Microkinetic ModelingCornelia BreitkopfTechnische Universitt MnchenInstitut fr Technische ChemieBerlin, January 8, 2010Modern Methods in Heterogeneous CatalysisLectures at Fritz-Haber-Institute

IntroductionTraditional approach introduce reactants in a black box (catalytic reactor)obtain macroscopic kinetic rate constantsuse rate equation for reactor design

New approachfeed new-age black box (computer) with rate constants of elementary steps in catalytic cycle

obtain reaction rate, selectivity + information on each step(irreversible, reversible, kinetically significant, rate determining, information about intermediates)

Microkinetic analysis is a different approach !Traditional approach

OutlineWhat is microkinetic analysis ?

Which parameters and theories are needed ?How to derive Brnsted-Evans-Polanyi and volcano plots ?How to apply Sabatier principle and bond energy descriptors ?What are Ying-Yang models ?

Which informative experiments exist ?How to build a microkinetic model ?

Literature and examples for self study

Why Kinetic Studies ?Industrial catalysisMajor aspect: effective catalytic processes Need for efficient approaches to enhance development

Development and optimization of catalytic processesChemical intuition and experienceSupplement with quantitative analysis

Aspects of kinetics studies

Kinetics studies for design purposesKinetics studies of mechanistic detailsKinetics as consequence of a reaction mechanism

1. Kinetics studies for design purposesResults of experimental studies are summarized in the form of an empirical kinetic expressionDesign of chemical reactorsQuality control in catalyst productionComparison of different brands of catalystsStudies of deactivationStudies of poisoning of catalysts

2. Kinetics studies of mechanistic detailsExperimental kinetic study used to determine details in the mechanismProblem:Different models may fit data equally well

Mechanistic considerations as guidance for kinetic studies

3. Kinetics studies as a consequence of a reaction mechanismDeduction of kinetics from a proposed reaction mechanismHistorically macroscopic descriptions of the reaction kinetics were usedToday, detailed scientific information availableGuidance for catalytic reaction synthesis at various levels of detailHierarchical studies

Levels of Catalytic Reaction Synthesis

Study of reaction mechanismsExperiments on well-defined systems

Spectroscopic studies on single crystal surfacesStructure and reactivity of well-defined catalyst modelsDetailed calculationsfor individual moleculesand intermediates

Electron structure calculations including calculations for transition statesMonte Carlo (Kinetic MC)

Key Problems of Kinetic Studies

Key problems for kinetic studies Deduction of kinetics from net reaction is not possible

Key problems for kinetic studies Analogy may misleading

Key problems for kinetic studies Simple kinetics simple mechanism

Key problems for kinetic studies Different reaction mechanisms may predict the same overall reaction rate; unable to distinguish between the two mechanisms

Microkinetic Analysis

MicrokineticsReaction kinetic analysis that attempt to incorporate into the kinetic model the basic surface chemistry involved in the catalytic reaction

The kinetic model is based on a description of the catalytic process in terms of information and /or assumptions about the active sites and the nature of elementary steps that comprise the reaction scheme.

MicrokineticsConvenient tool for the consolidation of fundamental information about a catalytic process and for extrapolation of this information to other conditions or catalysts involving related reactants, intermediates and products.

Use of kinetic model for description ofReaction kinetic dataSpectroscopic observationsMicrocalorimetry and TPD

Microkinetic AnalysisCombination of available experimental data, theoretical principles and appropriate correlations relevant to the catalytic process in a quantitative fashion Starting point is the formulation of the elementary chemical reaction steps that capture the essential surface chemistry Working tool that must be adapted continually to new results from experiments

MA what is different ?No initial assumptions !Which steps of the mechanism are kinetically significant ?Which surface species are most abundant ?Estimations of the rates of elementary reactions and surface coverages are a consequence of the analysis not a basis !Beyond the fit of steady-state reaction kinetic data

What delivers MA ?Expected to describe experimental data fromSteady-state reaction kinetic data +Data from related experimental studiesTPDIsotope-tracer studiesSpectroscopic studiesFeature: usage of physical and chemical parameters that can be measured independently or estimated by theory

Reaction MechanismNet reaction A2 + 2 B2 ABconsists of a number of steps A2 + BA2BA2B + B2 ABConcept of elementary steps: further subdivision and introduction of hypothetical intermediatesA2 + BA2BA2B + BA2B2A2B22 AB

Elementary ReactionsA step in a reaction mechanism is elementary if it is the most detailed, sensible description of the step.A step which consists of a sequence of two or more elementary steps is a composite step.What makes a step in a reaction mechanism elementary ?depends on available information

The key feature of a mechanistic kinetic model is that it is reasonable, consistent with known data and amenable to analysis.

