1. ChE 553 Lecture 4 Models For Physisorption And Chemisorption I 1

2. Objective For Today Quantify the results from lect 3 Forces that determine bonding Large trends –Physical forces –Electronegativity –Hardness/density of states 2

3. Forces Between a Molecule and Metal Surface Dipole-Induced dipoles Correlation – instantaneous dipole-dipole interactions Electron reorganization /bonding 3 http://chsfpc5.chem.ncsu.edu/~franzen/CH795N/dft_modules/surface_module/ni_111_co_bindin g.htm

4. Literature Discusses Two Types Of Adsorption Physisorption –Dipoles and correlations dominate Chemisorption –Electron reorganizations dominate 4 http://www.lightwave-scientific.com/LWADFMoreInformationP1.htm

5. Usually Not A Clear Distinction 5

6. Physisorption & Chemisorption Usually Treated Differently In The Literature Physisorption –Add up physical interactions assuming that there are no electronic rearrangements Chemisorption –Considering electron reorganization 6

7. Modeling Physisorption Usual model: add up the physical forces 7

8. Working Out The Algebra Assume Leonard-Jones potential Pages of algebra 8 Expected Theoretically for induced dipole/induced dipole

9. A Comparison Of Heats Of Adsorption Calculated To Measure 9

10. 10 Calc Experiment Starting to see reorganization of electrons

11. New Topic: Modeling Chemisorption Several different models Local chemical bonds Bonds to free electrons Ionic forces Local chemical bonds works on some semiconductors Bonds to free electrons dominate on metals Ionic forces dominate on oxides and other insulators 11

12. Modeling Bonds To Free Electrons Three models Algebraic models Jellium models Full QM –Clusters –Slabs 12 http://www.multi.jst.go.jp/en/theme/01_Oshiyama.html

13. Algebraic Model (Pauling Electro Negativity Model) Expand energy as a function of the number of electrons around each atom, molecule, surface as a Taylor series Assume electrons exchanged when molecules interact but Taylor coefficients constant Minimize energy as electrons transferred 13

14. Derivation Taylor series  A = Electronegativity  A = hardness = number of electrons 14

15. Derivation For The Interaction Of A and B 15

16. Derivation For The Interaction Of A and B 16

17. Result 17  H=0 Interaction

18. Numerical Comparison 18 TABLE 3.4 A Comparison of Eley’s [1950] Calculations of Heats of Adsorption to Measured Values Works for metals on metals, hydrogen on metals, sigma bonded species… Only works modestly for pi-bonding. Key Conclusion: Electronegativity and Hardness Key

19. For Ionic Systems The Equation Becomes EQU 3.48 19

20. Key Implication Of Theory: Hard-Hard And Soft-Soft Interactions Hard acids interact strongly with other hard acids and very strongly with hard bases. Soft acids interact strongly with other soft acids and very strongly with soft bases. Hard/soft interactions weak. 20

21. Definitions Hard acid: An acceptor with no low-lying unoccupied orbitals so that it has a small affinity for electrons and remains positively charged during a reaction. Such species will have a small ∆β AB and a very negative E bmo (hardness). Examples include solvated ions of Al 3+, Mg 2+, H +, and surfaces such as alumina or silica. Hard base: A donor with no high-lying donor orbiatls, so that it has little capacity to donate electrons and a small value of ∆β AB. Examples include F -, OH -, H 2 O, amines and surfaces such as MgO or TiO 2. 21

22. Definitions Continued Soft acid: A species that easily accepts charge. Generally, the species will have a high affinity for electrons, and a high polarizability (i.e., large ∆β AB ) so that it can easily form covalent bonds. Examples include Hg 2+, Ag +, and Pt +, and most small metal clusters. Soft base: A species that easily gives up charge. Generally, the species will have a high affinity for electrons, and a high polarizability (i.e., large ∆β AB ) so that it can easily form covalent bonds. Examples include I -, RS -, and H -, and most metal surfaces. 22

23. Rules Hard acids bind strongly to hard bases Soft acids bind strongly to soft bases Hard-soft interactions weak Example: Binding of H 2 O and H 2 S on platinum and alumina Limitations of method: still not properly considered molecules with discrete bonds. 23

24. Corrections For Molecular Adsorbates (Fukui Functions) Key idea: the electronegativity is not constant around a molecule so it is easier to add electrons in some places than others. 24 Figure 3.26 The LUMO (a) and HOMO (b) for CO.

25. Jellium Model 25 Figure 3.33 The electron density outside of a charge compensated jellium surface for r s = 2 and 5, after Halloway and Nørskov, [1991]. (a) Actual electron density, (b) scaled electron density.

26. Newns Anderson Jellium Model 26 Figure 3.34 A schematic of the density of states calculated via Equation 3.62 for the interaction of an adsorbate with a surface with (a) a narrow band and (b) a wide band.

27. Key Prediction Of Newns Anderson Model Bonds are dynamic - there is continuous exchange of electrons between bond and surface - one electron pairs up with an adsorbate then leaves, then another electron forms a bond. Implications: Very mobile, rather reactive surface species Energy levels broaden due to the uncertainty principle 27

28. Data Verifies Rapid Exchange 28 Figure 3.35 A comparison of the UPS spectrum of N 2 O adsorbed on a W(110) surface to the UPS spectrum of N 2 O in the gas phase. (Data of Masel et al. [1978].)

29. Quantification Of Model: Effective Medium Model Add up effects of electrons and d- electrons to get predictions: Assume only sigma bonds Key implication- bonding goes as electron density. 29

30. Table Of Electron Density 30 Source: Calculated by Morruzzi et al. [1978] and as fit to data by DeBoer [1988]. *The values from DeBoer should be multiplied by 0.9 to make them compatible with Morruzzi’s values. † Morruzzi’s value.

31. Comparison To Data 31 Figure 3.40 A correlation between the bonding mode of ethylene on various closed packed metal surfaces at 100 K and the interstitial electron density of the bulk metal. (After Yagasaki and Masel [1994].)

32. Comparison To Ethylene Data 32 Figure 3.41 A correlation between the carbon- carbon bond order on adsorbed ethylene on various closed packed metal surfaces at 100 K and the interstitial electron density of the bulk metal. (After Yagasaki and Masel [1994].) Figure 3.47 A correlation between the vibrational frequency of the C-C stretch in C 2 D 4 adsorbed on a series of closed packed metal surfaces at 100 K and the interstitial electron density of the metal.

33. Comparison To Ethylene Data 33 Figure 3.47 A correlation between the vibrational frequency of the C-C stretch in C 2 D 4 adsorbed on a series of closed packed metal surfaces at 100 K and the interstitial electron density of the metal.

34. CO Data 34 Figure 3.46 A correlation between the low coverage limit of the vibrational frequency of CO adsorbed on a series of closed packed metal surfaces and the interstitial electron density of the metal. Fails because not properly considering delta-bonds (model only considers sigma bonds)

35. Summary Physisorption Physical forces dominate Add up the forces Chemisorption Metals Metalic bonds dominate Radicals attached to Jellium Rapid exchange of electrons Hard-hard, soft-soft interactions strong Hard-soft interactions weak 35