reaction kinetics workshop, part i - iscreiscre.org/iscre24/vlachos_iscre-mkm.pdf · reaction...

1

Catalysis Center for Energy Innovation

Reaction Kinetics Workshop, Part I

CCEI is an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Sciences

University of DelawareDepartment of Chemical and Biomolecular Engineering Center for Catalytic Science and Technology (CCST)Catalysis Center for Energy Innovation (CCEI),

an Energy Frontier Research Center

June 12, 2016


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

Outline

2




Accuracy




MKM uses


Kinetic Monte Carlo

Outline


Surface Reaction Rate Calculation Paradigm

• Hierarchy of calculation of surface reaction rates

Empirical rate-law; typically fitted to experimental data

Langmuir-Hinshelwood rate-law; developed using rate determining step (RDS) and MF theory

Microkinetic analysis;No assumptions on RDS (Dumesic, 1993)

Complexity/Reliability/Accuracy

3


Reaction A+B Products

Typical power‐low expression

The parameters have no physical significanceExponents unrelated to stoichiometryApparent activation energies can be negative

Prediction is reliable within the given experimental space

Can describe overall rate and heat effects

Simple interpolation modelsNot good for process optimizationCan typically describe only one set of data

Global reaction rate models

effE / RTa beff A B eff effr=k C C ;k =A e


Literature rate expressions (mostly under ‘fuel‐rich’ conditions) indicate scatter in activation energies and rxn ordersIs the scatter a result of (1) different operating conditions and surface area, (2) catalyst preparation, (3) fitting procedure/inadequacy of power‐law kinetics?

An example of scatter in literature rate expressions for CH4

catalytic combustion on Pt

Investigator Ea(kcal/mol) aCH4 bO2

Yao (Ind. Eng. Chem. Prod. Res. Dev., 1980) 21 1.0 -0.6

Lam & Trimm (Chem. Eng. Sci., 1980) 18/40 1.0 1.0/0.75

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

4


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

Summary of LH rate expressions


CH4 total oxidation (combustion)CH4 + 2O2= CO2 + 2H2O

Steam reforming of CH4

CO2-reforming of CH4

RWGS

LH Rates on Rh

= effectiveness factor

5


Process is away from equilibrium

Model fits data fairly well

Reactions in series is proposed

Combustion of syngas is important

Comparison of model to data: Conversion

dashed lines=model w/o consecutive combustion of CO and H2; solid lines=model with consecutive CO and H2

combustion


Models may fit but most often than not include unrealistic parameters

Are the parameters/model reasonable?

Estimated parameters

Hads[kcal/mol]13.939.56.2

6


Microkinetic Modeling• 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

An example1

2( ) 2( ) 2 ( )2

2( )

2( )

2

2 2 ( )

Re

2* 2 *

2* 2 *

* * * *

* * * *

*

g g g

g

g

g

H O H O

Elementary actions

H H

O O

H O HO

HO H H O

H O H O

1Ring: Rangarajan et al., Computers & Chemical Engineering 45, 114 (2012).2Cantera (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)




Accuracy




MKM uses

Analysis

Catalyst discovery

Outline

7


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 ofChemistry, Fuels, and Catalysts

Quantum:ab initio, DFT, TST,

CPMD, QM/MM MD

Continuum: MF-ODEs

Discrete: KMC

Ideal: PFR, CSTR, etc.

Computational Fluid Dynamics

(CFD)

Mesoscopic:PDEs

Discrete:CG-KMC

Pseudo-homogeneous:Transport correlations

Quantum-based correlations:

BEPs, GA, LSRs

Catalyst scale:Reaction rate

Reactor scale:Performance

Electronic scale:Parameter estimation

Accuracy, cost

8




Accuracy




MKM uses


Kinetic Monte Carlo

Outline


Accuracy of MKM

• Myth: A microkinetic (detailed) model [even with DFT input] can quantitatively describe experimental data

9


C2H6O2 Steam Reforming

Good agreement with data*

No parameter fitting performed

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).

