1. ChE 553 Lecture 15 Catalytic Kinetics Continued 1

2. Object Examine the effects of pairwise interactions on rates of surface reactions –Interactions change apparent order –Can fit to Langmuir, but with the wrong mechanism 2

3. Started Catalytic Kinetics Last Time Catalytic reactions follow a catalytic cycle reactants + S  adsorbed reactants Adsorbed reactants  products + S Different types of reactions Langmuir Hinshelwood Rideal-Eley 3

4. Key Predictions Unimolecular reactions Rate increases with pressure, levels off Rate always increases with temperature Very sensitive to poisons Bimolecular reactions Rate rises reaches a maximum at finite temp and pressure, then drops Sensitive to poisons 4

5. Qualitative Behavior For Unimolecular Reactions (A  C) 5

6. Qualitative Behavior For Bimolecular Reactions (A+B  products) 6 Figure 12.32 A plot of the rate calculated from equation (12.161) with K B P B =10.

7. Physical Interpretation Of Maximum Rate For A+B  AB Catalysts have finite number of sites. Initially rates increase because surface concentration increases. Eventually A takes up so many sites that no B can adsorb. Further increases in A decrease rate. 7

8. Methods Do Not Always Work In Detail Pairwise interactions between adsorbed species –Leads to ordering, coverage dependent kinetics –Can produce oscillations, steady states that depend on how steady state is reached 8

9. Key Qualitative Effects Ordered Overlayers Island formation Fluctuations 9

10. The Effect Of An Ordered C(2x2) Overlayer Notice that the environment of B is independent of the coverage of A provided θ A > 0.5 The rate is almost independent of the A concentration –Not exactly independent because repulsions speed rate 10

11. Monte Carlo Calculation To Estimate Rate Montecarlo to estimate coverage: Randomly choose one of three steps –Adsorption/desorption step –Reaction –Diffusion Use Metropolis algorithm to see whether step should be choosen Calculate rate via an ensemble average 11

12. Adsorption/desorption Similar To Previous Work Pick a random site If empty adsorb A or B If filled desorb molecule If energy goes down accept the step If energy goes up accept the step with probability exp(-βΔE) Repeat 12

13. Diffusion Changes Algorithm Slightly Pick a random site Pick an adjacent site If adjacent site empty move molecule If adjacent site filled do nothing If energy goes down accept the step If energy goes up accept the step with probability exp(-βΔE) Repeat 13

14. Reaction Requires Additional Changes Pick a random site Pick an adjacent site If A adsorbed on one of the sites and B adsorbed on a different site Assume A and B react with a probability of p= k o exp(- E A /kT) Repeat Note only 1 in 10 8 attempts leads to reaction 14

15. Next: Estimate The Rate Rate = k o exp(-E A /kT) * (number of adjacent pairs of molecules) 15

16. Result Of Simulation Using Montecarlo 16 βh AA = -3 Fit Langmuir

17. Implications Can fit rate data to Langmuir kinetics even where coverage does not follow Langmuir isotherm –Langmuir kinetics calculated for the wrong mechanism (aqua line) fit the data –However, Langmuir kinetics calculated for the correct mechanism (orange line) do not fit the data Cannot use kinetics to infer mechanism 17

18. Dynamic Islanding If diffusion is slow see dynamic islanding A molecules next to B molecules react A molecules next to A unreactive B molecules next to B unreactive Leads to islands of A and B 18

19. Rate Oscillations Observed Experimentally Under Such Conditions 19

20. Interactions Between Molecules Seen In Transient Measurements Temperature programmed desorption (TPD) Adsorb gas on cold surface Heat at a constant 1- 100K/sec Measure gas evolution as a function of time 20

21. Typical TPD Spectrum 21 TPD of ethylene

22. Why Peaks In TPD? 22

23. Qualitative Effects In TPD 23

24. Qualitative Effects On TPD 24 E a =10 kcal/mole 20 30 40 50

25. Qualitative Effects On TPD 25

26. TPD To Estimate E a 26 E a = (0.06 kcal/mole-K) T p

27. Can Use Methods To Get Approximate Activation Energies 27 TPD of ethylene

28. Method Assumes No Interactions Between Molecules 28 Attractive Interactions Repulsive Interactions

29. 29

30. Attractive Interactions 30

31. E a Varies Non-linearly With Coverage 31

32. Summary Pairwise interactions change kinetics in unexpected ways –Data fits Langmuir-Hinshellwood rate expression – but for the wrong mechanism –E a varies non-linearly with coverage even though interactions linear with number of nearest neighbors –Multiple peaks in TPD 32

33. Key Implication Extreme care needed in using kinetics to infer mechanisms etc –Can easily get the wrong mechanisms with the wrong analysis to fit data. 33