Langmuir-Hinshelwood mechanismsSimplest class of reaction mechanismsThree types of reaction stepsAdsorption of molecules from gas phaseReaction between adsorbed moleculesDesorption of adsorbed moleculesNeglect of surface diffusion (surface diffusion is fast !)Validity of LH models has been subject of long and heated discussions

Arguments for LH mechanismsAdequate description of essential physicsDescription of adsorbates competing for adsorption sites based on thermodynamic stabilityLimits for r 0 and p 0 are qualitatively correctMany catalytic reactions happen to proceed at high coverages by intermediates. At these conditions the assumptions in the LH treatment are more or less correct.Different kinetic expressions results in the same fits.

Complications in Kinetic StudiesKinetic equations are non-linearElementary steps are not necessarily first-order.InertsInert surface species need to be treated.Non-consecutive stepsElusive intermediatesThe mechanism may contain intermediates, which have not been observed experimentally.Undetectable stepsOrder of slow and fast steps !Dead ends

Parameters and Theory

Parameters for MASticking coefficientsSurface bond energiesPreexponential factors for surface reactionsActivation energies for surface reactionsSurface bonding geometriesActive site densities and ensemble sizes

Theory behind the parametersCollision and transition-state theoryMolecular orbital correlationsBond-order-conservationElectronegativity scalesDrago-Wayland correlationsProton affinity and ionization potential correlationsActivation-energy-bond-strength correlationsEvans-Polanyi-correlation (volcano, Sabatier)Bond-energy-desciptors

Concepts A fundamental principle in microkinetic analysis is the use of kinetic parameters in the rate expressions that have physical meaning and, as much as possible, that can be estimated theoretically or experimentally.

-Framework for quantitative interpretation, generalization, and extrapolation of experimental data and theoretical concepts for catalytic processes

Collision Theory (CT)Rate for a gas-phase bimolecular reaction

Collision TheoryBimolecular rate constant

Preexponential factor

Example: with Ps 1 and estimate of AB upper limit for preexponential factor

CT- Bimolecular surface reactionModification to represent bimolecular reactions between mobile species on surfaces

CT- Adsorption processesUse for definition of rate constants for adsorption processes in terms of the number of gas-phase molecules colliding with a unit surface area Fi

Example: with (sticking coefficient) 1 upper limit for preexponential factor and rate constant for adsorption

Transition-State Theory (TS)Incorporation of details of molecular structureCritical assumption: equilibrium between reactants and activated complex and productsBimolecular gas-phase reaction A + B AB# C + DPotential energy diagram as multidimensional surface Definition of a reaction coordinate

Transition-State TheoryIdeal gas equilibrium constant for the activated complex AB#

Rate of chemical reaction

TS TheoryMacroscopic formulation of TS is obtained by writing K# in terms of standard entropy, S0#, and enthalpy, H0# changes

Microscopic formulation of TS is obtained by writing K# in terms of molecular partition functions Qi

TS TheoryMolecular partition function for a gas-phase species is a product of contributions from translational, rotational and vibrational degrees of freedom

TS Theory

Order-of-magnitude estimates

kBT/h = 1013 s-1qi,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)

TS Adsorption processes1)A(g) A# A*

Rate of reaction for an activated complex of complete surface mobility

TS Adsorption processes2) A(g) + * A# A*

Rate of reaction for an immobile activated complex

TS Desorption processes A* A# A(g)

Rate of desorption

TS Preexponential Factors Estimates

TS Preexponential Factors Estimates

Estimates for Activation EnergiesRate constant = f (A ; EA)EA estimation difficult1)Empirical correlations for EA from heats of reactionBond-order conservation (BOC) by Shustorovich

A2 A* + A*

Estimates for Activation Energies2)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 Evans-Polanyi correlation

Volcano curvesOne of the most fundamental concepts in heterogeneous catalysis is the volcano curveEmpirically established:activity of catalysts = f ( parameter relating to the ability of the catalyst surface to form chemical bonds to reactants, reaction intermediates, or products)Guidelines in the search for new catalysts

Problem:Which parameters determine the catalytic activity ?