1.8 1.9 2 2.1 2.2 2.310

-2

10-1

100

101

Ea: 18 kcal mol-1

Ea: 15 kcal mol-1

1000 T -1 / K-1

H2 R

ate

/ min

-1

1.8 1.9 2 2.1 2.2 2.310

-2

10-1

100

101

Ea: 17 kcal mol-1

Ea: 15 kcal mol-1

1000 T -1 / K-1

CO

Rat

e / m

in-1

1.8 1.9 2 2.1 2.2 2.310

-4

10-2

100

Ea: 26 kcal mol-1

Ea: 20 kcal mol-1

1000 T -1 / K-1

CO

2 Rat

e / m

in-1

1.8 1.9 2 2.1 2.2 2.310

-2

10-1

100

101

Ea: 13 kcal mol-1

Ea: 16 kcal mol-1

1000 T -1 / K-1

H2 R

ate

/ min

-1

Model (♦) Experiments (■)

* Kandoi et al., J. Phys. Chem. C 115 (4) 961 (2011)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Nor

mal

ized

Sen

siti

vity

Coe

ffic

ient

T = 483KExcess Water

T = 483KStoichiometric

T = 543KExcess Water

T = 543KStoichiometric

Feed Conditions

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


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).

10


• 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

Outline


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

11


Lateral Interactions Are Typically Critical

Adsorbate heterogeneity arises due to coverage effectsCombinatorial problem in a priori estimating kinetic parameters due to coverage effects

x (nm)

y (nm)

Spatial Occupation Probability Map for CO*

0 0.5 1 1.5

0

0.5

1

1.5

0

0.2

0.4

0.6

0.8

1

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 scaleAutomatic 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

12


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

196 m x 84 m x 1078 m

Mhadeshwar et al., Cat. Letters 96, 13‐22 (2004)

0

0.2

0.4

0.6

0.8

1

650 850 1050 1250

T [K]

N*

Empty sites (*)

0

20

40

60

80

100

Expts. [Ganley et al.]

PFR model

Exptl: Ganleyet al., AIChE J. 2003

*NH*NH 33 *H*NH**NH 23

*H*NH**NH 2 *H*N**NH *2N*2N 2 *2H*2H 2


DFT Estimates Lateral Interactions

• DACAPO (solid-state electronic structure package by Hammer and coworkers*)

• 3-Layer slab of Ru(0001)

• 2 2 unit cell

• All layers are relaxed

• Plane wave cutoff = 350eV

• 18 k-points for surface Brillouin zone

• Generalized gradient approximation (PW-91)

* Hammer et al., DACAPO version 2.7 (CAMP, Technical University, Denmark)

90

100

110

120

130

0 0.25 0.5 0.75 1(N*+H*) coverage [ML]

DFT Calculations (this work)Linear fit Q

N (at H*=0)=128.2-33.3N*

N on Ru(0001) 3 layer slab

Linear fit QN (at N*=0.25)=120.1-6.2H*

N-N interactions

N-H interactions


13


Exps: Ganley et al., AIChE J. (2004)

DFT‐Retrained Microkinetic Model

• H-H and N-H interactions are small

• N-N interactions completely change the chemistry

• Extensive validation against UHV and high P data

0

20

40

60

80

100

650 850 1050 1250

Expts. [Ganley et al.]

PFR modelwithout interactions

T [K]

PFR modelwith interactions

0

0.2

0.4

0.6

0.8

1

650 850 1050 1250T [K]

*

N* without interactions* without interactions

H*

N*

NH3*





Accuracy




MKM uses


Kinetic Monte Carlo

Outline

14


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

Semi‐Empirical Estimation Methods


Modeling Reactions of Large Molecules is Challenging

Combinatorial explosion in number of calculations for first‐principles (DFT) calculations

Semi‐empirical methods can potentially identify relevant species and reactions instantaneously

Major advances in systematic development of semi‐empirical methods and understanding of errors

10

102

103

104

105

106

IntermediatesReactions

Num

ber

of C

alcu

latio

ns

HO

HOOH

HO

OH

OHHO

OHHO

HO

HO

OH

OHHO

HO

Sugars

15


DFT‐Based Estimation Methods

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

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

Brønsted Evans Polanyi (BEP)

