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Microkinetic Modeling

Modern Methods in Heterogeneous Catalysis Lectures at Fritz-Haber-Institute. Microkinetic Modeling. Berlin, January 8, 2010. Cornelia Breitkopf Technische Universität München Institut für Technische Chemie. Introduction. Traditional approach

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Microkinetic Modeling

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  1. Modern Methods in Heterogeneous Catalysis Lectures at Fritz-Haber-Institute Microkinetic Modeling Berlin, January 8, 2010 Cornelia Breitkopf Technische Universität München Institut für Technische Chemie

  2. Introduction • Traditional approach introduce reactants in a black box (catalytic reactor) obtain macroscopic kinetic rate constants use rate equation for reactor design • New approach feed “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) no catalyst design catalyst + reactor design

  3. Traditional approach Microkinetic analysis is a different approach !

  4. Outline • What is microkinetic analysis ? • Which parameters and theories are needed ? • How to derive BrØnsted-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

  5. Why Kinetic Studies ? • Industrial catalysis • Major aspect: effective catalytic processes Need for efficient approaches to enhance development • Development and optimization of catalytic processes • Chemical intuition and experience • Supplement with quantitative analysis

  6. Aspects of kinetics studies • Kinetics studies for design purposes • Kinetics studies of mechanistic details • Kinetics as consequence of a reaction mechanism

  7. 1. Kinetics studies for design purposes • Results of experimental studies are summarized in the form of an empirical kinetic expression • Design of chemical reactors • Quality control in catalyst production • Comparison of different brands of catalysts • Studies of deactivation • Studies of poisoning of catalysts

  8. 2. Kinetics studies of mechanistic details • Experimental kinetic study used to determine details in the mechanism • Problem: Different models may fit data equally well • Mechanistic considerations as guidance for kinetic studies

  9. 3. Kinetics studies as a consequence of a reaction mechanism • Deduction of kinetics from a proposed reaction mechanism • Historically macroscopic descriptions of the reaction kinetics were used • Today, detailed scientific information available • Guidance for catalytic reaction synthesis at various levels of detail • Hierarchical studies

  10. Levels of Catalytic Reaction Synthesis

  11. Study of reaction mechanisms Experiments on well-defined systems • Spectroscopic studies on single crystal surfaces • Structure and reactivity of well-defined catalyst models • Detailed calculations • for individual molecules • and intermediates • Electron structure calculations including calculations for transition states • Monte Carlo (Kinetic MC)

  12. Key Problems of Kinetic Studies

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

  14. Key problems for kinetic studies • Analogy may misleading

  15. Key problems for kinetic studies • Simple kinetics  simple mechanism

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

  17. Microkinetic Analysis

  18. Microkinetics • Reaction 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.

  19. Microkinetics • Convenient 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 of • Reaction kinetic data • Spectroscopic observations • Microcalorimetry and TPD

  20. Microkinetic Analysis • Combination 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

  21. 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 no initial assumption

  22. What delivers MA ? • Expected to describe experimental data from • Steady-state reaction kinetic data + • Data from related experimental studies • TPD • Isotope-tracer studies • Spectroscopic studies • Feature: usage of physical and chemical parameters that can be measured independently or estimated by theory

  23. Reaction Mechanism • Net reaction A2 + 2 B 2 AB consists of a number of steps A2 + B A2B A2B + B 2 AB • Concept of elementary steps: further subdivision and introduction of hypothetical intermediates A2 + B A2B A2B + B A2B2 A2B2 2 AB

  24. Elementary Reactions • A 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 Thekey featureof a mechanistic kinetic model is that it isreasonable,consistent with known dataandamenable to analysis.

  25. Langmuir-Hinshelwood mechanisms • Simplest class of reaction mechanisms • Three types of reaction steps • Adsorption of molecules from gas phase • Reaction between adsorbed molecules • Desorption of adsorbed molecules • Neglect of surface diffusion (surface diffusion is fast !) • Validity of LH models has been subject of long and heated discussions

  26. Arguments for LH mechanisms • Adequate description of essential physics • Description of adsorbates competing for adsorption sites based on thermodynamic stability • Limits for r 0 and p 0 are qualitatively correct • Many 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.

  27. Complications in Kinetic Studies • Kinetic equations are non-linear • Elementary steps are not necessarily first-order. • Inerts • Inert surface species need to be treated. • Non-consecutive steps • Elusive intermediates • The mechanism may contain intermediates, which have not been observed experimentally. • Undetectable steps • Order of slow and fast steps ! • Dead ends

  28. Parameters and Theory

  29. Parameters for MA • Sticking coefficients • Surface bond energies • Preexponential factors for surface reactions • Activation energies for surface reactions • Surface bonding geometries • Active site densities and ensemble sizes

  30. Theory behind the parameters • Collision and transition-state theory • Molecular orbital correlations • Bond-order-conservation • Electronegativity scales • Drago-Wayland correlations • Proton affinity and ionization potential correlations • Activation-energy-bond-strength correlations • Evans-Polanyi-correlation (volcano, Sabatier) • Bond-energy-desciptors

  31. 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 estimatedtheoretically or experimentally. - Framework for quantitative interpretation, generalization, and extrapolation of experimental data and theoretical concepts for catalytic processes

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

  33. Collision Theory • Bimolecular rate constant • Preexponential factor • Example: with Ps 1 and estimate of AB •  upper limit for preexponential factor

  34. CT- Bimolecular surface reaction • Modification to represent bimolecular reactions between mobile species on surfaces

  35. CT- Adsorption processes • Use 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

  36. Transition-State Theory (TS) • Incorporation of details of molecular structure • Critical assumption: equilibrium between reactants and activated complex and products • Bimolecular gas-phase reaction A + B AB# C + D • Potential energy diagram as multidimensional surface • Definition of a reaction coordinate

  37. Transition-State Theory • Ideal gas equilibrium constant for the activated complex AB# • Rate of chemical reaction

  38. TS Theory • Macroscopic 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

  39. TS Theory • Molecular partition function for a gas-phase species is a product of contributions from translational, rotational and vibrational degrees of freedom

  40. 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)

  41. TS – Adsorption processes 1) A(g) A# A* • Rate of reaction for an activated complex of complete surface mobility

  42. TS – Adsorption processes 2) A(g) + * A# A* • Rate of reaction for an immobile activated complex

  43. TS – Desorption processes A* A#A(g) • Rate of desorption

  44. TS – Preexponential Factors Estimates

  45. TS – Preexponential Factors Estimates

  46. 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*

  47. 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 Evans-Polanyi correlation

  48. Volcano curves • One of the most fundamental concepts in heterogeneous catalysis is the volcano curve • Empirically 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 ?

  49. Volcano curves • Which 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.

  50. Volcano curves • Generally many volcano curves are plotted as function of a bulk heat of formation – only bulk thermo-chemical data are widely available • Need for databases of relevant surface thermo-chemical data • Concepts for describing activation energies – BrØnsted-Evans-Polanyi (BEP) relation

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