Volcano curvesWhich parameters ?activity = f ( electronic properties )

activity = f ( bond energies )Bond energies have been derived for bulk crystalline structures (carbides, sulfides)*, oxide properties**, various atomic or molecular chemisorption energies***Which is the most relevant energy ?

* J. Catal. 216 (2003) 63.** Catal. Lett. 8 (1991) 175.*** J. Catal. 50 (1977) 228.

Volcano curvesGenerally many volcano curves are plotted as function of a bulk heat of formation only bulk thermo-chemical data are widely availableNeed for databases of relevant surface thermo-chemical data

Concepts for describing activation energies Brnsted-Evans-Polanyi (BEP) relation

Brnsted-Evans-PolanyiBEP: Activation energy = linear function of reaction energyBackground: quantum-chemical calculations

Interesting outcome after extensive DFT calculationsClasses of similar reactions follow the same universal relationship*

* J. Catal. 209 (2002) 275.

vJ. Catal. 209 (2002) 275.This linear BEP correlation in a number of cases leads directly tovolcano curves where the fundamental parameter is the dissociative chemisorption energy ofthe key reactant.

Brnsted-Evans-Polanyi

J. Catal. 209 (2002) 275.Case studies:

(1) A2 + 2* 2 A*(2) A* + B AB + *

- A2 binds weakly coverage negligible (2) may involve several elementary steps including adsorption of B- approximation: negligible coverage of BIndustrial examples:Ammonia synthesis A = N B = 3/2 H2Brnsted-Evans-Polanyi

Brnsted-Evans-Polanyi* J. Catal. 209 (2002) 275.

Brnsted-Evans-Polanyi* J. Catal. 209 (2002) 275.

Brnsted-Evans-Polanyi* J. Catal. 209 (2002) 275.

Sabatier principleP. Sabatier, Berichte der Deutschen Chem. Gesellschaft 44 (1911) 1984.

Significant step in its time toward a rational understanding of catalysisDefinition: maximum rate will be achieved by a catalyst whose combination with reactants is of intermediate stability to be effectively activeRephrase: an optimal heterogeneous catalyst provides neither too weak nor too strong interactions of its surface with the reaction partners in the rate determining step*application to design of catalysts by means of quantitative description of interaction strengths - BED * J. Catal. 216 (2003) 63.

Brnsted-Evans-Polanyi - BEPEmpirical knowledge of catalysis and catalysts is enormous Handbook of Heterogeneous CatalysisPd, Pt-RhNO removalCo, Fe, RuFischer-Tropsch catalystsPt, Pd, AgOxidation Application to activation of diatomic moleculeN2 + 3 H2 2 NH3n CO + (2n+1) H2 CnH2n+2 + n H2O..NO activation ..O2 activation

* J. Catal. 209 (2002) 275.

BEPTwo main parts: dissociation of reacting moleculesremoval of dissociation productsRate of dissociation is determined by activation barrier for dissociation EaRate of product removal is given by stability E of surface intermediates* J. Catal. 209 (2002) 275.

BEP* J. Catal. 209 (2002) 275.fundamental Bronsted-Evans-Polanyicorrelation

BEPQuestionsWhy is the relationship between Ea and E linear ?Why is it structure-dependent ?Why is it adsorbate-independent ?AnswersFor a given metal surface, the transition state structures are essentially independent of the molecule and the metal consideredTransition states do depend on local structureTransition states are similar for different reactants

* J. Catal. 209 (2002) 275.

BED bond energy descriptors

Application of bond-energy conceptsDescriptors for chemical interactions between X = O, C, H and metals of the transition state rows of PSEYin-Yang method

* J. Catal. 216 (2003) 63.Total energy per unit cellof the bulk compoundEnergy of the same unit cellwith atoms X removedEnergy of the same unit cellwith all atoms except X removedNearest neighboures

BED bond energy descriptors

Application to LH-mechanisms for adsorption of oxygen, sulfur, ethene

Description of hydrogenation of ethene, benzene, HDS of DBT, alloying to predict matching effects

* J. Catal. 216 (2003) 63.

