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Graduate Workshop Lecture Series Estimating kinetics parameters in (photo)catalysis using simple and complex modeling approaches Vaidyanathan (Ravi) Subramanian Associate Professor, Chemical Engineering University of NEVADA, Reno Outline for this presentation At the end of this lecture the following information will be disseminated: Refresher on catalysis Key steps in a catalytic process General strategies to offset transport limitations Rate Definitions, Catalyst-reactant interactions Definitions, rate expressions Rate analysis Non-rigorous approach (Power law model) Rigorous approach (Langmuir model) Catalyst: Introduction What is a catalyst? A catalyst is a material that favorably influences a reaction but emerges from the reaction unchanged Examples Fuel cell Photocatalysis PtRu: Metal catalysts that promote oxidation of a fuel to produce current in a fuel cell TiO2: A photocatalyst that promotes degradation of pollutants without undergoing any change in itself Value added product formation Al2O3-Rh: Support – catalyst composite used in high temperature hydrogen production Types of catalytic reactions Homogeneous Homogenous catalysis concerns processes in which a catalyst is in solution with at least one of the reactants Manufacturing of n-isobutylaldehyde CO, propylene, H2 with liquid phase Co as catalyst Heterogeneous Involves more than one phase. A reaction involving gas and liquid Examples: TiO2 photocatalyst is usually in the solid phase while pollutants can be in liquid or gas phase Hydrogenation catalysts are in the solid phase whereas unsaturated oils are in the liquid phase Catalyst properties Usually the activities in the presence of a catalyst occur at the interface Gas-liquid, gas-liquid-solid For example, the photocatalytic process occurs at the surface of TiO2 Crucial physical aspects of the catalyst Surface area Pore size, pore volume: What are these? These dictate the extent of the catalyst surface available and that can be utilized by a catalytic process Active sites Higher the number of active sites greater the activity Generally, higher the surface area, higher the activity of the catalyst Catalyst properties … contd. Selectivity Pore size can control the selectivity of the reaction Example Benzene and toluene can react over zeolite to form xylene mixtures. But the pore of zeolite only allows a specific type of xylene to come out. Supported catalyst Catalyst is not used by itself but supported on another material Example Fuel cell catalysts: PtRu on carbon General catalyst – support configuration catalyst Surface support Pore interiors Pore mouth Definitions Active site Turn over frequency (TOF-f) The location on a catalyst where the reactant undergoes chemistry Point of the catalyst that facilitates strong interaction with reactant Number of molecules reacting per active site per second Dispersion Distribution of the catalyst. This term is usually used when a catalyst is prepared over a support One usually requires higher dispersion Higher dispersion typically yields higher activity Thermodynamics of a catalytic process The feasibility of a reaction is decided by the initial and final energy state of the reactants and products respectively Different pathways can be employed to facilitate a reaction Pathways mainly differ based on the energy barrier that exist between the reactant(s) and product(s) A catalyst promotes the reaction by following a different, usually a more energy efficient, pathway Thermodynamics…contd. Without catalyst:: higher energy barrier I impedes reaction Energy II With catalyst:: lower energy barrier facilitates reaction A B Reaction pathway Interaction between catalyst and reactant Prior to reaction the reactants have to come in contact with the catalyst Chemisorption Adsorbed atoms or molecules are held to the catalyst surface by chemical bonding(the same type which hold atoms bonded in molecules) Physisorption The atoms are held on the catalyst surface by physical forces Main steps in a catalytic reaction There are in general 7 key steps in a heterogeneous catalytic reaction 1. mass transport: diffusion of A from bulk phase to the catalyst surface 2. diffusion of A from pore mouth to pore interior 3. adsorption