• Activation energies• Reaction rate constants

• Screen reactions

Microkinetic Model

•Compute rates, conversion, selectivity, abundant species

• Identify key adsorbates and reactions

•Refine thermochemistry and barriers via DFT

• Include adsorbate-adsorbate interactions

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)


• 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)

GroupΔHf,298 Value

[kcal/mol][C(C,H2)-O(M,H)] -50.2[C(C,H,M)-O(H)] -46.8[C(C,M2)-O(H)] -39.3[C(C,H2)-O(M)] -26.1[C(C,H,M)-O(M)] -26.5[C(C,M,M)-O(M)] -33.4[C(C,M)=O] -33.4[C(C2,H)-O(M,H)] -51.1[C(C2,M)-O(H)] -42.9[C(C2,H)-O(M)] -25.1[C(C2,M)-O(M)] -23.0

C

HH

OH

Pt Pt Pt

C

H

H

H

Group Additivity for Adsorbed Species

Salciccioli, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010).

O

C CH2

A BO

HC CO

16


Group Additivity for Adsorbed SpeciesSecond‐order effects included:

4‐member ring strainWeak interactionsHydrogen bonding

Calculations of ΔHf,298 of C2HxO2 and C3HxO3 species show good quantitative agreement

This method can be used for initial screening of larger hydrocarbons and oxygenates

-160

-120

-80

-40

-160-120-80-40

C2H

xO

2

C3H

xO

3

Gro

up a

ddit

ivit

y [k

cal/

mol

]

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, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010).Salciccioli et al., J. Phys. Chem. C 114, 20155 (2010); J. Phys. Chem. C 116, 1873 (2012)


Molecular binding energy is linearly dependent on atomic binding energy1

These correlations relate molecular binding energy to atomic binding energy on different surfacesMultidentate species can be accounted for by summing the contributions of each bond to the surface2

Transferability Between Metals

[1] Abild‐Pedersen et al. PRL 99, (2007)[2] Salciccioli, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010)

M Pt A,i,M A,i,Pt S ROHA,i

Q Q Q Q x E E

C

HH OH C

HH OH

C

HOHC

HOH≈

17


This scheme was validated by testing the binding energy of all C2HxO2 intermediates on Ni(111) and Ni‐Pt‐Pt(111)

These correlations allow for metal transferability of the C2H6O2

decomposition mechanisms

-120

-80

-40

0-120-80-400

Pre

dict

ed Q

[kc

al/m

ol]

Q DFT [kcal/mol]

Ni(111)-120

-80

-40

0-120-80-400P

redi

cted

Q [

kcal

/mol

]

Q DFT [kcal/mol]

Ni-Pt-Pt(111) Pt(111)Qo,Qc

QC2HxO2

Salciccioli, Y. Chen, and Vlachos, J. Phys. Chem. C 114(47), 20155 (2010)

Transferability Between Metals


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

18


Distinct Homologous Series Developed

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

-1

0

1

2

3

4

5

-3 -2 -1 0 1 2 3

Combined C-HO-HCombined C-CC-OHC-O

Ac

tiv

ati

on

En

erg

y (

eV

)

Heat of Reaction (eV)

Sutton and Vlachos, ACS Catal. 2 1624 (2012); J. Catal. 297, 202 (2013)


Profound computational savings(Important) information content remains the same

1

102

104

106

CP

U h

rs

DFT

Scre

en

conf

orm

ers

via

GA

DFT

GA

/BE

P->

DFT

GA/BEP

Glycerol thermal decomposition

Chen et al., J. Phys. Chem. 115(38), 18707 (2011)

Computational Savings from Hierarchy

19


Hierarchical Multiscale Modeling Principle: Dealing with Size (No. of Reactions and Coverage)

Start with a sufficiently simple, physical model at each scaleAutomatic 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

0

0.2

0.4

0.6

0.8

1

300 320 340 360 380 400

DFT02345

Fra

cti

on

al C

on

vers

ion

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

3 2 4 2CH CH OH CH + CO + H

3 2 3 2CH CH OH CH CHO + H

3 2 4 22CH CH OH 3CH + CO

Ethanol MKM/Pt

160 reversible reactions

67 gas and surface species

0

0.1

0.2

0.3

0.4

0.5

0.6

300 320 340 360 380 400

Fra

cti

on

al C

Se

lect

ivit

y, C

H4

Temperature (°C)

Sutton and Vlachos, Chem. Eng. Sci., In press

20




Accuracy




MKM uses


Kinetic Monte Carlo

Outline


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

Thermodynamic Consistency of MKM

21


Most Literature Mechanisms Are Thermodynamically Inconsistent

0

20

40

60

80

100

473 573 673 773 873

CO

con

vers

ion

[%]

Temperature [K]

Coupling mechanismWGS

Equilibrium

Experiments(Xue et al.)

