (at N*=0.25)=120.1-6.2H*
N-H interactions
N-N interactions
110
100
N on Ru(0001)
3 layer slab
90
0
0.25
0.5
0.75
(N*+H*) coverage [ML]
1
* Hammer et al., DACAPO version 2.7 (CAMP,
Technical University, Denmark)
12
DFT‐Retrained Microkinetic Model
1
100
PFR model
80 with interactions
0.8
PFR model
without interactions
60
0.6
N* without interactions
* without interactions
NH *
3
40
0.4
20
H*
N*
0.2
0
0
Expts. [Ganley et al.]
650
850
T [K]
1050
*
1250
650
850
• H-H and N-H interactions are small
T [K]
1050
1250
Exps: Ganley et al., AIChE J. (2004)
• N-N interactions completely change the chemistry
• Extensive validation against UHV and high P data
Outline
Accuracy
MKM uses
Kinetic Monte Carlo
13
Semi‐Empirical Estimation Methods
Myth: First‐principles (DFT) MKM can be developed for any mechanism and feedstock
Estimation with first‐principles semi‐empirical methods (FPSEM) is possible
Refinement of important parameters is feasible
Modeling Reactions of Large Molecules is Challenging
Number of Calculations
106
Combinatorial explosion in number of calculations for first‐principles (DFT) calculations
Intermediates
Reactions
105
104
Semi‐empirical methods can potentially identify relevant species and reactions instantaneously
103
102
10
Sugars
HO
HO
HO
HO
HO
OH
HO
OH
HO
OH
OH
HO
OH
HO
OH
Major advances in systematic development of semi‐empirical methods and understanding of errors
14
DFT‐Based Estimation Methods
Linear Scaling
Relations
• Libraries of atomic
binding energies
• Binding energies of
AHx species vs.
heteroatom A valency
• Metal transferability
Group Additivity
• Single metal
thermochemistry
• Thermodynamic
consistency
• Screen adsorbates
Microkinetic Model
Brønsted Evans
Polanyi (BEP)
• Compute rates, conversion,
selectivity, abundant species
• Identify key adsorbates and
reactions
• Refine thermochemistry and
barriers via DFT
• Include adsorbate-adsorbate
interactions
• Activation energies
• Reaction rate
constants
• Screen reactions
Surface thermochemistry via group additivity
Brønsted‐Evans Polanyi relations for reaction barriers of homologous series
Transfer thermo from one material to another (linear scaling relations)
Perform high‐throughput microkinetic modeling (MKM) for materials prediction
Identify key steps and refine them via higher level theory
Review: Salciccioli et al., Chem. Eng. Sci. 66, 4319 (2011);
Salciccioli et al., J. Phys. Chem. C 114, 20155 (2010); J. Phys. Chem. C 116, 1873 (2012); Sutton and Vlachos, ACS Catal. 2, 1624 (2012); J. Catal. 297, 202 (2013)
Group Additivity for Adsorbed Species
• Binding for oxygenates traced to (CHyOx) groups
• Use alcohols and dehydrogenated alcohol intermediates to develop groups
• Include contributions for ΔHf,298, S(T) and Cp(T)
Group
[C(C,H2)-O(M,H)]
[C(C,H,M)-O(H)]
[C(C,M2)-O(H)]
[C(C,H2)-O(M)]
[C(C,H,M)-O(M)]
[C(C,M,M)-O(M)]
[C(C,M)=O]
[C(C2,H)-O(M,H)]
[C(C2,M)-O(H)]
[C(C2,H)-O(M)]
[C(C2,M)-O(M)]
ΔHf,298 Value
[kcal/mol]
-50.2
-46.8
-39.3
-26.1
-26.5
-33.4
-33.4
-51.1
-42.9
-25.1
-23.0
H
H
C
H
H
H
C
H
O
A
Pt
Pt
Pt
B
O
HC
C
O
O
C
CH2
Salciccioli, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010).
15
Group Additivity for Adsorbed Species
Group additivity [kcal/mol]
Second‐order effects included:
4‐member ring strain
Weak interactions
Hydrogen bonding
Calculations of ΔHf,298 of C2HxO2 and C3HxO3 species show good quantitative agreement
C2HxO2
C3HxO3
-160
-120
-80
-40
-40
This method can be used for initial screening of larger hydrocarbons and oxygenates
-80
-120
-160
DFT calculated [kcal/mol]
Values are taken with respect to the most highly hydrogenated species in the gas phase (C2H6O2, C3H8O2) and H adsorbed on a separate slab
Salciccioli
et al., J. Phys. Chem. C 114, 20155 (2010); J. Phys. Chem. C 116, 1873 (2012)
Salciccioli,
Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010).
