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ChE 553 Lecture 15 . Catalytic Kinetics Continued. Object. Examine the effects of pairwise interactions on rates of surface reactions Interactions change apparent order Can fit to Langmuir, but with the wrong mechanism. Started Catalytic Kinetics Last Time. - PowerPoint PPT Presentation
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ChE 553 Lecture 15 Catalytic Kinetics Continued
1
Object• Examine the effects of pairwise
interactions on rates of surface reactions– Interactions change apparent order– Can fit to Langmuir, but with the wrong
mechanism
2
Started Catalytic Kinetics Last Time
• Catalytic reactions follow a catalytic cycle reactants + S adsorbed reactantsAdsorbed reactants products + S
• Different types of reactionsLangmuir HinshelwoodRideal-Eley
3
Key PredictionsUnimolecular reactions• Rate increases with pressure, levels off• Rate always increases with temperature• Very sensitive to poisonsBimolecular reactions• Rate rises reaches a maximum at finite temp and
pressure, then drops• Sensitive to poisons
4
Qualitative Behavior For Unimolecular Reactions (AC)
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
5
0.01 0.1 1 10 1001E+16
1E+17
1E+18
1E+19
1E+20
770 K
1070 K
870 K
1270 K1670 K
Ammonia pressure, torr
Rat
e, M
olec
ules
/cm
-sec
2
rk3KA PAS0 k4KCPCS0
1 KA PA KBPB KCPC
Qualitative Behavior For Bimolecular Reactions (A+Bproducts)
PA
0 10 20 30 40 500.0E+0
5.0E+13
1.0E+14
1.5E+14
2.0E+14
2.5E+14
Rat
e, M
olec
ules
/cm
/se
c 2
6
Figure 12.32 A plot of the rate calculated from equation (12.161) with KBPB=10.
1012
1013
Rat
e, M
olec
ules
/cm
-sec
2
1011
10-6
CO pressure, torr10-710-8
390 K
410 K
450 K
440 K
Physical Interpretation Of Maximum Rate For A+BAB
• Catalysts have finite number of sites.
• Initially rates increase because surface concentration increases.
• Eventually A takes up so many sites that no B can adsorb.
• Further increases in A decrease rate.
7
Methods Do Not Always Work In Detail
• Pairwise interactions between adsorbed species– Leads to ordering, coverage dependent
kinetics– Can produce oscillations, steady states
that depend on how steady state is reached
8
Key Qualitative Effects• Ordered Overlayers
• Island formation
• Fluctuations
9
The Effect Of An Ordered C(2x2) Overlayer
• Notice that the environment of B is independent of the coverage of A provided θA > 0.5
• The rate is almost independent of the A concentration– Not exactly independent
because repulsions speed rate
10
Monte Carlo Calculation To Estimate Rate
Montecarlo to estimate coverage:• Randomly choose one of three steps
– Adsorption/desorption step– Reaction– Diffusion
• Use Metropolis algorithm to see whether step should be choosen
• Calculate rate via an ensemble average
11
Adsorption/desorption Similar To Previous Work
• Pick a random site• If empty adsorb A or B• If filled desorb molecule• If energy goes down
accept the step• If energy goes up accept
the step with probability exp(-βΔE)
• Repeat12
Diffusion Changes Algorithm Slightly
• Pick a random site• Pick an adjacent site • If adjacent site empty move
molecule• If adjacent site filled do nothing• If energy goes down accept the
step• If energy goes up accept the
step with probability exp(-βΔE)• Repeat
13
Reaction Requires Additional Changes
• Pick a random site• Pick an adjacent site • If A adsorbed on one of the
sites and B adsorbed on a different site Assume A and B react with a probability of p= koexp(-EA/kT)
• RepeatNote only 1 in 108 attempts
leads to reaction
14
Next: Estimate The Rate
Rate = koexp(-EA/kT) * (number of adjacent pairs of molecules)
15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Rat
e
A
h = -0.5AB
h = +0.5AB
Result Of Simulation Using Montecarlo
16
βhAA = -3
Fit
Langmuir
Implications• Can fit rate data to Langmuir kinetics even
where coverage does not follow Langmuir isotherm– Langmuir kinetics calculated for the wrong
mechanism (aqua line) fit the data– However, Langmuir kinetics calculated for the
correct mechanism (orange line) do not fit the data• Cannot use kinetics to infer mechanism
17
Dynamic Islanding
If diffusion is slow see dynamic islanding
• A molecules next to B molecules react
• A molecules next to A unreactive
• B molecules next to B unreactive
Leads to islands of A and B
18
Rate Oscillations Observed Experimentally Under Such Conditions
19
Interactions Between Molecules Seen In Transient Measurements
Temperature programmed desorption (TPD)
• Adsorb gas on cold surface
• Heat at a constant 1-100K/sec
• Measure gas evolution as a function of time
20
Pumps
Heat
Temperature
Rat
e
Typical TPD Spectrum
21
100 200 300 400 500 600 700 800 900 1000
Temperature (K)
Des
orpt
ion
Rat
e5
4
3
2
1
0
2 AMU (Hydrogen)
30 AMU (Ethane)
27 AMU (Ethylene)
x10 16 AMU (Methane)
TPD of ethylene
Why Peaks In TPD?