A/V=450 cm-1

Deutschmann et al.mechanism

WGS: CO+H2O=CO2+H2

10-12

10-8

10-4

100

104

300 700 1100 1500 1900K

eq

surf

ace /K

eq

gas

Temperature [K]

Hickman and Schmidt mechanism

Optimized mechanism

CO oxidation: CO2= CO+O


Reaction

TST

Pre‐exponentials of a reversible reaction

Enthalpic consistency for single reaction

Carry out a thermodynamic loop on a state variable X:

Thermodynamic Loop

f ,bS / RBf ,b

k TA e

h

fbfb A/AlnR/)SS(R/S

HEE bf

f

b

A

AA B A B

A* B*

Gas

SurfaceSurface

Surface

A Bads surf adsX X X gasX

A * A*

A* B*

B* B *

A B

‘Exact’

22


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

Linear Independence and Parameter Tuning

• 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).




Accuracy




MKM uses


Kinetic Monte Carlo

Outline

23


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 designComposition

Size

Shape

What Can We Use MKMs for?Tr

aditi

onal

Mod

ern


Process

Reaction mechanism

Reactordesign

Catalystdiscovery

Catalysis and reaction engineering (experimental and computational)

Chemical kinetics

Microchemical systems for portable and distributed energy

In silico catalyst discovery

MKM at WorkJP8 (cat combustion)NH3

CH4; small HCs (POX, SR, hydrogenolysis, dehydrogenation)Alcohols (SR)WGS, PROX

2NH3=N2+3H2Hansgen et al., Nature Chem. 2, 484 (2010)

24


0

0.2

0.4

0.6

0.8

1

200 240 280 320 360

C2H5pi-C2H4sigma-C2H4CCH3Vacancies

Cov

erag

e

Temperature [K]

-1 0 1

H2=50 torr

150665

Normalized Sensitivity Coefficient

j

iij A

RS

ln

ln

Hydrogenation rxns are rate controlling (π-C2H4**→C2H5**, C2H5**→C2H6)

Ethylene Hydrogenation: Analysis


Ethylene Hydrogenation Reaction

H2 + 2* ↔ 2H*

C2H4 + 2* ↔ π-C2H4**

C2H6 + 3* ↔ C2H5** + H*

π-C2H4** + 2* ↔ σ-C2H4****

π-C2H4** + H* ↔ C2H5** + *

C2H5** + 3* ↔ σ-C2H4**** + H*

σ-C2H4**** ↔ C2H3** + H* + *

C2H2** + H* ↔ C2H3** + *

CHCH3** ↔ CCH3* + H*

CCH3* + 2* ↔ CCH2** + H*

C2H5** + * ↔ CHCH3** + H*

CHCH3** + *↔ C2H3** + H*

C2H3** + * ↔ CCH2** + H*

C2H** + H* ↔ CCH2** + *

10-510-410-310-210-1100101

1 10 100 1000

Reduced modelExperimentalOne step rate expressionC

H4 T

OF

[1/

s]

Ethane Pressure [Torr]

673K

623K

573K

0.01

0.1

1

10

100

100 1000

ExperimentalReduced microkinetic model Reduced rate expression

C2H

6 TO

F [s

-1]

Hydrogen Pressure [Torr]