Consistency of the ModelStoichiometric consistencyreactants products :reactants, intermediates have to be formed and consumed to form products

Thermodynamic consistencyIf two or more different sequences lead from reactants to products, these sequences must describe the same gas-phase thermodynamics.

Thermodynamic ConsistencySince the thermodynamic properties of the reactants and products are known, it is essential to ensure that the kinetic model is build so that it is consistent with these properties.

Depending on how the model is parameterized (e.g. in terms of ki,for and Ki,eq, or in terms of ki,rev and Ki,eq), one of the previous equations of thermodynamic consistency must be used for each linear combination of steps that leads to an overall stoichiometric reaction.

Informative Experiments

Experimental TechniquesHow can information from these techniques be used inmicrokinetic analysis ?Physical techniques bulk structure, surface area, pore structureSpectroscopic studies probe of composition and morphology of the surfaceKinetic & therm. studies probe catalytic properties of the surface; quantification of kinetic parameters

X-ray DiffractionCrystal structure determines the coordination of the various catalyst components and bond distances between elementssurface structure and nature of active sites

Measurement of average particle sizes with help of Scherrer equationstructure-sensitive behaviour

Analysis of peak shapes can be used to probe the size of crystallitesparticle size distribution

Photoelectron Spectroscopy - XPSQuantitative analysis of surface composition! Surface and bulk composition may be different

Information about surface oxidation state

Use of treatment chamber quantification of surface coverage by a particular species

UPS: probe of valence levels of the catalyst surface

Infrared SpectroscopyProbe for vibrational properties of the catalyst surface groups

Example: O-H stretching vibrationIntensity of O-H band in the IR spectrum provides a measure of the surface hydroxyl concentration depending on the catalyst treatment Position of O-H band gives information about the nature of the hydroxyl group

Building a Microkinetic Model

Building a Microkinetic ModelBuild a set of elementary reactions which reflect all experimental and theoretical informationCalculate for each reaction the thermodynamics(for all gaseous species and all adsorbed species)

Choose material balance of an appropriate reactor and characterize in and out flows

Reactor ModelsGeneral types of ideal reactorsBatch reactorContinuous-flow stirred tank reactor (CSTR)Plug flow reactor (PFR)

Typical characteristics of reactorsBatch: reactor volume VR and holding time tFlow: reactor volume VR and space time

Reactor Models in MAFor catalytic reactions the space time may be replaced by P, defined as number of catalytic sites in the reactor, SR, divided by the molecular flow rate of feed to the reactor, FMaterial balance for species i in a general flow reactor is given by

Reactor Models in MABatch reactor

with I as turnover frequency (number of reaction events per active site per second)

CSTR

PFR

Microkinetic AnalysisCombination of available experimental data, theoretical principles and appropriate correlations relevant to the catalytic process in a quantitative fashion

Way down South in the land of cottonWhere good mints juleps are not forgottenAn old farmer sits on his plantationThinking up problems to astound the nationLindemann and Hinshelwood can stand it no moreWhile Smith and Carberry have run for the doorNow there is one as he told it to meAnd I give it to you, completely for freeWe know kinetics is a staid sort of sportIf reaction order is all theres to reportSo weve studied about reactor designIn detail and elegance quite so fineMixing models have been disussedWhere proper equations are a mustAge distributions become important hereAn intricate analysis, it is clearNow this is the question to give you fitsAn excellent chance to test your witsOf these distributions there are many its sureDerived from a theory assuredly most pure

Residence time, internal, and exit age All we owe to Danckwerts, that clever sage What are they, please, a clear explanation Combining words with an appropriate equation Relationships between them are almost horrendous A discussion of this would be simply tremendous When youve written all this consider youre done Now wasnt that all just good clean fun If you did what was asked, and that I hope Then with chemical reactors youre able to cope 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 soThe more we learn, the less we know !John B. Butt

LiteratureR.D. Cortright, J.A. DumesicKinetics 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. RekoskeThe Microkinetics of Heterogeneous CatalysisACS, Washington 1993.

P. StoltzeMicrokinetic simulation of catalytic reactionsin: Progr. Surf. Sci. 65 (2000) 65-150.

O. HinrichsenDechema-Kurs Angewandte Heterogene Katalyse, Bochum 2001.

Research Topic task started on Wed Dec 23, 2009 at 8:13 AM

4 Research Topic candidates were identified in CAPLUS and MEDLINE. using the phrase "microkinetic modeling and heterogeneous catalysis"

33 references were found containing both of the concepts "microkinetic modeling" and "heterogeneous catalysis".

