Presentation on theme: "Prof. Gregory S.Yablonsky"— Presentation transcript:
1 Prof. Gregory S.Yablonsky What happens at the crossroads between Chemical Engineering and Mathematics?Prof. Gregory S.YablonskyParks CollegeSaint Louis University. USADept. of Chemical Engineering,Washington University in St. Louis, USA
2 “I gave my mind a thorough rest by plunging into a chemical analysis” (Sherlock Holmes, “The Sign of Four”, Chapter 10)
3 Different points of view David Hilbert( ), the greatest German mathematician : “Chemical stupidity”…Auguste Comte ( ), the French philosopher, founder of sociology:“Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry…if mathematical analysis should ever hold a prominent place in chemistry--an aberration which happily almost impossible--it would occasion of rapid and widespread degeneration of that science”
4 What is Mathematics? What is Chemistry? It is always difficult to answer simple questions.One can say:Mathematics is about specialsymbolic reasoning or symbolic engineeringChemistry is about transformation of substancesOr in another way:Mathematics is Newton, Leibnitz, Hilbert,Hardy…Chemistry is Lavoisier, Dalton, Avogadro, Mendeleev…Chemical Engineering is Danckwerts, Damkoehler,Aris, Amundson, Frank-Kamenetsky…
5 What is Chemical Engineering? Chemical Engineering = Chemistry + Transport Material PropertiesMost of chemical processes (> 90%) occur with participation of special materials – catalysts, which composition is ill-defined.Main topics:1) Chemistry2) Transport3) Catalyst properties
6 Mathematical Chemistry There are more than 6 millions of references on“mathematical chemistry”(Internet)Journal of Mathematical Chemistry (since 1987)MaCKiE, “Mathematics in Chemical Kinetics and Chemical Engineering” (regular workshopsince 2002)MATCH, Communications in Mathematics and Computer Chemistry
7 The mathematical impact into chemistry is growing Models of quantum chemistry (DFT-modeling)Computational Fluid DynamicsMonte-Carlo modelingStatistical analysisFT (Fourier Transformation) based experiment
8 The most important chemical problems Sustainability Problems = Energy via Chemistry,e.g. development of the efficient C1 transformation system (CO2 sequestration, CO+H2, CO2+CH4), photocatalytic system of water splitting, hydrocarbon oxidation system, etc.These problems have to be solved urgently.
9 Revealing chemical complexity What is a chemical complexity?There are many substanceswhich participate in many reactions.Typically, chemical reactionsare performed over the catalysts.Typically, chemical systemsare non-uniform and non-steady-state.The chemical composition is changing in space and time.
10 Structure-Activity Relationships “Materials-Pressure Gap” Well-definedSurface StructureSingle CrystalSingle ComponentPolycrystallineIncreasing ComplexityIncreasing PressureOne of the goals in our lab is to understand the relationship between catalyst structure and its activity. One way for us to understand this relationship is to bridge the pressure and materials gap. Under process conditions, it is often difficult to extract intrinsic properties of a catalyst. Intrinsic properties are properties that are directly related to the catalyst composition. Therefore, in order to extract these intrinsic properties, scientists must use surface science techniques under vacuum conditions to study single crystals. By performing single particle experiments using a single component polycrystalline material, we are developing an initial methodology to bridge this pressure and materials gap. Using the TAP reactor, we can define single particles as either single crystals or an industrial catalyst and perform identical experiments under the same conditions on both materials and directly compare the two results.?Multi-componentMulti-scalePolycrystallineHeterogeneous SurfaceDefectsChanges with ReactionTechnical Catalyst
11 However we still are very far from revealing chemical complexity, from solving “chemical structure -activity”problem
12 Decoding Chemical Complexity: Questions Questions before the decoding:What we are going to decode?What are experimental characteristics based on which we are going to decode the complexity?3. In which terms we are going to decode?