336 K

298 K

273 K

248 K

223 K

H2 + 2* ↔ 2H*

CH4 + 2* ↔ CH3* + H*

C2H4 + 2* ↔ π-C2H4**

C2H4 + 4* ↔ σ-C2H4****

C2H2 + 2* ↔ C2H2**

C2H6 + 3* ↔ C2H5** + H*

π-C2H4** + 2* ↔ σ-C2H4****

π -C2H4** + H* ↔ C2H5** + *

C2H5** + 3* ↔ σ-C2H4**** + H*

σ-C2H4**** ↔ C2H3** + H* + *

C2H2** + H* ↔C2H3** + *

C2H** + H* ↔ C2H2** +*


CCH3* + 2* ↔ CCH2** + H*

C2H5** + * ↔ CHCH3** + H*

CHCH3** + *↔ C2H3** + H*

C2H3** + *↔CCH2** + H*

C2H** + H* ↔CCH2** + *

C2H5** ↔ CH3* + CH2*

2CH2* + 2* ↔ σ-C2H4****

C2H3** ↔ CH* + CH2*

C2H2** ↔ 2CH*

C2H** ↔ CH* + C*

CHCH3** ↔ CH3*+ CH*

CH3* + C* ↔ CCH3* + *

CCH2** ↔ CH2* + C*

CHCH3** + 2* ↔ C2H4****

C2H3** ↔ CCH3* + *

C2H2**↔ CCH2**

C* + H* ↔ CH* + *

CH2* + * ↔ CH* + H*

CH3* + * ↔ CH2* + H*

Ethane Hydrogenolysis Reaction

H2 + 2* ↔ 2H*

CH4 + 2* ↔ CH3* + H*

C2H6 + 3* ↔ C2H5** + H*

C2H5** + 3* ↔ σ-C2H4**** + H*

σ-C2H4**** ↔ C2H3** + H* + *


CCH3* + 2* ↔ CCH2** + H*

C2H5** + * ↔ CHCH3** + H*

CHCH3** + *↔ C2H3** + H*

C2H3** + *↔CCH2** + H*

C2H5** ↔ CH3* + CH2*

CHCH3** ↔ CH3*+ CH*

CH2* + * ↔ CH* + H*CH3* + * ↔ CH2* + H*

Model Reduction to Rate Expressions

Full mechanism

Reduced mechanism

Rate equation

Sensitivity analysisPrincipal component analysis

Elementary rate comparisonRate determining stepPartial equilibriumAbundant adsorbate assumptions

Full mechanism

Reduced mechanism

Rate equation

Full mechanism

Reduced mechanism

Rate equation

Full mechanism

Reduced mechanism

Rate equation

10-510-410-310-210-1100101

Reduced modelExperimental One step rate expressionC

H4 T

OF

[1/

s] 673K623K

573K

PC2H6

= 5 Torr

10-4

10-3

10-2

10-1

100

101

10 100 1000

Reduced modelExperimental One step rate expressionC

H4 T

OF

[1/s

]


673K623K573K

PC2H6

= 25Torr

Ethane Hydrogenolysis

Ethylene Hydrogenation

25


Ethylene Hydrogenation Rate Expression

Due to multiple abundant adsorbates, the reduced rate expression is too complex for a closed form equation

0.01

0.1

1

10

100

100 1000

ExperimentalReduced microkinetic model Reduced rate expression

TO

F [s

-1]


336 K

298 K

273 K

248 K

223 K


Search is done on atomic descriptors while running the full chemistry and reactor models

Optimal catalyst properties are identified

High Throughput MultiscaleModel‐based Catalyst Design

350 oC1 atm

Prasad et al., Chem. Eng. Sci. 65, 240 (2010)

4550

5560

6570

110120

130140

0

0.1

0.2

0.3

0.4

0.5

QH

[kcal/mol]QN

[kcal/mol]

Con

vers

ion

NH3 decomposition*NH*NH 33

*H*NH**NH 23 *H*NH**NH 2

*H*N**NH *2N*2N 2 *2H*2H 2

26


Identifying Bimetallic Catalysts

• Optimum heat of chemisorption of N of ~130 kcal/mol

• NiPtPt is a good prospective bimetallic surface

Surface Sub-surface

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 102.1 Ni 113.8


Emergent Behavior Verified Experimentally

3.0 Langmuir NH3

at 350K at UHV

Ammonia decomposes on Ni‐PtNo decomposition on other surfacesN‐Pt is the most active catalyst

Inte

nsity

(ar

b. u

nits

)

750700650600550500450400350

Temperature (K)

