ChE 553 Lecture 4 Models For Physisorption

And Chemisorption I

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Objective For Today

• Quantify the results from lect 3

• Forces that determine bonding

• Large trends– Physical forces– Electronegativity– Hardness/density of states

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Forces Between a Molecule and Metal Surface

• Dipole-Induced dipoles

• Correlation – instantaneous dipole-dipole interactions

• Electron reorganization /bonding

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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

Literature Discusses Two Types Of Adsorption

• Physisorption– Dipoles and

correlations dominate

• Chemisorption– Electron

reorganizations dominate

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http://www.lightwave-scientific.com/LWADFMoreInformationP1.htm

Usually Not A Clear Distinction

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Physisorption & Chemisorption Usually Treated Differently In The Literature

• Physisorption– Add up physical interactions assuming that

there are no electronic rearrangements

• Chemisorption– Considering electron reorganization

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Modeling Physisorption

Usual model: add up the physical forces

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sMsMa

sMMS rrErE

Working Out The Algebra

Assume Leonard-Jones potential

Pages of algebra

8

612

6150

sMsM

se

LondsMa

rrrr

r.CE

39

6120

MM

se

LondsMMszz

r.CzE

ExpectedTheoretically for induced dipole/induc

ed dipole

A Comparison Of Heats Of Adsorption Calculated To Measure

Gas

Surface

Calculated Heat of

Adsorption (cal/mole)

Measured Heat of

Adsorption (cal/mole)

Nonmetals He Graphite 357 340 Ne Graphite 830 830 Ar Graphite 2220 2700 Kr Graphite 2950 3900 C5H12 Graphite 9300 10000 C6H14 MgO 9200 9900 C7H16 MgO 10600 11400 C6H14 Graphite 11000 11800 Ar NaCl 1978 2180 Ar KBr 2325 2440

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A Comparison Of Heats Of Adsorption Calculated To Measure

Metals He Pt 230 265 Ne Pt 330 370 Ar Pt 940 1320 Kr Pt 1240 2110 Ar Zn 1100 1570 Ar Cu 1090 2090

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Calc Experiment

Starting to see reorganization of

electrons

New Topic: Modeling Chemisorption

Several different modelsLocal chemical bondsBonds to free electronsIonic forces

 Local chemical bonds works on some semiconductors Bonds to free electrons dominate on metals Ionic forces dominate on oxides and other insulators

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Modeling Bonds To Free Electrons

Three models

• Algebraic models

• Jellium models

• Full QM– Clusters– Slabs

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http://www.multi.jst.go.jp/en/theme/01_Oshiyama.html

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

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Derivation

Taylor series

A = Electronegativity

A= hardness

= number of electrons

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2

21111 A

AAAAAn

nEE

1An

Derivation For The Interaction Of A and B

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Derivation For The Interaction Of A and B

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Result

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22

1

2

1BA

BA

BBDAADBAD

H=0 Interaction

Numerical Comparison

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Gas

Surface

Measured Heat of Adsorption (kcal per mole

of H2)

Eley’s Calculation (kcal/mole)

Calculation With Flores’

[1981] Values of the

Parameters (kcal/mole)

H2 Cu(111) -10 -13.6 -12 H2 Ni(111) -23 -17.2 -19 H2 W(110) -33 -43.6 -35 H2 Fe(110) -27 -19.5 -28 H2 Pt(111) -18 -19.2 -22

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

For Ionic Systems The Equation Becomes

• EQU 3.48

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momo

momo

momo

ab

ABbB

aA

bdonortheonorbitalsfilled

aacceptortheonorbitalsemptyAB

BAr EE

CC

R

ZZE

2

___

___

)(2

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.

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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.

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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.

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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.

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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.

24Figure 3.26 The LUMO (a) and HOMO (b) for CO.

Jellium Model

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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.

Newns Anderson Jellium Model

26Figure 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.

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

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Data Verifies Rapid Exchange

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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].)

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.

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Table Of Electron Density

Metal Morruzzi DeBoer Metal Morruzzi DeBoer Metal DeBoer K 0.29 0.27 Rb 0.23 0.22 Cs 0.17 Ca 0.87 0.75 Sr 0.70 0.59 Ba 0.53 Sc 1.80 2.05 Y 1.57 1.77 La 1.64 Ti 2.93 3.51 Zr 2.58 2.80 Hf 3.05 V 4.17 4.41 Nb 3.60 4.41 Ta 4.33 Cr 5.01 5.18 Mo 4.59 5.55 W 5.93 Mn 5.14 4.17 Tc 4.67 5.93 Re 6.33 Fe 5.24 5.55 Ru 4.68 6.13 Os 6.33 Co 4.98 5.36 Rh 4.24 5.45 Ir 6.13 Ni 5.08 5.36 Pd 3.38 4.66 Pt 5.64 Cu 3.60 3.18 Ag 2.50 2.52 Au 3.87 Na 0.49 0.55 Mg 1.44 1.60 Al† 3.73

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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.

Comparison To Data

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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].)

Comparison To Ethylene Data

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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 C2D4

adsorbed on a series of closed packed metal surfaces at 100 K and the interstitial electron density of the metal.

Comparison To Ethylene Data

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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.

CO Data

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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)

SummaryPhysisorption• Physical forces dominate

Add up the forces

Chemisorption Metals• Metalic bonds dominate

Radicals attached to JelliumRapid exchange of electrons

• Hard-hard, soft-soft interactions strong• Hard-soft interactions weak

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