13 Examples of chemical reactions: Overall Reactions:2 H2 + O2 2H2O2SO2 +O2 2SO3According to chemical thermodynamics,Keq(T) = C2H2 0/ (C2H2 C02)Keq(T) = C2SO3 / (C2SO2 CO2)
14 An example:Hydrogen Oxidation 2H2 +O2 = 2H2O Detailed MechanismDetailed mechanism is a set of elementary reactions which law is assumed , e. g. the mass-action-lawAn example:Hydrogen Oxidation 2H2 +O2 = 2H2O1) H2 + O2 = 2 OH ; 2) OH + H2= H2O + H ; 3) H + O2 = OH + O;4) O + H2 = OH + H ; 5) O + H20 = 2OH; 6) 2H + M = H2 + M ; 7) 2O + M = O2 + M;8) H + OH + M = H2O + M; 9) 2 OH + M = H2O2 + M; 10) OH + O + M = HO2 + M;11) H + O2 + M = HO2 + M; 12) HO2 + H2 = H2O2 + H;13) HO2 +H2 = H2O +OH;14) HO2 + H2O = H2O2 + OH; 15) 2HO2 = H2O2 + O2; 16) H + HO2 = 2 0H;17) H + HO2 = H2O + O; 18) H + HO2 = H2 + O2; 19) O + HO2 = OH +H;20) H + H2O2 = H20 + OH; 21) O + H2O2 = OH +H02; 22) H2 + O2 = H20 + O;23) H2 + O2 + M = H202 + M; 24) OH +M = O + H + M; 25) HO2+OH=H2O+O2;26) H2 + O +M = H2O +M; 27) O + H2O + M = H202 + M; 28) O + H2O2 = H20 + O2;29) H2 + H2O2 = 2H2O; 30) H + HO2 + M = H2O2 +M
15 A matrix is the mathematical image of complex chemical system ( a chemical graph as well)“Atomic”(“molecular” matrix)Stoichiometric matrixDetailed mechanism matrixEnglish mathematician Arthur Cayley ( ), one of the first founders of linear algebra, applied its methods for enumerating isomers
16 Complexity 1. Catalytic reaction is complex itself Multi step character of the reactionIncluding generation of different intermediates2. Industrial catalysts are usually complex multicomponent solidsE.g. mixed transition metal oxides used in the selective oxidation+ supportA specifically prepared catalyst can exist in different catalyst statesthat are functions of oxidation degree, water content, bulk structure, etc.that have different kinetic properties (activity and selectivity)3. Catalyst composition changes in time under the influence of the reaction medium.
17 Chemical Kinetics = Reaction Rate Analysis Answers:Our Holy Grail is the Detailed MechanismOur main experimental basis isthe Reaction Rate, R(+data of some structural measurements)
18 Different goals of chemical kinetics: To characterize chemical activity of reactive media and reactive materials, particularly catalysts; to assist catalyst designTo reveal the detailed mechanismTo be a basis of kinetic model for reactor design and recommendations on optimal regimes
19 Different types of chemical kinetics Applied chemical kineticsDetailed kinetics (Micro-kinetics)Mathematical kinetics
20 Steady–state and non-steady-state measurements (1) In most of previous studies, a focus was doneon the steady-state experiments.Convectional transport was usedas a ‘measuring stick’.(2) In our studies, a focus was doneon non-steady-state experiments.Diffusional transport was used
21 Time Domain of Chemical Reactions (Paul Weisz window) Rates of reactions, moles product per cm3 of reactor volume per secondPetroleum geochemistry 5 x x 10-13Biochemical processes x x 10-8Industrial catalysis x 10-5
22 3 Methods to Kill Chemical Complexity Describe it in detail (“kinetic screening”)Panoramic description = Forget about it in a correct way (“thermodynamics”)Recognize complexity via the fingerprints (analysis of informative domains, critical behavior etc.)
23 State-by-State Kinetic Screening of Active Complex Materials A statement: For revealing and describing chemical complexity the following chemico-mathematical approaches are extremely usefulState-by-State Kinetic Screening of Active Complex MaterialsDescription of Models of Complex Behavior assisted by Advanced Thermodynamic ApproachesAnalysis of Complexity Fingerprints
24 Chemico-Mathematical Idea #1 = “Chemical Calculus” State-by-State Transient Screening (e.g., Temporal Analysis of Products, TAP)- John Gleaves, 1988To kinetically test a catalyst with a particular composition (particular state of the catalyst) that does not change significantly during this non-steady-state test.To perform such tests over a catalyst within a wide range of different composition prepared separately and scaled (the reduction/oxidation scale).Three Requirements:Insignificant catalyst change during a single non-steady-state experiment (e.g. one-pulse);Control of reactant amount stored/released by catalyst in a series of non-steady-state experiments (e.g. multi-pulse);Uniform chemical composition within the catalyst zone.Kinetic CharacterizationPreparing & ScalingSimple Stateof the Catalyst
25 Chemico-mathematical idea #2: Comparison between characteristics related to transport-only model (standard transport curves) and characteristics related to transport-reaction model.The goal is extracting the intrinsic chemical information.
