L18b-1
Review: Growth of Silicon Film by CVD
H
H
H
adsorption
Si
Si
Si
Si
Si
Si
H
Surface
reaction
Si
Si
Si
Si
Si
Si
Si
Si
Si
Write out elementary reactions and assume a rate-limiting step
1. Adsorption
SiH2  g  S
SiH2  S
Rate of adsorption = rate of attachment – rate of detachment

fSiH2 
rAD  k SiH2 PSiH2 fv  k SiH2 fSiH2
 rAD  k SiH2  PSiH2 fv 


K SiH2 

fv & fSiH2: fraction of the surface covered by vacant sites or SiH2, respectively
2. Surface reaction:
SiH2  S
Si  S  H2  g 
CSiCH2 fv 

rS  k S fSiH2  k S CSiPH2 fv
 rS  k S  fSiH2 

K
S


Surface coverage is in terms of fraction of surface, not conc of active sites
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-2
Review: Growth of Germanium Films
by CVD
Germanium films have applications in microelectronics & solar cell fabrication
GeCl2(g)  Cl2(g)
Gas-phase dissociation GeCl4(g)
GeCl2(g)  S
Adsorption (1)
kA
kA
kH
k H
GeCl2  S
Adsorption (2)
H2(g)  2S
2H  S
Surface reaction
S  Ge s  2HCl g  2S
GeCl2  S  2H  S 
 
 
k
Surface reaction is believed to be the rate-limiting step:
Rate of Ge deposition (nm/s):
"
rDep
 k S fGeCl fH2
2
ks: surface specific reaction rate (nm/s)
fGeCl2: fraction of the surface covered by GeCl2
fH2: Fraction on the surface occupied by H2
*Surface coverage is in terms of fraction of surface, not conc of active sites
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-3
Review: Catalyst Deactivation Kinetics
• Adjustments for catalyst decay need to be made in the design of reactors
• Catalyst activity a(t) is used as a quantitative specification
Catalyst activity at time t: a  t  
0  at  1
rA' (t)
rA' t 0
Reaction rate for catalyst used for time t
Reaction rate for fresh, unused catalyst
For fresh, unused catalyst, a t 0  1
Rate of consumption of reactant A on catalyst used for time t is:
r 'A  a  t  k  T  fn  CA,CB,....etc 
a(t): time-dependent catalyst activity k(T): T-dependent specific rate constant
fn(CA, CB…etc): function of gas-phase conc. of reactants, products &
Functionality of rd on reacting
contaminants
Function of activity
Rate of catalyst decay: rd  
species conc. h=1: no conc
dependence; h=Cj: linearly
dependent on concentration
da
 p a  t   k d  T  h  CA ,CB ,...,etc 
dt
Temperature-dependent specific decay constant
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-4
Review: Types of Catalyst Deactivation
1. Sintering (aging): loss of active surface due to high temperature
Second-order decay of reaction rate with respect to present activity:
Catalyst activity at time t:
Sintering decay constant:
rd  k da2
1
 Ed  1 1  
at 
k

k
T
exp
   
d
d 0
1  k dt
 R  T0 T  
2. Coking or fouling: carbonaceous material (coke) deposits on surface
Catalyst activity at time t:
Concentration of carbon CC  Atn
1
on surface (g/m2):
at 
m
1

k
'
t
A, n & m: fouling parameters
3. Poisoning: molecules (product, reactant or impurity) irreversibly bind
k'd
to the active site
P  S 
N  S
da
rd    a  t  k 'd CP
dt
a(t): time-dependent catalyst activity
kd: specific decay constant
CP: concentration of the poison
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-5
Review: Moving-Bed Reactor
• When catalyst decay occurs at a significant rate, they require frequent
regeneration or replacement of the catalyst
• Moving-bed reactor enables continuous regeneration of spent catalyst
• Operates in the steady state, like a PBR
• Reactant & catalyst enter at top of reactor
• Reactant & catalyst flow down the length of
the reactor together as a plug
• Product and spent catalyst (black) flow out of
reactor outlet
• Spent catalyst is regenerated by passing it
through a separate regeneration unit, and
newly regenerated catalyst is fed back into
the top of the reactor
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-6
Review: Moving-Bed Reactor Design
fresh
catalyst
US (g/s)
Z
Z + DZ
Reactants
u0 (dm3/s)
Catalyst flow US << reactant flow u0
As far as the reactants are concerned,
the reactor acts like a PBR:
dX A
FA0
 r 'A
dW
da
Assume the decay rate law is:
 k dan
dt
Find -da/dW and dXA/dW. Will need dt/dW.
W
W + DW
dt
1
W
dW