Transferability Between Metals
Molecular binding energy is linearly dependent on atomic binding energy1
These correlations relate molecular binding energy to atomic binding energy on different surfaces
Multidentate species can be accounted for by summing the contributions of each bond to the surface2
H
H
H
C
OH
H
C
OH
≈
HO
H
H
C
C
OH
Q M  Q Pt    Q A,i,M  Q A,i,Pt   x   ES  E ROH
A,i
[1] Abild‐Pedersen et al. PRL 99, (2007)
[2] Salciccioli, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010)
16
Transferability Between Metals
This scheme was validated by testing the binding energy of all C2HxO2 intermediates on Ni(111) and Ni‐Pt‐Pt(111)
-120
Pt(111)
Qo,Qc
Ni-Pt-Pt(111)
-80
-40
0
0
-40
-80
-120
Q DFT [kcal/mol]
QC2HxO2
Predicted Q [kcal/mol]
Predicted Q [kcal/mol]
These correlations allow for metal transferability of the C2H6O2
decomposition mechanisms
-120
Ni(111)
-80
-40
0
0
-40
-80
-120
Q DFT [kcal/mol]
Salciccioli, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010)
Linear Free‐Energy Relations (LFR) Two types of relations are found
Transition State Scaling (TSS)
Brønsted‐Evans‐Polanyi (BEP)
There is reductionistic trend of combining multiple reaction types into a homologous series
Minimal calculations
Accuracy may be sacrificed
Connection between the two LFR types and distinct homologous series
17
Distinct Homologous Series Developed
A c tiv at io n E n e r gy ( eV )
5
Combined C-H
O-H
Combined C-C
C-OH
C-O
4
3
Performed DFT calculations for methane, methanol, ethane, and ethanol
45 stable intermediates and 124 transition states
Considered C‐H (a and b positions), O‐H, C‐C, C‐O, and C‐OH reactions
Statistical tests are used
2
1
0
-1
-3
-2
-1
0
1
2
3
Heat of Reaction (eV)
Sutton and Vlachos, ACS Catal. 2 1624 (2012); J. Catal. 297, 202 (2013)
Computational Savings from Hierarchy
Glycerol thermal decomposition
6
10
DFT
2
10
1
DFT
GA/BEP
->DFT
4
10
Screen
conformers via GA
CPU hrs
Profound
computational
savings
(Important)
information
content
remains the
same
GA/BEP
Chen et al., J. Phys. Chem. 115(38), 18707 (2011)
18
Hierarchical Multiscale Modeling Principle: Dealing with Size (No. of Reactions and Coverage)
Start with a sufficiently simple, physical model at each scale
Automatic mechanism generation
First‐principles based semi‐empirical parameter estimation
Link all models Identify important scale and parameter(s)
Sensitivity and flux analyses
Use higher level theory for this scale and parameter(s)
Kinetically relevant steps, inclusion of coverage effects, internal diffusion, etc.
Iterate First‐principles accuracy at orders of magnitude reduced cost
Speed of Convergence of FPSEM Models
1
0.6
Ethanol MKM/Pt
4
0.6
0.4
DFT
0
2
3
4
5
0.2
0
300
320
340
360
380
Temperature (°C)
Fractional C Selectivity, CH
Fractional Conversion
0.8
400
0.5
160 reversible reactions
67 gas and surface species
0.4
0.3
CH 3CH 2 OH  CH 4 + CO + H 2
0.2
CH 3CH 2 OH  CH 3CHO + H 2
0.1
2CH 3CH 2 OH  3CH 4 + CO 2
0
300
320
340
360
380
400
Temperature (°C)
It takes only a few iterations to converge the semi‐empirical model to be nearly indistinguishable with the DFT‐based MKM
Interaction parameters in the first two iterations are most critical for qualitative agreement
Sutton and Vlachos, Chem. Eng. Sci., In press
19
Outline
Accuracy
MKM uses
Kinetic Monte Carlo
Thermodynamic Consistency of MKM
Myth: Your model is thermodynamically consistent A mechanism based solely on a single DFT mechanism is thermo consistent
Challenges
DFT is not accurate for gas‐phase thermo 
overall thermo is not accurate; thus, we often mix high level ab initio data or NIST thermo data
Kinetic parameters are adjusted to describe data
Either adjustment leads to thermo incosistencies
20
Most Literature Mechanisms Are Thermodynamically Inconsistent
CO oxidation: CO2= CO+O
WGS: CO+H2O=CO2+H2
100
Equilibrium
0
10
Keqsurface/Keqgas
CO conversion [%]
80
4
10
Experiments
(Xue et al.)