26 Accumulation = Transport term + Reaction Term Mass - BalanceAccumulation =Transport term + Reaction Term
27 Kinetic Model-Free Analysis Reactor Model:Accumulation - Transport Term = Reaction RateBatch Reactor:NonCSTR:ConvectionPFR:ConvectionTAP:Diffusion
28 Chemico-mathematical idea #3: Propose a hypothesis about the reaction mechanism based on the kinetic fingerprints.
29 Typical Kinetic Dependence in Heterogeneous Catalysis (Langmuir Type Dependence) Irreversible ReactionReversible ReactionReaction RateReaction RateEquilibriumConcentrationConcentration
30 Critical Phenomena in Heterogeneous Catalytic Kinetics: Multiplicity of Steady-States in Catalytic Oxidation(CO oxidation over Platinum)C“Extinction”Reaction RateBA“Ignition”DCO Concentration
31 KINETIC CHARACTERIZATION OF ACTIVE MATERIALS, PARTICULARLY OF CATALYSTS
32 Complexity 1. Catalytic reaction is complex itself Multi step character of the reactionIncluding generation of different intermediates2. Industrial catalysts are usually complex multicomponent solidsE.g. mixed transition metal oxides used in the selective oxidation+ supportA specifically prepared catalyst can exist in different catalyst statesthat are functions of oxidation degree, water content, bulk structure, etc.that have different kinetic properties (activity and selectivity)3. Catalyst composition changes in time under the influence of the reaction medium.
33 Combinatorial catalysis (mostly steady-state procedure) It is the most typical method of catalyst preparation.Combination of catalyst compositionsCombination of regime parameters(temperature, pressure etc)Testing under steady-state conditions using a battery of simple reactors (plug-flow reactors, PFR)
34 Kinetic Characterization Our Key Idea of State-by-State Transient ScreeningTo kinetically test a catalyst with a particular composition (particular state of the catalyst) that does not change significantly during this non-steady-state test.To perform such tests over a catalyst within a wide range of different composition prepared separately and scaled, (e.g. the reduction/oxidation scale).Three Requirements:Insignificant catalyst change during a single non-steady-state experiment (e.g. one-pulse);Control of reactant amount stored/released by catalyst in a series of non-steady-state experiments (e.g. multi-pulse);Uniform chemical composition within the catalyst zone.Kinetic CharacterizationPreparing & ScalingSimple Stateof the Catalyst
35 The main methodological and mathematical idea is to perform the integral analysis of data obtained using an insignificant perturbation: 1) insignificant perturbation 2) integral analysis
38 Dimensionless Gas Concentration Dimensionless Axial Coordinate Thin-Zone (TZ) IdeaCatalyst zoneInert zone0.0.1.2.22.214.171.124.7.8.91.00.00.25.50.751.001.251.501.752.000.0.1.126.96.36.199.188.8.131.52.00.00.25.50.751.001.251.501.752.00Dimensionless Gas ConcentrationL/LVacuum SystemDimensionless Axial Coordinate
39 Thin-Zone (TZ) TAP Reactor Inert zoneCatalyst zoneThin-Zone ApproachMatching Two Inert Zones Through the Catalyst Zone:Dimensionless ConcentrationFor concentrationsFor flowsTZ-model can be consideredas a diffusional CSTR:ConversionApparent rate constantDiffusional residence time inthe catalyst zone
40 Uniformity Is Achieved by Mixing Uniformity Is Insured by Diffusion TZTR vs CSTRCSTR:TAP:ConvectionDiffusionTZ-model can be consideredas a diffusional CSTR:ConversionApparent rate constantDiffusional residence time inthe catalyst zoneUniformity Is Achieved by MixingUniformity Is Insured by Diffusion(finite gradient)
41 TZTR vs Differential PFR ConvectionTAP:DiffusionConversionDifferential PFR:TZTR
42 Interrogative Kinetics (IK) Approach Was firstly introduced in the paper:Gleaves, J.T., Yablonskii, G.S., Phanawadee, Ph., Schuurman, Y.“TAP-2: An Interrogative Kinetics Approach” Appl. Catal., A: General, 160 (1997) 55.The main idea is to combine two types of experiments:A state-defining experiment in which the catalyst composition and structure change insignificantly during a kinetic testA state-altering experiment in which the catalyst composition is changed in a controlled manner
43 Unsteady-State Kinetics The Same Unsteady-State Kinetics Inert zoneCatalyst zoneState-definingPulsestimeInsignificant change0.0State-defining ExperimentThe StateState-Defining Kinetic Regime in a TAP ExperimentObserve Transient ResponsesFor the Reactant and ProductsUnsteady-State KineticsThe Gas Adsorbs, Reacts and DesorbsThe Small Amount of Gas in the ReactorThe Observed Responses AreEssentially the Same in a Small train of PulsesThe Same Unsteady-State KineticsThere is Something about The CatalystThat Stays the Same
44 Criteria of State Defining Experiment: Insignificant changeThe same shapeSmall number of pulsesState-defining ExperimentAn insignificant change in the pulseresponses within a train of pulsesIndependence of the shape of pulseresponse curves on pulse intensity.