22
340 360 380 400 420 4400
0.2
0.4
0.6
0.8
1
CoverageRate
Constant
(TPD Spectrum)
Temperature, K
1/sec
Fractional
Rate
Qualitative Effects In TPD
23
350 400 450 500
Des
orpt
ion
Rat
e
Temperature, K350 400 450 500
n =1 n =2
Temperature, K
Qualitative Effects On TPD
24
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(Thousands)
6
5
4
3
2
1
0
Ea =10 kcal/mole
20
30 40 50
Qualitative Effects On TPD
25
300 350 400 450 500 550250 300 350 400 450 500
Temperature Temperature
Des
orpt
ion
Rat
e
First Order Second Order
1011
1015
1011
1015
TPD To Estimate Ea
26
0 10 20 30 40 50
800
700
600
500
400
300
200
100
TPD
Pea
k Te
mpe
ratu
re, K
E A ,Kcal/mole
k 0
= 10
14/K
k 0
= 10
10/K
H
H
Ea = (0.06 kcal/mole-K) Tp
Can Use Methods To Get Approximate Activation Energies
27
100 200 300 400 500 600 700 800 900 1000
Temperature (K)
Des
orpt
ion
Rat
e5
4
3
2
1
0
2 AMU (Hydrogen)
30 AMU (Ethane)
27 AMU (Ethylene)
x10 16 AMU (Methane)
TPD of ethylene
Method Assumes No Interactions Between Molecules
28
200 220 240 260 280 300 320 340 360 380 400 420 440 460
Temperature, K
Mas
s Sp
ec S
igna
l
300 320 340 360 380 400 420 440 460 480 500
Temperature, KD
esor
ptio
n R
ate
k dConstant
k dVaries WithNumber OfNeighbors
x3
x3
x3
x3
x3
Attractive InteractionsRepulsive Interactions
Repulsive Interactions
29
= 0.44 = 0.73Adsorption Site Adsorbed Molecule
200 220 240 260 280 300 320 340 360 380 400 420 440 460
Temperature, K
Mas
s Spe
c Si
gnal
Attractive Interactions
30
300 320 340 360 380 400 420 440 460 480 500
Temperature, KD
esor
ptio
n R
ate
k dConstant
k dVaries WithNumber OfNeighbors
x3
x3
x3
x3
x3
Ea Varies Non-linearly With Coverage
310 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
32
30
28
26
24
22
20
18
16
EaP
, Kca
l/Mol
ed h = -2 kcal/mole
h = 2 kcal/mole
h = 0
Summary• Pairwise interactions change kinetics in
unexpected ways– Data fits Langmuir-Hinshellwood rate
expression – but for the wrong mechanism– Ea varies non-linearly with coverage even
though interactions linear with number of nearest neighbors
– Multiple peaks in TPD
32
Key Implication• Extreme care needed in using kinetics
to infer mechanisms etc– Can easily get the wrong mechanisms with
the wrong analysis to fit data.
33
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