of A on active site 4. reaction on active site AB 5. desorption 6. diffusion of B from pore interior to pore mouth 7. mass transport: diffusion of B from catalyst surface to bulk Steps: Pictorial A B Catalyst Buk A B 1 7 Pore surface 2 Pore interior 6 5 3 4 Active site Steps…contd. Factors that play a role Diffusion limited: steps 1,2, and/or 6,7 Kinetic limited : step 3,4,or 5 Overall rate = rate of the slowest step Analogous to saying Strength of chain = strength of weakest link Step 1 Diffusion from bulk to the external transport Reactant travels from bulk concentration CAb to CAs at the catalyst surface over a boundary layer thickness Diffusion rate = kC(CAb-CAs) Where kC=mass transport coefficient kC=f(fluid velocity(U),particle diameter(Dp)) kC 1/ Step 1:…contd. (Q) what happens to overall rate of diffusion when the velocity increases for a constant particle diameter? Overall rate increases Overall rate U External mass transport no longer the slowest step External diffusion is the slowest step U/DP Step 2 Internal diffusion Assumption: no external diffusion Internal diffusion = f (pellet size) For larger pellets Reactants consumed at the pellet surface Therefore, bulk of the catalyst may not be used in reaction For small pellets Larger the pellet size – longer it will take to diffuse to the bulk from the surface Most of the catalyst surface is used Rate of transport = krCAs CAs= concentration at external surface kr=overall rate constant =f(DP) Step 2…contd. (Q) what happens to rate constant when the diameter of catalyst particle increases? (hint: higher DP longer time to diffuse) Rate constant decreases Surface reaction sequence is the slowest step kr Internal diffusion is the slowest step DP What is the need for estimating kinetic parameters? Kinetic parameters are needed to answer several of the following questions How fast the reaction can occur? How efficient of a chemical transformation is the reaction What is the extent of desired and undesired product(s) formation How doe the cost and sustainability (environmental impact) aspect of the process work out What supporting infrastructure/ facilities are required to run the chemical reaction? Rate is a key measure of kinetics Rate of a reaction What is Rate? Rate of a reaction Rate can be defined as transformation or changes that occur causing the concentration of a specie to increase or decrease with time Is a measure of how a reaction occurs with respect to time Examples Rate of consumption Depletion of a reactant with time Rate of formation Increase in the formation of a product with time Rate of a reaction…contd. Rate is generally defined as: Change in the concentration of a reactant per unit time per unit volume It is typically represented by the symbol r r = dCA/dt where dCA = change in concentration of a component A dt = duration when the change in concentration occurs Positive : indicate formation of A with time negative: indicates consumption of A with time Some examples of units mol/dm3.s Kg/m3.hr Rate of a reaction…contd. For example consider the reaction AB As time progresses A gets consumed and B get formed. i.e. the concentration of A decreases while the concentration of B increases. This can be graphically represented as shown in the adjacent plot B CA CB A Time (t) CA CB B dCA A dt Time (t) Rate of consumption of A = change in the concentration of A with time = dCA/dt Other definitions of reaction rate We saw that rate can be expressed in terms of per unit volume of fluid as shown bellow: Based on unit volume of reacting fluid (homogeneous systems) r1 = 1 dNi moles of i formed V dt (volume of fluid) (time) What are other possible types? Heterogeneous systems: more than one phase Based on unit mass of solid in a fluid – solid reaction r2 = 1 dNi moles of i formed W dt (mass of solid) (time) Based on interfacial area in a two phase reaction system r3 = 1 dNi moles of i formed S dt (surface) (time) Based on a unit volume of solid in a gas-solid system r4 = 1 dNi moles of i formed Vs dt (volume of solid) (time) All rates are related How you relate them with one another? r1 = 1 dNi V dt dNi = Vr1 dt dNi = Vr1 = Wr2 = Sr3 = Vsr4 dt Thus, rate expressions can be expressed in different interchangeable forms Other facts about rate It is an algebraic