Transcript che 377 lectures - Classnotes For Professor Masel's Classes

ChE 553 Lecture 12
Theory Of Sticking
1
Objective
• Develop a qualitative understanding of
sticking
• Go over some models for the process
2
Topics For Today
•
•
•
•
•
Definition of sticking probability
Types of sticking vs coverage
Langmuir’s model
Precursor model
Immobile adsorption
3
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
4
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.
5
Sticking Probability
Num berof m oleculesthat stick
S ( ) 
Num berof m oleculesthatim pingeon a surface
(5.40)
The rate of adsorption, ra, is realted to the
sticking probability by
ra  S ( )Iˆz
(5.41)
Where Iˆz is the total flux of molecules onto the
surface in molecules/cm2 sec.
6
Sticking Probability Varies
With
•
•
•
•
Adsorbate
Trapping probability
Coverage/number of bare sites
Type of Adsorption
– Molecular or dissociated
• Mobility of adsorbed layer
7
Variation In Sticking
Probability With Coverage
Figure 5.14 A general classification of the variation in the sticking probability with
coverage. (Adapted from Morris et al. [1984].)
8
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.
9
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.
10
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.
11
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.
12
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.
13
Type F Behavior
• Multiple plateaus and
dips.
• Common on
polycrystalline
samples
14
Sticking Probability Also Varies With Gas
Temperature, Incident Energy
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].)
15
Theories Of Sticking
• Langmuir’s Model
• Precursor Model
– Equation also works for mobile adsorption
• Immobile adsorption
16
 
n
Pbare
( )  (1   ) n
ra  S (O ) Iˆz (1   ) n
(5.46)
(5.47)
2
.
0
-
8
PB =0
1
.
5
E
-
8
1
.
0
E
-
8
5
.
0
E
-
0
E
+
0
.
0
(5.48)
E
2
S    S (O) P
n
bare
Rate, M oles/cm /sec
Langmuir’s Model
1
9
PB =25
02
0
0 3
04
0 5
PA
Figure 12.34 A plot of the rate of the
reaction AC calculated from Equation
(12.143) with k4=0, PB = 0, 1, 2, 5, 10 and
25., KA = KB =1.
17
0
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.
18
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
19
Model Equations
Figure 5.16 The precursor mechanism for nondissociative adsorption.
AFI=precursor over a filled site
AMT=precursor over an empty site
20
Pages of Algebra Give Very
Complex Equation
ra
1  

 FI 

MT



I
P

K
K

K
K

K
K
1



K
K


MT
F 2 MT
FI
FI
MT
MT 2 F FI
 z trap

d




MT
FI
  I z Ptrap 1   K d K MT  K MT K F 2 MT  K MT K FI 1    K FI K F 2 MT 

KdMT  K MT 2 F  K MT 1  KdFI  K F2 MT  K FI 1    K F2 MT K MT 2 F  







(5.59)
21
Simplification
If sticking of AFI
negligible
 K P   1  
 1

rA  MT  
K 2P 
S    P
1 




1



I z  trap  K P 
 3
P 
K

2 
(5.60)
Sticking higher than Langmuir’s
22
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
23
Saturation Coverage Can Be Less Than Full Coverage
Because Isolated Sites Cannot Adsorb Gas
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.
24
Approximation: Roberts &
Miller
 4 
2
S  S0
1  
 4  
25
Roberts & Miller Predicts Higher
Initial Sticking Than Langmuir
i.e.
SMR ( )S (0)(1  )  SMobile ( )
2
(5.80)
Works at low concentrations
26
Why Higher Sticking Prob?
Figure 5.19 Site blocking by (a) two adjacent atoms, and (b) two atoms that separate.
27
Saturation Density Less Than
Unity
For random adsorption on
two adjacent sites
 max  86.4% 1D
 max  90.3% 2D
Vette’s approximation
S ( ) 


S (0)
(1   ) 3 (1    1
2
28
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
29