ChE 553 Lecture 11 New Topic: Kinetics Of

Adsorption

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Objective

• Start to Look at rates of adsorption– Qualitative features– Models

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Topics

Definitions of scattering, trapping, sticking

Theory of trapping Role of thermal accommodation Models: hard spheres, ion cores in jellium,

spring models

Introduction of sticking Definition of sticking probability

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What Occurs When A Molecule Sticks?

• Molecule attracted to surface• Hits surface

– Too much momentum to stick

• Loses excess energy and momemtum

• Diffuses along surface until it finds a place with strong binding

Rate usually determined by• Mass transfer – how often do

molecules collide• Energy and momentum transfer

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Definitions

Scattering, trapping, sticking

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Figure 5.1 A schematic of the processes that can occur when a molecule collides with a solid surface.

Definitions

• Elastic Scattering• Inelastic Scattering• Trapping• Sticking

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Figure 5.2 A series of trajectories seen when a molecule collides with a surface. The trajectories were calculated with the computer program in Examples 5.C and 5.D.

Physics Of Trapping

a) Molecule comes in and hits the surface.

b) Loses energy, so the molecule no longer leaves the surface.

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Figure 5.2 A series of trajectories seen when a molecule collides with a surface. The trajectories were calculated with the computer program in Examples 5.C and 5.D.

Basic Theory Of Trapping

Calculate how much energy the molecule loses as it collides with the lattice. Does it lose enough to fall into the well.

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Figure 5.4 The potential energy seen by a normal incidence molecule when it collides with a solid surface. A series of lines is shown because the potential is different when the incoming atom hits at different places along the surface.

Need To Understand Energy Flow In Gas Surface Collisions To Proceed

• Key concept (Baule) – temperature discontinuity when gases interact with surface

• Implication – when a molecule collides with a surface, it exchanges some but not all of energy with the surface

• If molecules hotter then surface they cool

• If molecules cooler than surface they heat

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WallGas

ConventionalTheory

Knudsen'sexperiment

-3 -2 -1 0 1 2 3

Distance, microns

900

1000

1100

1200

1300

Tem

pera

ture

Knudsen's experiments of the temperature of flames near surfaces.

The Thermal Accommodation Coefficient

Ein = incident energy

Eout = exiting energy

Es = energy if molecule accommodated with the surface

=1 implies that the temperature of a desorbing molecule equals the surface temperature

=O implies Ein = Eout

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EsE

EE

in

outin

Baule’s Model For Accommodation Coefficients:

• Assume molecules behave like billiard balls

• Use material from freshman physics to calculate how much energy is transferred during collisions

11Figure 5.3 A diagram of the collision between a hard sphere

adsorbate molecule and a hard sphere surface atom.

Lots Of Algebra Yields

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2

1

42

s

g

s

g

m

m

m

m.

ˆ

(5.10)

Weinberg-Merrill Model For Trapping Probabilities

Molecule

1) Gains W

2) Loses energy when it collides with atomic cores – assume given by Baule result

3) Bounces

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Does molecule have enough energy to leave? (need to have more energy than W after collision)

Result: Molecule Will Be Trapped Whenever

(5.13)

Algebra yields

(5.17)

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wEo '

s

s

g

s

g

crit Ew

m

m

m

m

E

2

1

4

Masel-Weinberg-Merrill Ion Cores In Jellium Model

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Figure 5.5 A schematic of all idealized jellium potential over a closed packed metal surface.

otherwise

provided

cos

cos

2

2

0

0

4

1

1

2

trap

T

siis

g

iis

g

trap

P

P

wEEm

m

Em

m

P

Comparison To Data

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Figure 5.7 A comparison of the trapping probability for Xe on Pt(111): (a) Equation 5.26, with ms = 195 AMU, w = 8 kJ/mole; (b) Arumainayagam et al.’s

[1990] data and Langevin results.

Key Prediction Of Model

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Figure 5.8 A plot of the trapping probability predicted by Equation 5.26 as a function of the incident energy of the molecule for various vales of mg/ms.

Figure 5.9 A plot of Equation 5.26 as a function of mg/ms for Eicos2(Фi)/w = 0.1, 0.5, 1, 2, 5, 10.

Model Works Well On Metals, Not As Well On Insulators

Reason: metals – atoms cores move separately

Insulators – atom cores are bumping up against each other – you cannot move one atom, you have to move several atoms

In effect the mass that you have to move goes up so energy transfer goes down.

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Zwanzig-Ehrlich Model:

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s

gME

s

MEME

m

m

m

KB

2

Figure 5.10 Zwangig’s [1960] model of the interaction of a gas molecule with a one-dimensional chain of surface atoms.

Figure 5.12 The critical energy for trapping. (Adapted from calculations of McCarroll and Ehrlich [1963].)

(5.31)

Never seen experimentally - reason atoms not connected by springs.

Summary Of Trapping:

• Rate determined by how energy lost during collisions

• Larger well depths increase trapping• Lighter adsorbates decrease trapping• Hotter surfaces decrease trapping• Heavier surface atoms decrease trapping• Stiffer surfaces decrease trapping

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Trapping And Sticking Are Similar

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 and 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 much more time for energy transfer, so molecule thermally equilibrates with the surface. Rate determined by whether particles stick.

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Recall Langmuir’s Model Of Adsorption

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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.

Sticking Probability

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surfaceaonimpingethatmoleculesofNumber

stickthatmoleculesofNumberS

(5.40)

Rate Of Adsorption

The rate of adsorption, ra, is related to the

sticking probability by

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

From kinetic gas theory

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4

v

sin

sin gi

yl

ixx

d

dII

(5.43)

za ISr (5.41)

Practical Exposures Measured In Langmuirs

1L = 1 second exposure at 10-6 torr pressure

 

1 torr = 1/760 atm.

 

Corresponds to 3x1014 molecules of CO, 2x1015 molecules of H2 (H2 moves faster than CO)

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LangTMW

.

EXg

ALangmuirAMUKcm

molecules10x972

1/21/2216

(5.44)

Sticking Probability Can Be Made By Measuring Coverage vs Exposure And Differentiating

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AdEX

AdS (5.45)

Figure 5.13 The amount of carbon monoxide that sticks on a Pt(410) surface as a function of the carbon monoxide exposure. (Data of Banholzer and Masel [1986].)

Summary

• Trapping and Sticking

• Trapping rate determined by energy accommodation– Baute’s model related

• Sticking rate determined by finding bare sites

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