-First-Principles Modeling of Coverage-Dependent Rates of Catalytic Oxidations. Schneider, William F. Abstracts, 38th Great Lakes Regional Meeting of the American Chemical Society, Chicago, IL, United States, May 13-16 (2009).-A C1 microkinetic model for methane conversion to syngas on Rh/Al2O3. Maestri, Matteo; Vlachos, Dionisios G.; Beretta, Alessandra; Groppi, Gianpiero; Tronconi, Enrico. AIChE Journal (2009), 55(4), 993-1008. -Heterogeneous catalysis for hydrogen production and purification: First-principles, experiments, and microkinetic modeling. Mavrikakis, Manos. Abstracts of Papers, 237th ACS National Meeting, Salt Lake City, UT, United States, March 22-26, 2009 (2009),

for the latest literature search please contact:Cornelia.Breitkopf@mytum.de

Example

Methane Oxidation by Mo/V-OxidesM.D. Amiridis,J.E. Rekoske, J.A. Dumesic, D.F. Rudd, N.D.Spencer, C.J. Peireira. AIChE J. 37 (1991) 87.

Development of a microkinetic model of the partial oxidation of methane over MoO3-SiO2 and V2O5- SiO2catalysts

Problem: limited data availableStart : seek of experimental data and theoretical concepts from related or analogous catalytic systems

continuedAim is to reproduce the kinetic data for methane partial oxidation CH4 CH3OH, HCHO, CO, CO2, H2O

Macrokinetic analysis of the problemKinetic investigations showed quantitative differences in the performances of MoO3-SiO2 and V2O5-SiO2 catalystsSelectivity to CO2 at low CH4 conversion was zero for the V-catalyst; for the Mo-catalyst it was between 10-20 %CO2 is a direct product of methane oxidation over Mo-catalyst and a secondary over V-catalystNeed of two pathways to CO2 to describe both catalysts

Macrokinetic analysis of the problemAddition of sodium leads to decrease in conversion level and drop in the selectivity to HCHO for both catalystsEffect to be analyzed by semiempirical MO calculationsd-band characteristics: empty, to reduce CO2 formationlocated at sufficient low energy to accept electrons during methane activation to form methoxy and hydroxyl surface speciestetrahedral coordination for high conversion

Development of the modelOxidation of CO

Kinetic investigations on V-catalyst@ 733 K reaction is first order in CO and zero order in oxygenActivation energy in T: 673-773 K is 25.2 kcal/mol

Development of the modelOxidation of HCHOKinetic investigations on Mo-catalyst @ 600-925 KCO is principal product with small amounts of CO2 at higher TKinetic investigations on V-catalyst @ 500-900 KCO production passes through a maximum near 800 K and CO2 production increases monotonically with TIR data

Development of the modelOxidation of CH3OH

Catalytic activity of Mo-catalyst starts at 500 K withcomplete conversion at 700 KMethoxy species (IR, EPR)

Development of the modelOxidation of CH4

Two possible ways of methane adsorption on the surface1) initial formation of a precursor state on the surface and consecutive dissociation into methoxy- and hydroxyl groups2) activation of surface Oxygen to O- and consecutive dissociative adsorption of methane

Development of the modelMechanism as combination of all steps

Development of the modelCombined consideration of the oxidations of carbon monoxide, formaldehyde, methanol, and methane

Agreement with available literature

No assumptions about the existence of rate-determining steps or most abundant surface intermediates

All steps reversible; two pathways for CO2 formation

Calibration of the modelEstimation of preexp. factors

Estimation of H for each elementary step+ additional use of Evans-Polanyi correl.

Estimation of bond strength (constrained to physically reasonable limits)

Comparison of Experiment and Model

Comparison of Experiment and ModelAgreement of model and experimental data for different temperatures and different experimental conditions

Active Steps during CH4 partial oxidation

Molecular Orbital Studies Coordination number affects the electronic structure of transition metal oxides

Major effect of cation coordination is the energy of the d bands

The number of d-orbitals with high energy number increases with coordination

Analysis of Adsorption