45 TAP Multi-Pulse Experiment Combines State-Defining & State-Altering ExperimentInertReactantProductSmall number of pulsesInsignificant change0.0State-defining ExperimentLarge number of pulses0.0State-altering Experiment
46 Thin-zone and Single Particle Reactor Configurations Previously, the most recent reactor configuration has been the thin zone configuration in which the catalyst zone is made very thin in comparison to the whole length of the reactor. By changing to the single particle configuration, we are able to create a more uniform temperature and composition profile in the catalyst zone. These pictures are actually drawn to scale showing the size of the active particle surrounded by a sea of inactive, inert particles.Single-particle
47 Single Particle Catalyst Platinum powder catalystDiameter ~400 µmPacked in reactor middle surrounded by inert quartz particles with diameters between ~ µmReaction: CO oxidation400 μm platinum particleThe catalyst used for all of the experiments I will talk about today is a platinum powder catalyst. The size of the platinum particle was up to 400 micrometers in diameters. This picture gives you a sense of the small size of the particle in relation to a pencil point. Here I have some SEM images of the platinum particle showing that the particle is a polycrystalline material. For all my experiments, the platinum particle was packed in the middle of the reactor surrounded by inert quartz particles with diameters between 250 to 300 micrometers and the reaction used was always CO oxidation.
48 “Needle in a Haystack” “Pt Needle in a Quartz Haystack”
49 The main principle We are not able to control the surface state However we are able to control an amount of consumed reactants and released productsKnowing the total amount of consumed reactants, e.g. hydrocarbons, we introduce a catalyst scale
50 The total amount of transformed furan is TAP Multipulse Data Reaction of Furan Oxidation over ‘Oxygen Treated’ VPOThe total amount of transformed furan is1.4 x 1018 molecules per 1 g of VPO catalystdiffers for different reactants
51 the same for different reactants TAP Multi-pulse Characterization of Furan Oxidation over Oxygen-treated VPOC4H4O + (3MA + 2AC + 9CO2+ 5CO)Ocat MAC4H2O3+ACC3H4O +[CO2+(1/4) AC]4CO2 +CO4CO +[(1/2) MA + CO + CO2)] 2H2OThe total amount of active oxygen consumed in the reaction was approximately the same for all four reactant molecules: 7.7 x 1018 atoms per 1 g VPOthe same for different reactants
52 Apparent Kinetic Constants for Furan Oxidation as a Function of Oxidation State Non-steady-state TOF defined as the apparent constant divided by the oxidation degree, for furan and products (MA, CO2 and AC) versus the catalyst oxidation degree.
53 Apparent “Intermediate-Gas” Constant and Time Delay at least four intermediates can be involved
54 Detailed Mechanism of Furan Oxidation Over VPO At least three independent routesAt least four specific intermediatesO2 + 2Z 2ZO;Fr + ZO X;Fr + ZO Y;Fr + ZO U;X MA+ Z + H2O;YAC + Z + CO2 + H2O;UZ + CO2+ H2O;ZO + L LO + Z;CO2 + Z1 Z1CO2.where X, Y, U, Z1CO2 are different surface intermediates, ZO and LO – surface and lattice oxygen respectively, Z and Z1 are different catalyst active sites.Stoichiometric coefficients of surface substances will be specified in the course of reaction. Steps 2-4 are supposed to differ kinetically.
55 State-by-State Transient Screening Diagram Multi-Pulse Thin-Zone TAP ExperimentState-Altering ExperimentA long train of pulsesState-Defining ExperimentChecking state-defining regime for one-pulse TAP experimentMoment-based analysis of all pulse-response curvesIntegral State CharacteristicsNumber of consumed/released gas substancesIntroduction of the Catalyst ScaleCatalyst state substancesKinetic Characteristics of Catalyst StatesBasic kinetic coefficientsMechanism Assumptions(routes, intermediates, etc.)Relationships between the coefficientsDistinguishing MechanismsDependence of the coefficients on catalyst state substancesStructure-Activity RelationshipsConsiderations regarding the structure/activity of the active sites
56 Complexity, General Kinetic Law and Thermodynamic Validity: Algebraic Analysis in Chemical Kinetics
57 Chemical Kinetics. Textbook Knowledge (1) The main law of chemical kinetics isthe Mass-Action LawThe first-order reaction: A B R = kCaThe second-order-reaction 2A B R = k (C )2aor A+B C R= k Ca CbThe third-order reaction3A B; R= k (Ca)3;2A + B C ; R=k (C )2a Cb
58 Chemical Kinetics Textbook Knowledge (2) All steps of complex chemical reactionsare reversible,e.g. A BKeq (T) =(k+/k-) = Ca / Cb
59 Chemical Kinetics Textbook Knowledge (3) Detailed mechanism is a set of elementary reactions which law is assumed , e. g. the mass-action-lawAn example:Hydrogen Oxidation 2H2 +O2 = 2H2O1) H2 + O2 = 2 OH ; 2) OH + H2= H2O + H ; 3) H + O2 = OH + O;4) O + H2 = OH + H ; 5) O + H20 = 2OH; 6) 2H + M = H2 + M ; 7) 2O + M = O2 + M;8) H + OH + M = H2O + M; 9) 2 OH + M = H2O2 + M; 10) OH + O + M = HO2 + M;11) H + O2 + M = HO2 + M; 12) HO2 + H2 = H2O2 + H;13) HO2 +H2 = H2O +OH;14) HO2 + H2O = H2O2 + OH; 15) 2HO2 = H2O2 + O2; 16) H + HO2 = 2 0H;17) H + HO2 = H2O + O; 18) H + HO2 = H2 + O2; 19) O + HO2 = OH +H;20) H + H2O2 = H20 + OH; 21) O + H2O2 = OH +H02; 22) H2 + O2 = H20 + O;23) H2 + O2 + M = H202 + M; 24) OH +M = O + H + M; 25) HO2+OH=H2O+O2;26) H2 + O +M = H2O +M; 27) O + H2O + M = H202 + M; 28) O + H2O2 = H20 + O2;29) H2 + H2O2 = 2H2O; 30) H + HO2 + M = H2O2 +M
