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 reactants

Adsorbed reactants products + S• Different types of reactions

Langmuir Hinshelwood

Rideal-Eley

3

Key Predictions

Unimolecular reactions• Rate increases with pressure, levels off• Rate always increases with temperature• Very sensitive to poisons

Bimolecular 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

-se

c2

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

-se

c2

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 reaction14

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

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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

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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

3040

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

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0 10 20 30 40 50

800

700

600

500

400

300

200

100

TPD

Pea

k T

empe

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

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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

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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

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= 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 S

pec

Sig

nal

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

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0 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/M

ole

d

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

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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.

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