ChE 553 Lecture 11 New Topic: Kinetics Of Adsorption 1.
-
Upload
basil-hudson -
Category
Documents
-
view
218 -
download
1
Transcript of ChE 553 Lecture 11 New Topic: Kinetics Of Adsorption 1.
ChE 553 Lecture 11 New Topic: Kinetics Of
Adsorption
1
Objective
• Start to Look at rates of adsorption– Qualitative features– Models
2
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
3
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
4
Definitions
Scattering, trapping, sticking
5
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
6
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.
7
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.
8
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
9
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
10
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
12
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
13
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)
14
wEo '
s
s
g
s
g
crit Ew
m
m
m
m
E
2
1
4
Masel-Weinberg-Merrill Ion Cores In Jellium Model
15
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
16
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
17
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.
18
Zwanzig-Ehrlich Model:
19
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
20
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
21
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.
22
Recall Langmuir’s Model Of Adsorption
23
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
24
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
25
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)
26
LangTMW
.
EXg
ALangmuirAMUKcm
molecules10x972
1/21/2216
(5.44)
Sticking Probability Can Be Made By Measuring Coverage vs Exposure And Differentiating
27
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
28