60 What about the General Law of Chemical Kinetics. What is a LAW? DependenceCorrelationMODELEquationLAW !!!
61 This definition is too fuzzy Some definitions“A physical law is a scientific generalization based on empirical observations” (Encyclopedia)This definition is too fuzzyPhysico-chemical law is a mathematicalconstruction(functional dependence)with the followingproperties:1) It describes experimental data in some domain2) This domain is wide enough3) It is supported by some basic considerations.4) It contains not so many unknown parameters5) It is quite elegant
62 How to kill complexity, or “Pseudo-steady-state trick” Idea of the complex mechanism:“Reaction is not a single act drama” (Schoenbein)Intermediates (X) and Pseudo-Steady-State-HypothesisAccording to the P.S.S.H.,Rate of intermediate generation = Rate of intermediate consumptionRi.gen (X, C) = Ri.cons(X, C)Then, X = F(C)and Reaction Rate R(X, C)=R (C, F(C))=R(C)
63 Chain Reaction Fragment of the mechanism: 1) H + Cl2 HCl + Cl 2) Cl + H2 HCl +HOverall reaction: H2 + Cl2 2HClR=(k 1k2CH2CCl2- k-1k-2C2HCl) / ,where = k 1CH2 +k2CCl2 + k-1CHCl +k-2 CHCl
64 Thermodynamic validity The equationR=(k 1k2CH2CCl2 - k-1k-2C2HCl) / ,where = k 1CH2 +k2CCl2 + k-1CHCl +k-2 CHClis valid from the thermodynamic point of view.Under equilibrium conditions, R=0,and(C2HCl / CH2 C Cl2) = (k1k2 /k-1k-2)= K eq(T)
65 Catalytic mechanism. Two-step mechanism: Temkin-Boudart Z + H2O ZO + H2;ZO + CO CO2 + ZThe overall reaction is CO + H2O= CO2 +H2,R=[(k1Cco)(k2CH2O)- (k1CH2)(k2CCO2)] / ,where = k1CH2O +k2CCO+ (k-1CH2)(k-2CCO2)],R = R+ - R- ; (R+/ R- ) = (K+CcoCH2O)/(K-CH2CCO2)
67 R = Cy / , Cy = K+ f+(C) - K- f- (C) , One-route catalytic reaction with the linear mechanism. General expression (Yablonsky, Bykov, 1976)R = Cy / ,where Cy is a “cyclic characteristics”,Cy = K+ f+(C) - K- f- (C) ,Cy corresponds to the overall reaction; presents complexity of complex reaction;
68 Kinetic model of the adsorbed mechanism 1) 2 K + O2 2 KO2) K + SO2 KSO23) KO + KSO2 2 K + SO3Steady state (or pseudo-steady-state) kinetic model isKO : 2k1CO2(CK )2 - 2 k-1 (CKO )2 - k3 (CKO ) (CKSO2 )+ k-3 CSO3 (CK )2 = 0 ;KSO2: k2CSO2CK - k-2 (CKSO2) - k3 (CKO ) (CKSO2 )++k-3CSO3 (CK )2 = 0 ;CK + CKO +CKSO2 =1
69 Mathematical basis Our basis is algebraic geometry, which provides the ideas of variable eliminationAizenberg L.A., and Juzhakov,A.P. “Integral representations and residues in multi-dimensional complex analysis”, Nauka, Novosibirsk, 1979Tsikh, A.K., Multidimensional residues and their applications, Trans. Math. Monographs, AMS, Providence, R.I., 1992Gelfand,I.M., Kapranov, M.M., Zelevinsky, A.V., Discriminants, Resultants, and Multidimensional Determinants, Birkhauser, Boston, 1994Emiris, I.Z., Mourrain,B. Matrices in elimination theory, Journal of Symbolic Computation, 1999, v.28, 3- 43Macaulay, F.S. Algebraic theory of modular systems, Cambridge, 1916
70 Our main resultIn the case of mass-action-law model, it is always possible to reduce our polynomial algebraic system to a polynomial of only variable, steady- state reaction rate.For this purpose, an analytic technique of variable elimination is used. Computer technique of elimination is used as well.Mathematically, the obtained polynomial is a system resultant. We term it a kinetic polynomial.
