1. IC T IC-1/26 Lecture-4B 30-0910-2004 Reaction Rate Theory  E reaction coordinate E + + k A B AB

2. IC T IC-2/26 Lecture-4B 30-0910-2004 Partition Functions Similarly can we separate the internal motions of a molecule in Part involving vibrations, rotation and nuclei motion, and electronic motion i.e. for a mulecule we have Now we create a system of many molecules N that are in principle independent and as they are indistinguishable we get an overall partition function Q

3. IC T IC-3/26 Lecture-4B 30-0910-2004 Partition Functions Summary 

4. IC T IC-4/26 Lecture-4B 30-0910-2004 Partition Functions What was the advantage of having the Partition Function?

5. IC T IC-5/26 Lecture-4B 30-0910-2004 Surface Collisions Consider a box with volume V What are the numbers?

6. IC T IC-6/26 Lecture-4B 30-0910-2004 Surface Collisions How many are successful in reacting? Simple Maxwell-Boltzman distribution

7. IC T IC-7/26 Lecture-4B 30-0910-2004 Transition State Theory Consider the following reaction : How? We assume that R and R # are in Equilibrium R P R#R# q `# is a frequency or trial factor in the reaction coordinate

8. IC T IC-8/26 Lecture-4B 30-0910-2004 Transition State Theory By splitting the partition function in the transition state Assuming

9. IC T IC-9/26 Lecture-4B 30-0910-2004 Transition State Theory R P R#R# q` # =q `# v q # 0 e -  E/kT q `# Which basically is the Arrhenius form If q 0 # ~ q  ~1x10 13 s -1 Relation to Thermodynamics The partition function q # can conveniently be split further:

10. IC T IC-10/26 Lecture-4B 30-0910-2004 Transition State Theory Think of some examples Temperature dependence of prefactor

11. IC T IC-11/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces An atom adsorbs into a 2-dim mobile state, we have N g gas atoms, M sites on the surface, and N # atoms in the transition state Indirect adsorption of atoms:

12. IC T IC-12/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Now what is K # ?

13. IC T IC-13/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces This corresponds to the collision on a surface since the atoms are still free to move in two dimensions

14. IC T IC-14/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Direct adsorption of atoms: M is total number of sites M´ is number of free sites Why?

15. IC T IC-15/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces

16. IC T IC-16/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Notice adsorption always result in loss of entropy There may also be steric hindrance leading to reduced S

17. IC T IC-17/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces What happens in the regime between direct and indirect adsorption? The atoms breaks free of the site and start to diffuse around in Eventually

18. IC T IC-18/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Indirect adsorption of molecules: Notice that if the precursor is sufficiently loose S 0 (T)=1.

19. IC T IC-19/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Direct adsorption of molecules:

20. IC T IC-20/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces

21. IC T IC-21/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Reactions between surface species:

22. IC T IC-22/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces The reverse process:

23. IC T IC-23/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Considering both processes and equilibrium: Notice how the K eq is alone determined from initial and final state partition functions.

24. IC T IC-24/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces Desorption:

25. IC T IC-25/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces System Prefactor s -1 E a kJ/mol CO/Co(0001) 10 15 118 CO/Ni(111) 10 15 130 CO/Ni(111) 10 17 155 CO/Ni(111) 10 15 126 CO/Ni(100) 10 14 130 CO/Cu(100) 10 14 67 CO/Ru (001) 10 16 160 CO/Rh(111) 10 14 134 How?

26. IC T IC-26/26 Lecture-4B 30-0910-2004 Transition State Theory on Surfaces If the details of the transition state can be determined can the rate over the barrier be calculated. Details of the transition state are difficult to access: Low concentration Short lifetime. Often determined by ``First Principle´´ calculations, but are only accurate to say 0.1 eV or 10 kJ/mol.