ChE 553 Lecture 12 Theory Of Sticking

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Objective

• Develop a qualitative understanding of sticking

• Go over some models for the process

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Topics For Today

• Definition of sticking probability

• Types of sticking vs coverage

• Langmuir’s model

• Precursor model

• Immobile adsorption

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Review: Trapping Vs Sticking

Trapping• Lose enough energy to go below the zero in

potential• Can easily desorb

Sticking• Lose enough energy to fall into the bottom of the

well• Desorption much harder

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Rate Determining Step Different In Trapping And Sticking

Trapping – energy transfer is rate determining step – a gas surface collision only last 10-13 sec so need to transfer energy quickly

Sticking – finding an empty place on the surface to bond to is rate determining step – once trapped molecule stays on the surface for at least 10-6 sec. There is so much more time for energy transfer, so molecule thermally equilibrates with the surface. Rate determined by whether particles stick.

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Sticking Probability

The rate of adsorption, ra, is realted to the sticking probability by

Where is the total flux of molecules onto the surface in molecules/cm2 sec.

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surfaceaonimpingethatmoleculesofNumber

stickthatmoleculesofNumberS )(

(5.40)

za ISr ˆ)(

zI

(5.41)

Sticking Probability Varies With

• Adsorbate

• Trapping probability

• Coverage/number of bare sites

• Type of Adsorption– Molecular or dissociated

• Mobility of adsorbed layer

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Variation In Sticking Probability With Coverage

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Figure 5.14 A general classification of the variation in the sticking probability with coverage. (Adapted from Morris et al. [1984].)

Type A Behavior

• Curve A shows the simplest behavior: a linear drop in the sticking probability with coverage.

• Sticking probabilities drop with increasing coverage because the adsorbate takes up sites.

• If another adsorbate molecule comes in and hits the filled sites, the new adsorbate molecule cannot stick; instead it desorbs.

• Type A: Not usually observed.

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Type B Behavior

• Type B behavior in non-linear drop in the sticking probability with increasing coverage.

• Curvature in the sticking can arise for different reasons.

• If the adsorbate dissociatively adsorbs so it blocks two or more sites.

• Strong adsorbate/adsorbate interactions.

• Variation in the heat of adsorption with coverage.

• Immobile adsorbates.• Type B behavior is quite common.

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Type C Behavior

• Type C behavior is when the sticking probability is nearly constant up to some intermediate coverage and then drops at higher coverages.

• Type C behavior arises when the incoming molecules are initially trapped into a weakly bound ”precursor” state. The molecules then move around the surface and find a site to adsorb.

• Type C behavior also arises when adsorbate layer is mobile.

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Type D Behavior

• Type D behavior occurs when the sticking probability initially drops with increasing coverages, then rise again.

• Type D arises in systems that show a phase transition.

• One phase adsorbs more strongly than another.

• Surface reconstructions are a common phase transition.

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Type E Behavior

• Type E behavior – the sticking probability initially rises as one adsorbs gas. Probability drops as one fills up sites.

• Experimentally, type E behavior occurs mainly in trapping-dominated systems and in other systems where energy transfer plays an important role.

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Type F Behavior

• Multiple plateaus and dips.

• Common on polycrystalline samples

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Sticking Probability Also Varies With Gas Temperature, Incident Energy

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Figure 5.15 The initial sticking probability of hydrogen on a Ni(111), Ni(110), Cu(111), Pt(110) Фi = 10˚ and 60˚ as a function of the energy

of the incident gas. (Data of Rendulic and Winkler [1989].)

Theories Of Sticking

• Langmuir’s Model

• Precursor Model– Equation also works for mobile adsorption

• Immobile adsorption

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Langmuir’s Model

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nza

nnbare

nbare

IOSr

P

POSS

)1(ˆ)(

)1()(

)(

(5.46)

(5.47)

(5.48)

P =25B

PA

0 10 20 30 40 500.0E+0

5.0E-9

1.0E-8

1.5E-8

2.0E-8

Rat

e, M

oles

/cm

/se

c 2

P =0B

Figure 12.34 A plot of the rate of the reaction AC calculated from Equation (12.143) with k4=0, PB = 0, 1, 2, 5, 10 and

25., KA = KB =1.

Langmuire Model Limited

• Only explains type A&B behavior.• In reality, species can be trapped and

move around to find sites.• Adsorbates interact. These interactions

are not included in the Langmuir analysis.

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Precursor Model

Precursor model• Gas phase molecules trapped into a

precursor state• Move around• Can stick when over a bare site• Can move atoms out of the way when

over and empty site

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Model Equations

AFI=precursor over a filled site

AMT=precursor over an empty site20

Figure 5.16 The precursor mechanism for nondissociative adsorption.

Pages of Algebra Give Very Complex Equation

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F2MTMT2FFIMT2F

FIdMTF2MT

MTd

MT2FFIFIMTMT2FMTMTFId

MTtrapz

FIF2MTMTFIFIMT2FMTFItrapz

a

KK1KKK1KKK

KK1KKKKKK1PI

KK1KKdMT

KKKKPI

1

r

(5.59)

Simplification

If sticking of AFI negligible

(5.60)

Sticking higher than Langmuir’s

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11

1

23

21

PP

PP

z

A

KK

KK

trapMTP

Ir

S

Immobile Adsorption

• Molecules stick when they land on a bare site

• Do not stick elsewhere• Leads to variation from Langmuir when

molecules adsorb on more than one site

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Saturation Coverage Can Be Less Than Full Coverage Because Isolated Sites Cannot Adsorb Gas

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Figure 5.18 Some of the arrangements formed with immobile dimers on a square surface. (a) Bare surface. (b) One dimer. (c) Two dimers. (d) Saturated surface.

Approximation: Roberts & Miller

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214

40SS

Roberts & Miller Predicts Higher Initial Sticking Than Langmuir

i.e.

(5.80)

Works at low concentrations

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)()1)(0()( 2 MobileMR SSS

Why Higher Sticking Prob?

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Figure 5.19 Site blocking by (a) two adjacent atoms, and (b) two atoms that separate. 

Saturation Density Less Than Unity

For random adsorption on two adjacent sites

Vette’s approximation

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D

D

2%3.90

1%4.86

max

max

11(3)1(2

)0()( S

S

Summary

• Sticking determined by ability of molecules to find sites

• Sticking varies with T and • S(0) approximated by ion cores in jellium• S() three models

– Langmuir– Precursor/mobile– Immobile

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