60
40
WGS
Coupling mechanism
Deutschmann et al.
mechanism
20
-4
10
-8
10
0
A/V=450 cm
473
573
673
773
Temperature [K]
-1
873
Optimized mechanism
-12
10
Hickman and Schmidt mechanism
300
700
1100
1500
Temperature [K]
1900
Thermodynamic Loop
Reaction

B
A 
Af
Ab
k T S / R
A f ,b  B e
TST
h
Pre‐exponentials of a reversible reaction
f ,b
Gas
A
Surface
A*
B
Surface
Surface
B*
S / R  ( S b  Sf ) / R  ln A b / A f
Enthalpic consistency for single reaction
A * A*
E f  E b  H
A*  B*
Carry out a thermodynamic loop on a state variable X:
‘Exact’ B*  B  *
A
B
X ads
 X surf  X ads
 Xgas
AB
21
Linear Independence and Parameter Tuning
For every surface reaction, one can write a corresponding gas reaction and a thermo loop
The number of surface species usually determines the number of independent variables
Cannot simply change barriers or pre‐exponentials to fit data without paying attention to thermo consistency
• Mhadeshwar et al., Thermodynamic consistency in microkinetic development of surface
reaction mechanisms, Journal of Physical Chemistry B 107, 12721-12733 (2003).
• Salciccioli et al., A review of multiscale modeling of metal-catalyzed reactions: Mechanism
development for complexity and emergent behavior, Chem. Eng. Sci. 66, 4319–4355
(2011).
Outline
Accuracy
MKM uses
Kinetic Monte Carlo
22
Modern
Traditional
What Can We Use MKMs for?
Reconcile apparently contradictory experimental data at different conditions (TPD, steady state, various operating conditions)
Mechanistic understanding
Perform reactor optimization
Model‐based design of experiments to assess model
Rational catalyst design
Composition
Size
Shape
MKM at Work
Catalysis and reaction engineering (experimental and computational)
Chemical kinetics
Microchemical systems for portable and distributed energy
In silico catalyst discovery
JP8 (cat combustion)
NH3
CH4; small HCs (POX, SR, hydrogenolysis, dehydrogenation)
Alcohols (SR)
WGS, PROX
Reaction mechanism
Hansgen et al., Nature Chem. 2, 484 (2010)
2NH3=N2+3H2
Catalyst
Process
discovery
Reactor
design
23
Ethylene Hydrogenation: Analysis
S ij 
 ln1 R i 
 ln A j 
C2H5 H =50 torr
pi-C2H4 2
150
sigma-C2H4
CCH3 665
Vacancies
Coverage
0.8
0.6
0.4
0.2
0
200
240
280
320
Temperature [K]
360
-1
0
1
Normalized Sensitivity Coefficient
Hydrogenation rxns are rate controlling (π-C2H4**→C2H5**, C2H5**→C2H6)
Model Reduction to Rate Expressions
H2 + 2* ↔ 2H*
CH + 2* ↔ CH * + H*
Ethane Hydrogenolysis
C H + 2* ↔ π-C H **
4
3
2
1
4
2
4
10
C2H4 + 4* ↔ σ-C2H4****
0
673K
C2H2 + 2* ↔ C2H2**
10
-1
+ 3* ↔ CHydrogenolysis
C2H6Ethane
2H5** + H* 623K Reaction
Ethylene10
Hydrogenation
Reaction
π-C2H4** + 2* ↔ σ-C2H4****
-2
H2 + 2* ↔
H + 2* ↔ 2H* + *
10 2H*
π -C2H24** + H* ↔ C2H5** 573K
-3
C2H4 + 2*
+ 2*
↔2HCH
H*
10↔ π-C2H4**
↔ σ-C
C2HCH
4 3*
3* ++H*
5** +
4****
Reduced
model
-4
Sensitivity
analysis
σ-C
H4****
↔ C HExperimental
H***
+ * + H*
2C
3**
C2H6 + 3*
10↔ C2H5** + H*
C+2H
2H6 + 3* 2↔
5
step rate expression
-5
C2H2** + H* ↔C2HOne
Experimental
3** + *
10+ 2* ↔ σ-C2Hcomponent
π-C2H4**
Canalysis
H5** + 3* ↔ σ-C2H4**** + H*
Principal
4****
2+
C2H**
H* ↔ C2100
H2** +*
1
10
1000
Reduced
microkinetic
model
CH TOF [1/s]
Full mechanism Full mechanism
4
Ethylene Hydrogenation
CH TOF [1/s] -1
C4 H TOF [s ]
+ H* ↔ C2Reduced
H5** + *rateEthane
π-C2H4**100
↔ C H ** + H* + *
σ-C
Pressure
[Torr]
2H
