ChE 553 Lecture 4

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

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

3. Forces Between a Molecule and Metal Surface • Dipole-Induced dipoles • Correlation – instantaneous dipole-dipole interactions • Electron reorganization /bonding http://chsfpc5.chem.ncsu.edu/~franzen/CH795N/dft_modules/surface_module/ni_111_co_binding.htm http://chsfpc5.chem.ncsu.edu/~franzen/CH795N/dft_modules/surface_module/ni_111_co_binding.htm

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

5. Usually Not A Clear Distinction

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

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

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

9. A Comparison Of Heats Of Adsorption Calculated To Measure

10. A Comparison Of Heats Of Adsorption Calculated To Measure Experiment Calc 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

12. Modeling Bonds To Free Electrons Three models • Algebraic models • Jellium models • Full QM • Clusters • Slabs 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

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

15. Derivation For The Interaction Of A and B

16. Derivation For The Interaction Of A and B

17. Result Interaction H=0

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

19. For Ionic Systems The Equation Becomes • EQU 3.48

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.

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 ∆βAB and a very negative Ebmo (hardness).Examples include solvated ions of Al3+, Mg2+, 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 ∆βAB. Examples include F-, OH- , H2O, amines and surfaces such as MgO or TiO2.

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 ∆βAB) so that it can easily form covalent bonds. Examples include Hg2+, 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 ∆βAB) so that it can easily form covalent bonds. Examples include I-, RS-, and H-, and most metal surfaces.

23. Rules • Hard acids bind strongly to hard bases • Soft acids bind strongly to soft bases • Hard-soft interactions weak Example: Binding of H2O and H2S on platinum and alumina Limitations of method: still not properly considered molecules with discrete bonds.

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. Figure 3.26 The LUMO (a) and HOMO (b) for CO.

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

26. Newns Anderson Jellium Model 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

28. Data Verifies Rapid Exchange Figure 3.35 A comparison of the UPS spectrum of N2O adsorbed on a W(110) surface to the UPS spectrum of N2O 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.

30. Table Of Electron Density 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 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 Figure 3.47 A correlation between the vibrational frequency of the C-C stretch in C2D4 adsorbed on a series of closed packed metal surfaces at 100 K and the interstitial electron density of the metal. 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].)

33. Comparison To Ethylene Data Figure 3.47 A correlation between the vibrational frequency of the C-C stretch in C2D4 adsorbed on a series of closed packed metal surfaces at 100 K and the interstitial electron density of the metal.

34. CO Data 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