71 The Kinetic Polynomial For the linear mechanism, the kinetic polynomial has a traditional form: R = (K+ f+(C) - K- f- (C))/ ( ) ,or ( ) R = Cy, or ( ) R - Cy = 0,where Cy is the cyclic characteristic; is the “Langmuir term” reflecting complexityFor the typical non-linear mechanism the kinetic polynomial is represented as follows:BmRm+…+ B1R +BoCy=0 ,where m are the integer numbers
72 The Kinetic Polynomial Coefficients B have the same “Langmuir’ form as in the denominator of the traditional kinetic equation,i.e. they are concentration polynomials as well. Therefore, the kinetic polynomial can be written as follows
73 Simplification of the polynomial: Four-term rate equation It is a “thermodynamic branch” of the kinetic polynomial
74 Apparent “Kinetic Resistance”= Driving Force/Steady-State Reaction Rate KRapp = [ f +(c)- f -(c) /K eq ]/ R ,where [ f +(c)- f -(c) /K eq ] – “driving force”, or “potential term” ,R – reaction rate ,KR app –”kinetic resistance”
75 Reverse and forward water-gas shift reaction H2 + CO = H2O + CO2
76 Steady-state rate dependences at different temperatures Water –gas shift reaction
77 Apparent “Kinetic Resistance”= Driving Force/Steady-State Reaction Rate KRapp = [ f +(c)- f -(c) /K eq ]/ R ,where [ f +(c)- f -(c) /K eq ] – “driving force”, or “potential term” ,R – reaction rate ,KR app –”kinetic resistance”
80 Conclusion: A New Strategy: (1) Calculate the kinetic resistance based on the reaction net-rate and its driving force;(2) Present this resistance as a function of concentrations and temperature on” both sides of the equilibrium”.An advantage of this procedure is that the kinetic resistance is just is a linear polynomial regarding its parameters in difference from the non-linear LHHW-kinetic models
81 Kinetic FingerprintsSuch temporal or parametric patterns that help to reveal or to distinguish the detailed mechanismE.g., the fingerprint of consecutive mechanism is a concentration peak on the “concentration - time” dependence
82 Critical Phenomena in Heterogeneous Catalytic Kinetics: Multiplicity of Steady-States in Catalytic Oxidation(CO oxidation over Platinum)C“Extinction”Reaction RateCritical Simplification:RC=k2+CCORA=k2-BA“Ignition”DCO Concentration
83 Critical Simplification Analyzing kinetic polynomial,critical simplification was foundAt the extinction point Rext. = k+2CcoAt the ignition point Rign = k-2Therefore, the interesting relationship is fulfilledRext / Rign = k+2Cco /k-2 = Keq CcoIt can be termed as a “Pseudo-equilibrium constant of hysteresis”Therefore, we have the similar equation for (R + / R- ) interms of bifurcation points.
84 Experimental evidence It was found theoretically that at the point of ignition the reaction rate is equal to the constant of CO desorption.It was found experimentally, that the temperature dependence of reaction rate at this point equals to the the activation energy of the desorption process.(Wei, H.J., and Norton, P.R, J. Chem. Phys.,89(1988)1170; Ehsasi, M., Block, J.H., in Proceedings of the International Conference on Unsteady-State Processes in Catalysis, ed.by Yu.Sh. Matros, VSP-VIII, Netherlands, 1990, 47
85 SCIENTISTS ARE JUST PEOPLE A SIMPLE IDEASCIENTISTS ARE JUST PEOPLE
86 Relationships among scientists Discussion is a necessary part of the scientific process “Dog-eat-dog”FightingQuarrelArgumentationDiscussionReconciliationCollaborationMutual UnderstandingHARMONY
87 Collaboration between Sciences The most interesting events are occurred on the frontiersScientists are collaborating,not Sciences
88 Ghent - St. Louis chemical-mathematical crossroads ResultsTransfer matrixY-procedureCoincidences.
89 Dramatis Personae Denis Constales, UGent Guy Marin, UGent Roger Van Keer, UGentGregory S. Yablonsky, St.-Louis + UGent dr h.c.