Thick Ni

Ni-Pt

Pt-Ni-Pt

Pt(111)

14 amu

Hansgen, Chen, and Vlachos, Nature Chem. 2, 484-489 (2010)

Ni-Pt-Pt

27




Accuracy




MKM uses


Kinetic Monte Carlo

Outline


Co

Ni

Co/Pt

Ni/Pt

Theory

Pt

-5.6 -5.4 -5.2 -5.0 -4.8 -4.6600

650

700

750

800

850

900

950

Co826 K

Ni/Pt627 K

Co/Pt745 K

TP

D p

eak

(K

)

N binding energy (eV)

Experiment

Hansgen, D. A. et al. J. Chem. Phys. 2011, 134(18), 184701.

Typical Descriptor Fails to Describe Experimental Trends

20 exp( ( ) / ( ))NN a N B

H

d kE k T

dT

• Binding energy on terrace sites is not a good descriptor, especially for bimetallic surfaces

28


Tupy et al., ACS Catal. 2, 2290 (2012)

Can be Important

0 2 4 6 8 100

1

2

3x 10

4

Particle Diameter, d (nm)

TOF (s‐1)

Octahedral

Lean Kitchin et al., Surf. Sci. 544, 295, (2003)

Single Metal

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8

TO

F, s

-1

Particle size, nm

NH3 on Ru

Bimetallics

CO+O2 Pt/Au Ni/Pt

Stamatakis and Vlachos, in prep.Karim et al., J. Am. Chem. Soc. 131, 12230 (2009)

Tupy et al., ACS Catal. 2, 2290 (2012)


Instead of simulating dynamics, KMC focuses on rare events

Simulates reactions much faster than Molecular Dynamics

Incorporates spatial information contrary to micro‐kinetic models

The Kinetic Monte Carlo Approach

CO(gas) + OH COOH

reactants

products

Potential Energy Surface

Metal surface

transitionstate

‡

B

E‡k TB

rxnrxn

k T Qk e

h Q

29


Graph‐Theoretical KMC Approach

• Lattice, reactions represented as graphs

Stamatakis and Vlachos, J. Chem. Phys. 134, 214115 (2011); http://www.dion.che.udel.edu/downloads.php

O2(top,top)

O(fcc)

O2**

O*

O*

O2* 2O*

O(fcc)

• Subgraph isomorphism used to identify possible reactions & map them on the lattice


Features of Graph‐Theoretical KMCComplex chemistries1

Accurate lateral interactions1

Microscopic reversibility and

thermodynamic consistency

Fast algorithms2

Multiple facets, nanoparticles,

clusters, multifunctional materials1

Au6‐1/MgO

stepsterraces

Pt(211)

DFT Energies (eV)

Model H

amiltonian Energies (eV)

CV = 0.027384 eV per site

‐5 ‐4 ‐3 ‐2 ‐1 0

‐5

‐4

‐3

‐2

‐1

0

1Cat KMC Review: Stamatakis and Vlachos, ACS Cat. 2, 2648 (2012)2Multiscale KMC Review: Chatterjee and Vlachos, J. Comp.-Aided Mat. Design 14, 253 (2007)

Ni/Pt ‐ EXAFS

30


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

Schematic of Overall Process on Bimetallics: Minimum Energy Path Thinking


NiPtPt

CoPtPt

N = 0.3

Exp. 625 K 745 K

N2 Desorption on NiPtPt and CoPtPt

CoPtPt is worse catalyst than NiPtPt

Weaker N binding

N‐N attractive interactions render desorption slower

31


First‐Principles KMC Resolves Structure Sensitivity

Co

Ni

Co/Pt

Ni/Pt

Theory

Pt

-5.6 -5.4 -5.2 -5.0 -4.8 -4.6600

650

700

750

800

850

900

950

Co826 K

Ni/Pt627 K

Co/Pt745 K

TP

D p

eak

(K

)

N binding energy (eV)

Experiment

• Flat surfaces: strong N binding results in high desorption temperature, well described by Redhead theory

KMC

Ni-Pt-Pt

• Steps are responsible for the low N2

desorption temperature on Ni/Ptand Co/Pt surfaces


End

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