↔4****
CCH
CHCH
expression
3**
3* + H* 2 3
CCHCHCH
CCH
+ H*3* +336
C2H5** + 3*1 ↔ σ-C2H4**** + H*
↔2**
CCH
H* K
3* + 2* ↔
3**
10
C2H5** + * ↔ CHCH3** + H*
σ-C2H4****0 ↔ C2H3673K
** + H* + *
CCH3* + 2* ↔ CCH
=+ 5H*
Torr
P 2**298
K
1010
CHCH3** + *↔ C2H3** + H* C2H6
623K
C2H2** + H*
C H ** + * ↔ CHCH3** + H*
-1 ↔ C2H
3** + *
C2H3**2 + 5*↔CCH2** + H*
10
273
K
CHCH3** ↔
+ H*
CHCH
+ H*
-2 CCH3*573K
C2H**
+ H* ↔CCH
** + *C2H3**
3** + 2*↔
10
↔ CH * + CH2*
C2HC
5**H
CCH3* + 2*-31↔ CCH2** + H*
2 3** 3+ *↔CCH
2** + H*
Reduced
model
10
2CH2* + 2* ↔ σ-C2H4****
C2H5** + *-4↔ CHCHExperimental
C H ** ↔ CH * + CH2248
* K
3** + H*
C2H3**2 ↔5 CH* + CH2*3
10
step
+-5 *↔ C2HOne
H* rate expression
CHCH3**0.1
3** +
3** ↔ CH3*+ CH*
C2HCHCH
2** ↔ 2CH*
10
C2H**
C* CH* + H*223 K
C2H3** + *1↔ CCH2** + H*
+ *+ ↔
CH↔2*CH*
10
CHCH
CH3*+ CH* + H*
3***↔
H*0 ↔ CCH2** + *
CH
C2H** +0.01
3 + * ↔ CH2*
= 25Torr
P
6
Reduced mechanism
Reduced mechanism
3
3
2
10
4
Rate equation
CH TOF [1/s]
2
Elementary rate comparison
Rate determining step
Partial673K
equilibrium
CH * + C* ↔ CCH * + * C2H6
10
100
1000
CCH assumptions
** ↔ CH * + C*
Abundant
623K adsorbate
-1
10
Hydrogen Pressure [Torr]
-2
-3
2
CHCH3** + 2* ↔ C2H4****
573K
C2H3** ↔ CCH3* + *
Reduced model C2H2**↔ CCH2**
Experimental
C* + H* ↔ CH* + *
One step rate expression
CH2* + * ↔ CH* + H*
+ * ↔ CH2* + H*
CH3*100
10
Rate equation
10
-4
10
1000
24
Ethylene Hydrogenation Rate Expression
Due to multiple abundant adsorbates, the reduced rate
expression is too complex for a closed form equation
Experimental
Reduced microkinetic model
Reduced rate expression
TOF [s-1]
100
336 K
10
298 K
273 K
1
248 K
0.1
223 K
0.01
100
1000
High Throughput Multiscale
Model‐based Catalyst Design
0.5
NH3 decomposition
Conversion
0.4
0.3
0.2
0.1
350 oC
1 atm
0
140
130
120
Q [kcal/mol]
N
110
45
50
60
55
65
70
Q [kcal/mol]
H
NH 3  *  NH 3 *
NH 3 * *  NH 2 *  H *
NH 2 * *  NH *  H *
NH * *  N *  H *
2N *  N 2  2 *
2H *  H 2  2 *
Search is done on atomic descriptors while running the full chemistry and reactor models
Optimal catalyst properties are identified
Prasad et al., Chem. Eng. Sci. 65, 240 (2010)
25
Identifying Bimetallic Catalysts
Metals
BEN (kcal/mol)
PtTiPt
56.5
PtVPt
59.5
PtCrPt
72.6
PtMnPt
84.9
PtFePt
83.9
PtCoPt
87.0
PtNiPt
89.8
NiPtPt
137.5
CoPtPt
159.9
FePtPt
169.9
MnPtPt
162.2
CrPtPt
166.5
VPtPt
184.1
TiPtPt
191.5
Pt
Ni
Surface
Sub-surface
• Optimum heat of chemisorption of N of ~130 kcal/mol
• NiPtPt is a good prospective bimetallic surface
102.1
113.8
Emergent Behavior Verified Experimentally
Intensity (arb. units)
14 amu
Thick Ni
3.0 Langmuir NH3
at 350K at UHV
Ni-Pt-Pt
Ni-Pt
Pt-Ni-Pt
Pt(111)
350
400
450
500
550
600
650
700
750
Temperature (K)
 Ammonia decomposes on Ni‐Pt
 No decomposition on other surfaces
 N‐Pt is the most active catalyst
Hansgen, Chen, and Vlachos, Nature Chem. 2, 484-489 (2010)
26
Outline
Accuracy
MKM uses
Kinetic Monte Carlo
Typical Descriptor Fails to Describe Experimental Trends
950
Co/Pt
TPD peak (K)
900

Ni/Pt
850
Ni
800
Co
826 K
Co
Co/Pt
745 K
750
Pt
700
650
600
Experiment
Theory
Ni/Pt
627 K
-5.6
-5.4
-5.2
-5.0
-4.8
dN k0 2
 N exp(Ea (N ) / (kBT ))
dT H
• Binding energy on terrace sites is not a good descriptor, especially for bimetallic surfaces
-4.6
N binding energy (eV)
Hansgen, D. A. et al. J. Chem. Phys. 2011, 134(18), 184701.