90 1. Transfer Matrix for solving RD eqs. Advantage: we can calculate the exit flow for any configuration of reaction zones. In TAP case:
92 2. Y-procedureMathematically, it is a combination of the reverse Laplace Transformation method with the Fast Fourier Transformation Method for extracting Reaction Rate with no Assumption about the Detailed Mechanism (“Kinetic model”-free method)
93 Thin Zone TAP experiments Inert zoneCatalyst zoneSpatial uniformity and well defined transport in the inert zones allow“kinetically model-free” analysis via:Primary kinetic coefficients (r0, r1, r2)Y-Procedure - reconstruction of C(t) and R(t) (Constales, Yablonsky)
94 G.S.Yablonsky, D.Constales et al. (2007) Y-ProcedureDirect ProblemInverse ProblemY-Procedure extracts gas concentration and reaction rate on the catalyst without any assumptions about the reaction kineticsG.S.Yablonsky, D.Constales et al. (2007)94
95 G.S.Yablonsky, D.Constales et al. (2007) Y-ProcedureDirect ProblemInverse ProblemY-Procedure extracts gas concentration and reaction rate on the catalystwithout any assumptions about the reaction kineticsOnce the reaction rate is known, the surface coverage can be estimated asG.S.Yablonsky, D.Constales et al. (2007)95
96 First order irreversible reaction D.Constales, G.S.Yablonsky, et al. (2007)96
97 Irreversible adsorption Addressing measurement of total number of active sites, SZ,tot :Usually SZ,tot is measured by simple titration0th MomentPulse NumberIs titrated number of active sites different fromtotal number of WORKING active sites?Measurement of SZ,tot from intrinsic kinetics
98 State Defining experiment Catalyst state remains unchanged(or relatively unchanged) during the pulse.Exit fluxFtConcentrationReaction RateSurface CoverageRSCttt
102 State Altering experiment R vs. CR/C vs. SRR/CkCSSZ,tot102
103 Multipulse State Defining vs. State Altering kap and Sfor each pulseR/C,kapkSequence of state defining pulses(gradual change of the catalyst)SSZ,tot
104 Multipulse State Defining vs. State Altering kap and Sfor each pulseR/C,kapkSequence of state defining pulses(gradual change of the catalyst)SSZ,totR vs. CRSequence of state altering pulsesC
105 Thin Zone TAP experiments for transient catalyst characterization with application to silica-supported gold nano-particlesPart IIEvgeniy Redekop, Gregory S. Yablonsky, Xiaolin Zheng, John T. Gleaves, Denis Constales, Gabriel M. VeithCREL , February 12th, 2010105
106 Outline Summary of Part I (Y-Procedure theory) Application to the real datacatalysis on goldCO adsorptionConclusions106
108 “kinetically model-free” Summary of Part IExit flow dataF(t)Thin-Zone TAP10-8 torrYTransient kineticson the catalystC(t)R(t)S(t)“kinetically model-free”
109 “kinetically model-free” Summary of Part IExit flow dataF(t)Thin-Zone TAPYTransient kineticson the catalystC(t)R(t)S(t)“kinetically model-free”Model reaction mechanismsData interpretation1st order (Constales et al.)Irreversible adsorption?Reversible adsorption
110 Scanning Transmission Electron Microscopy (STEM) Catalyst: n-Au/SiO2 (11 wt.%)Scanning Transmission Electron Microscopy (STEM)Gabriel M. Veith110
111 CO oxidation on the catalyst Introduction The overall reaction:CO + O2 → CO2Probable mechanism:O2 → O*2CO ↔ CO*CO* + O*2 → CO2111
112 CO oxidation on the catalyst Introduction The overall reaction:CO + O2 → CO2Probable mechanism:O2 → O*2CO ↔ CO*CO* + O*2 → CO2Oxygen is NOT activated on the surface under TAP conditions112
114 CO adsorption on catalyst Exit fluxThin-Zone reaction rateYFRσ = 0ttReaction rate:Acceptable filtering at σ = 6Rσ = 4, 6Loss of peak rate valuet
115 CO adsorption on catalyst Rate vs. ConcentrationRate vs. ConcentrationRRCCFrom experimentFrom modeling
116 CO adsorption on catalyst From experimentFrom modeling
117 CO adsorption on catalyst From experimentFrom modeling
118 “kinetically model-free” Catalyst developmentExit flow dataF(t)Thin-Zone TAPYTransient kineticson the catalystC(t)R(t)S(t)“kinetically model-free”Model reaction mechanismsData interpretation(qualitative andquantitative)Catalystmodification1st order (Constales et al.)Irreversible adsorptionReversible adsorptionMechanisticUnderstanding
119 CO adsorption on catalyst KΔHads ≈ kJ/mollog(K)1/T
120 The new phenomenological representation of the transformation rate The ‘Rate-Reactivity’Model (RRM)Rgi = ∑Rj (CM, , CMOx, Cad, Cint.r, NS, S, T) Cgj+ Roj (CM, CMOx, Cad, Cint.r, NS, S, T)Ri, Roj are catalyst reactivities.Catalyst reactivities are functions ofintermediate concentrations.The last ones can be estimated as (Integral uptake of reactants – Integral release of products)
121 3. CoincidencesSurprising properties of the simple kinetic models; in particular, A->B->C.