equation It is independent of reactor configuration (you will learn about types of reactor later) It is generally a function of the dependent variables Meaning, operations in algebra (+,-,x,/) are used for expressing rate P,V,T, n, and material properties It has a few key factors that are critical to understand the details of the chemical reaction rate constant, equilibrium constant, Molecularity and reaction order Rate constant (k) The rate of reaction is proportional to the concentration of the reactants rC (for simplicity the power terms are excluded) The proportionality constant is called the rate constant (k) r=kC or k = r/C From the above expression the units of rate constant can be identified as dependent on time and concentration Equilibrium constant (K) Dual site reaction Adsorbed atom/molecule site can (1) another adsorbed atom/molecule or (2) react with another site An adsorbed molecule may isomerizes or decomposes at the said site The rate law for reaction 1 is: A.S+C.S Example: CO oxidation to CO2 over Pt sites Forward reaction: rS=kS.CA.S backward reaction: r-S=k-S. CC.S So overall rate RS= forward – backward =kS.CA.S - k-S. CC.S =kS(CA.S- CC.S) KS Where KS=kS/k-S=reaction equilibrium constant Molecularity and reaction order Molecularity of an elementary reaction is the number of molecules involved in the reaction Usually 1, 2, occasionally 3 only applicable to elementary reactions Order, overall order if r= kCAaCBb, then the order of reaction with respect to A is a order of reaction with respect to B is b overall order is a+b Rate dependency on temperature For elementary reaction of the form A products, rate=f1(temperature)xf2(concentration) This is usually the case with all reactions The temperature dependency is manifested as a part of the rate constant k=f(constant, temperature) Arrhenius’ law states the relation between rate constant and temperature It is written as k = k0exp(-E/RT) Where k0=frequency factor, E=activation energy (calories) Rate analysis? The modeling approaches to estimating the rate parameters can be classified based on rigor Non-rigorous Rigorous Power law model (one size fits all) Linearized power law model Numerical based power law model Langmuir model (iterative and semi empirical) Highly empirical (statistical analysis driven) The choice of method to be adapted is driven based on the (i) accuracy desired, and (ii) the level of details needed from the analysis. The rate law (power law model) The power law model correlates reaction with two basic parameters: the reaction rate constant and the order (participating species) The general expression for the power law model for an elementary reaction AB is written as: -rA = kCAn (where n is 1 ) This expression can be applicable to complex reactions as well. How will you write the rate expression for the following reaction if it were elementary? aA+bBcC+dD -rA = kCAaCBb The Langmuir Model The Langmuir model is a popular kinetics model that can be applied to heterogeneous photocatalytic reactions Key aspects include: Unlike the power law model, it allows for decoupling rate constant (k) from equilibrium adsorption constant (K). Allows for an iterative path way to propose and validate mechanistic aspects associated with the reaction process Single site Dual site Offers options to customize equation to include light – matter interactions Adsorption Adsorption is a prerequisite for a catalytic process For the reaction A Products, the adsorption is symbolically written as A+S A.S A= reactant (atom or molecule) S= active site on catalyst surface with no atom (or molecule) adsorbed on it A.S = a reactant adsorbed on the active site Note: the reaction is shown to be reversible. This is mainly to indicate that some atoms might just adsorb and desorb without reaction and represent the Single site and dual site reaction A+S products A A2+2S products A A Adsorption …contd. Occupied sites (CA.S ,CB.S) A B Vacant site (CV) Active site concentration (Ci,S) (mol.g-1.catalyst-1) where i stands for reactant or product Number of active sites per unit mass of catalysts Avogadro number Units: mol./ g of catalyst For the system shown, the total concentration (Ct) of sites (also called as site balance) Ct=CV+CA.S+CB.S An exercise on Langmuir model