27
Can be Important
Bimetallics
Single Metal
2
NH3 on Ru
x 10
TOF (s‐1)
TOF, s-1
Kitchin et al.,
Surf. Sci. 544,
295, (2003)
Lean
1
0.5
0
Ni/Pt
Octahedral
CO+O
2 Pt/Au
4
3
1.5
0
1
2
3
4
5
Particle size, nm
6
7
Karim et al., J. Am. Chem. Soc.
131, 12230 (2009)
8
2
1
0
0
2
4
6
8
10
Particle Diameter, d (nm)
Stamatakis and Vlachos, in prep.
Tupy et al., ACS Catal. 2, Tupy et al., ACS
2290 (2012)
Catal. 2, 2290 (2012)
The Kinetic Monte Carlo Approach
E‡
Metal surface
k rxn
transition
state
reactants
CO(gas) + OH
k  T Q‡  k B T
  B 
e
h
Q rxn
products
Potential Energy Surface
COOH
Instead of simulating dynamics, KMC focuses on rare events
Simulates reactions much faster than Molecular Dynamics
Incorporates spatial information contrary to micro‐kinetic models
28
Graph‐Theoretical KMC Approach
O2(top,top)
O(fcc)
O(fcc)
O2* 
 2O*
• Lattice, reactions represented as graphs
O*
O2*
O*
*
• Subgraph isomorphism used to identify possible reactions & map them on the lattice
Stamatakis and Vlachos, J. Chem. Phys. 134, 214115 (2011); http://www.dion.che.udel.edu/downloads.php
Features of Graph‐Theoretical KMC
CV = 0.027384 eV per site

Model Hamiltonian Energies (eV)
Complex chemistries1
Accurate lateral interactions1
Microscopic reversibility and thermodynamic consistency
Fast algorithms2
Multiple facets, nanoparticles, clusters, multifunctional materials1
0
‐1
‐2
‐3
‐4
‐5
‐5
‐4
‐3
‐2
‐1
0
DFT Energies (eV)
terraces
steps
Pt(211)
Au6‐1/MgO
1Cat
Ni/Pt ‐ EXAFS
KMC Review: Stamatakis and Vlachos, ACS Cat. 2, 2648 (2012)
KMC Review: Chatterjee and Vlachos, J. Comp.-Aided Mat. Design 14, 253 (2007)
2Multiscale
29
Schematic of Overall Process on Bimetallics: Minimum Energy Path Thinking
Ni/Pt serves as a reservoir of N due to strong binding
N diffuses at interfacial sites invoking steps and Pt terraces and associates and desorbs from there
N2 Desorption on NiPtPt and CoPtPt
Exp.
625 K
NiPtPt
745 K
N = 0.3
CoPtPt
CoPtPt is worse catalyst than NiPtPt
Weaker N binding
N‐N attractive interactions render desorption slower
30
First‐Principles KMC Resolves Structure Sensitivity
950
Ni-Pt-Pt
• Flat surfaces: strong N binding results in high desorption temperature, well described by Redhead theory
Co/Pt
TPD peak (K)
900
Ni/Pt
850
Ni
800
Co
826 K
Co
Co/Pt
745 K
750
Pt
• Steps are responsible for the low N2 KMC
desorption Experiment
temperature on Ni/Pt
Theory
and Co/Pt surfaces 700
650
600
Ni/Pt
627 K
-5.6
-5.4
-5.2
-5.0
-4.8
-4.6
N binding energy (eV)
End
31

Reaction Kinetics Workshop, Part I Outline

Transcription

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