123 Coincidences (cont’d) New problem is posed: what do we know about the points of intersection, the maximum point of CB(t), and their ordering?Example: k1=k2we call it Euler point.
124 Coincidences (cont’d) Nonlinear problem, even for a linear system.Many analytical results can be obtained.Of 612 possible arrangements, only six can actually occur.We introduce separation points for domainsA(cme), G(olden), E(uler), L(ambert),O(sculation), T(riad) points.Each point has special ordering or behavior.
130 Coincidences (cont’d) Inspecting the peculiarities of the experimental data, we may immediately infer the domain of the parameters.Intersections, extrema and their ordering are an important source of as yet unexploited information.
131 Different scenarios of interaction Conceptual Transfer“Spark”Joint Activity“Something”
132 Ideal scenarioA“creative pair” , people who are able to share interests and valuesOptimal time of “knowledge circulation”A clear link to possible realization
133 Different scenarios of interaction InspirationThe great American mathematician J.J. Silvester wrote after becoming acquainted with the records odf Prof. Frankland’s lectures for students chemists:“I am greatly impressed by the harmony of homology (rather than analogy) that exists between chemical and algebraical theories. When I look through the pages of “records”, I feel like Alladin walking in the garden where each tree is decorated by emeralds, or like Kaspar Hauser first liberated from a dark camera and looking into the glittering star sky. What unspeakable riches of so far undiscovered algebraic content is included in the results achieved by the patient and long- term work of our colleagues -chemists even ignorant of these riches”.
134 Different scenarios of interaction Transfer of concepts. Fick’s Law (1)Adolph Fick, “On liquid diffusion”,Ueber Diffusion, Poggendorff’s Annalen der Physik and Chemie, 94(1855)59-86, see also, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , Vol. X (1855) 30-39“It was quite natural to suppose that this law for the diffusion of salt in its solvent must be identical with that, according to which the diffusion of heat in a conducting body takes place; upon this law Forier founded his celebrated thery of heat, and it is the same which Ohm applied with such extraordinary success, to the diffusion of electricity in a conductor”…
135 Different scenarios of interaction Transfer of concepts. Fick’s Law (2)“…According to this law, the transfer of salt and water occurring in a unit of time, between two elements of space filled with differently concentrated solutions of the same salt, must be,caeteris paribus, directly proportional to the difference of concentrations, and inversly proportional to the distance elements from one another”
136 Different scenarios of interaction Transfer of concepts. Fick’s Law (3)“The experimental proof just alluded to, consists in the investigation of cases in which the diffusion-current become stationary, in which a so-called dynamic equilibrium has been produced, i.e. when the diffusion-current no longer alters the concentration in the spaces through which it passes, or it other words, in each moment expels from each space-unit as much salt as enters that unit in the same time. In this case the analytical condition is therefore dy/dt=0.”…
137 Different scenarios of interaction Transfer of concepts. Fick’s Law (4)“Such cases can be always, if by any means the concentration n two strata be maintained constant. This is most easily attained by cementing the lower end of the vessel filled with the solution, and in which the diffusion-current takes place, into the reservoir of salt, so that the section at the lower end is always end is always maintained in a state of perfect saturation by immediate contact with solid salt; the whole being then sunk in a relatively infinitely large reservoir of pure water, the section at the upper end, which passes into pure water, the section at the upper end, which passes into pure water, always maintains a concentration =0. Now, for a cylindrical vessel, the condition dy/dt =0 becomes by virtue of equation (2), 0 = d2y/dx2 (3)”…
138 Different scenarios of interaction Transfer of concepts. Fick’s Law (5)“The integral of this equation y=ax + b contains the following proposition: - “ If in a cylindrical vessel, dynamic equilibrium shall be produces, the differences of concentration between of any two pairs of strata must be proportional to the distances of the strata in the two pairs,” or in other words the decrease of concentration must diminish from below upwards as the ordinates of a straight line. Experiment fully confirms this proposition”.
139 “I gave my mind a thorough rest by plunging into a chemical analysis” (Sherlock Holmes, “The Sign of Four”, Chapter 10)Read in its context, it is clear that this phrase does not imply any deprecation of chemistry:“Well, I gave my a thorough rest by plunging it into a chemical analysis. One of our greatest statesmen has said that a change of work is the best rest. So it is. When I had succeeded in dissolving the hydrocarbon which I was at work at, I came back to our problem of the Sholtos [etc.]”