derivation Derive the expression for the Langmuir singe site model General approach Determine the expression for the net adsorption rate. It is given as: attachment rate – detachment rate Define adsorption equilibrium constant as KA=kA/k-A Perform a site balance LH isotherm is an expression for the concentration of adsorbed species Linearized form is to write the above expression in Y=mX + C form Adsorption equilibrium constant Assume a gas phase reaction as follows yst R Photocatal products Before the reaction can occur, the molecules needs to interact with the site via chemisorption or physisorption method The attachment rate (proportional to the PR and CV) = kA.PR.CV The detachment rate = - k-A.CR.S The adsorption equilibrium constant (KA) represents the situation under a dynamic steady state KA=kA/k-A Adsorption equilibrium constant At equilibrium, Net adsorption rate = attachment rate – detachment rate (1) Substituting the adsorption equilibrium constant (KA) rAD = kA.PR.CV - k-A.CR.S KA=kA/k-A And rearranging eq (1) we can get rAD = kA.(PR.CV - CR.S) KA (2) Site balance The total number of sites is given as, At equilibrium, Ct=vacant sites + adsorbed sites In this case, Ct=CV+CR.S (3) The net rate of adsorption (rAD)should be zero. (dynamic steady state) Or rAD = kA.(PR.CV - .CR.S) =0 KA Rearranging, CR.S =KAPR.CV (4) Site balance… contd. Rearranging, Substituting the value of CV from eq (3) in eq(4) Since in many cases, only the adsorbed sites can only be identified; it is helpful to substitute CV in terms of CR.S CR.S =KAPR.CV CR.S =KAPR. (Ct-CR.S) Rearranging, CR.S = KAPR.Ct (5) 1+ KAPR This equation gives the concentration of R adsorbed on the catalyst surface as a function of the partial pressure of R. This is called the Langmuir adsorption expression after the Nobel laureate Irving Langmuir. Langmuir isotherm analysis Rearrange eq(5),by linearizing, PR = PR + 1 (6) CR.S Ct KACt Y = mX + C Which is the linearized form of the Langmuir equation Thus one can check if an experimental data set follows the Langmuir kinetics P R CR.S This expression gives the equilibrium adsorption constant and an estimate of total sites utilized in the reaction 1 KA.Ct PCO 1 Ct Photocatalytic degradation of dye The power law and LH models can be applied to a common photocatalytic reaction – the photodegradation of dyes. Dyes are often toxic (carcinogenic) and alter the ecosystems where there are introduced Photocatalysis is a pathway to remediate this dye. The options are: Example: Dye discharge into water stream by textile industries Complete mineralization (CO2 and Water) Decontamination to a more benign intermediate Examples of dyes Methyl orange, Victoria blue, Acid orange Overall rate: power law model 0.12 constant 0.10 rMO ,M min -1 0.08 0.06 0.04 0.02 0.00 0 20 40 60 [MO] x 10 80 -6 Power law model rMO 100 d [ MO ] dt The rate vs. methyl orange concentration [MO] plot Subramanian et.al. Ind. Eng. Chem. Res. (2009) LH kinetics for photocatalytic reactions rMO f ( I , s, [ MO ], K ) I Intensity, s area, [ MO ] MO concentration , K equilbrium const . rMO k1as I 1 k1as I K [ MO ] 1 K [ MO ] a, , consts. K [ MO ] rMO k r 1 K [ MO ] where k1as I kr 1 k1as I PC: Langmuir Hinshelwood Model 100 1/rMO [min M] 80 60 K [ MO ] rMO k r 1 K [ MO ] 1 1 1 rMO k r K [ MO ] k r 40 y = 6.451 + 62.28x 2 R = 0.996 20 0 0.0 0.1 0.2 0.3 0.4 0.5 1/[MO] Single site – single molecule adsorption and reaction mechanism of MO degradation Subramanian et.al. Ind. Eng. Chem. Res. (2009) Other factors influencing kinetics Other general parameters that influence reaction kinetics are: Catalyst loading External effects (addition of external fields) Additives (pH adjustors) Specific to photocatalytic processes other key parameters that affect the rate reaction rate are: light intensity, light screening, adsorption-desorption equilibrium Summary A key aspect in catalysis is the determination of rate of reactions The main contributors to rate of reaction are: rate constant, equilibrium constants, concentration (pressure) of participating reactant species The analysis of rate can be carried out using simple and complex models Simple: Power law model Complex: Langmuir Hinshelwood The models can provide insights into the mechanistic details of the reaction