Relate t to US: t  U  dt  U
dW US
S
S
Multiply dt/dW by -da/dt to get –da/dW:
Products & coked catalyst
da  dt 
n 1 

k
a



d 
dt  dW 
U
 S
da k d n


a
dW US
 
If the rate of consumption of A for catalyst used for time t:r 'A  a  W  k  T  fn C j
dX A r ' A

dW
FA0
dXA a  W  k  T  fnC j


dW
FA0
XA
W
FA0dX A
 
  a  W  dW
0 k  T  fnC j
0
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-7
Guidelines for Deducing Mechanisms
• More than 70% of heterogeneous reaction mechanisms are surface
reaction limited
• If a species appears in the numerator of the rate law, it is probably a
reactant
• If a species appears in the denominator of the rate law, it is probably
adsorbed in the surface
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-8
The overall reaction for the hydrogenation (H) of ethylene (E) over a cobaltmolybdenum catalyst to form ethane (A) is H2(g) + C2H4(g) → C2H6 (g) and the
observed rate law is:
kPEPH
r 'E 
1  KEPE
Suggest a mechanism and rate-limiting step that is consistent with the rate law
PE appears in the denominator of the observed rate eq, so PE is adsorbed on
the surface. Neither PH or PA are in the denominator, so neither H or A are
adsorbed on the surface.

CES 
Adsorption :
ES
E  S rAD  k A  PEC V 

K

AD 
We’ll assume that the surface reaction is rate limiting
Surface rxn :
E  S  H  A  S rS  k SCESPH
No desorption step - PA isn’t in the r
AD  0  P C  CES
 K ADPEC V  CES
E V
denominator. Eliminate conc of k
K
AD
occupied & vacant sites on surface: A
Ct

 CV
site balance: Ct  C V  CES  Ct  C V  K ADPEC V
1  K ADPE
kPEPH
k K PP C
rS  kSCESPH  rS  S AD E H t k  kSK ADCt & K AD  KE  rS 
1  KEPE
1  K ADPE
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
L18b-9
Run
PA (atm)
PB (atm)
PC (atm)
-r’A(mol/g∙s)
1
0.1
1
2
0.073
2
1
10
2
3.42
3
10
1
2
0.54
4
1
20
2
6.80
5
1
20
10
2.88
6
20
1
2
0.56
7
1
1
2
0.34
8
1
20
5
4.5
0.6
-r'A
-r'A
0.4
0.2
0
8
8
6
6
4
4
-r'A
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
2
0
0
10
PA (atm)
20
2
0
0
10
PB (atm)
20
0
5
10
PC (atm)
We need to use these graphs to determine whether A, B, & C are in
the numerator, denominator, or both.
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
L18b-10
Run
PA (atm)
PB (atm)
PC (atm)
-r’A(mol/g∙s)
1
0.1
1
2
0.073
2
1
10
2
3.42
3
10
1
2
0.54
4
1
20
2
6.80
5
1
20
10
2.88
6
20
1
2
0.56
7
1
1
2
0.34
8
1
20
5
4.5
0.6
-r’A increases rapidly at low PA (means its in the
numerator), but it levels off at high PA (means its in
the denominator)→ PA in numerator & denominator
of -r’A
-r'A
0.4
0.2
0
0
10
20
PA (atm)
r 'A 
kPA ...
1  kPA ...
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
L18b-11
Run
PA (atm)
PB (atm)
PC (atm)
-r’A(mol/g∙s)
1
0.1
1
2
0.073
2
1
10
2
3.42
3
10
1
2
0.54
4
1
20
2
6.80
5
1
20
10
2.88
6
20
1
2
0.56
7
1
1
2
0.34
8
1
20
5
4.5
0.6
8
6
-r'A
-r'A
0.4
0.2
0
-r’A increases linearly as
PB increases → PB is
only in the numerator
4
2
0
0
10
PA (atm)
r 'A 
kPA ...
1  kPA ...
20
0
10
20
PB (atm)
r 'A 
kPAPB ...
1  kPA ...
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Run
PA (atm)
PB (atm)
PC (atm)
-r’A(mol/g∙s)
1
0.1
1
2
0.073
2
1
10
2
3.42
3
10
1
2
0.54
4
1
20
2
6.80
5
1
20
10
2.88
6
20
1
2
0.56
7
1
1
2
0.34
8
1
20
5
4.5
8
8
6
6
4
4
-r'A
-r'A
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
L18b-12
2
0
2
0
0
10
20
0
PB (atm)
r 'A 
kPAPB ...
1  kPA ...
5
10
-r’A ↓ with ↑PC→ rnx is
irreversible so PC must
be in the denominator
of -r’A. Therefore, C is
adsorbed on surface
PC (atm)
r 'A 
kPAPB
1  K APA  K CPC
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given for the gas-phase,
catalytic, irreversible reaction A + B→C is:
r 'A 
L18b-13
kPAPB
1  K APA  K CPC
Suggest a mechanism for this rate law.
PA and PC are in the denominator. A (reactant) and C (product) must be
adsorbed on the surface, but B is not adsorbed on the surface:
Adsorption of reactant A:

C A S 

r

k
P
C

AS
A  S rAD  k APACV  k  ACAS
AD
A A V
K A 

Desorption of product C:

PCC V 

r

k
C

CS
C  S rDC  kDCCS  k DPCCv
DC
D  CS
KD 

Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given for the gas-phase,
catalytic, irreversible reaction A + B→C is:
r 'A 
L18b-14
kPAPB
1  K APA  K CPC
Suggest a mechanism for this rate law.
PA and PC are in the denominator. A (reactant) and C (product) must be
adsorbed on the surface, but B is not:
Adsorption of reactant A:

C A S 

r

k
P
C

r

k
P
C

k
C
AS
A  S AD
AD
A A V

A A V
 A AS
K

A 
Desorption of product C:

PCC V 

r

k
C

r

k
C

k
P
C
CS
C  S DC
DC
D  CS

D CS
D C v
K

D 
Surface reaction step: B is not adsorbed on the surface, so B must be in the
gas phase when it reacts with A adsorbed on the surface.
The overall reaction is irreversible, so this step is likely irreversible.
A S B  CS
rS  kSCASPB
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given on slide 14 for the L18b-15
gas-phase, catalytic, irreversible reaction A + B→C is:
kPAPB
r 'A 
1  K APA  K CPC
Suggest a mechanism for this rate law.

CAS 
r

k
P
C

AS
A S
Adsorption of reactant A:
AD
A A V

K

A 
Surface reaction:
rS  kSCASPB
A S B  CS

PCCV 
r

k
C

Desorption of product C:
DC
D  CS

K

D 
Postulate that the surface reaction is the rate limiting step since that is true
the majority of the time. Check if that is consistent with the observed kinetics
Eliminate CA∙S & Cv C  C  C
r ' A  rS  kSC ASPB
t
v
AS  CCS
from rate eq
C
C
rAD
 0  PAC V  AS
 PAC V  AS
 K APA C V  C AS
kA
KA
KA
CS
rDC
P C
 0  CCS  C V
kD
KD
CS
 CCS 
PCC V
KD
Insert into site balance
and solve for Cv
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
L18b-16
The rate law suggested for the experimental data given on slide 13 for the gasphase, catalytic, irreversible reaction A + B→C is:
kPAPB
r 'A 
Suggest a mechanism for this rate law.
1  K APA  K CPC
Adsorption of reactant A:
AS
A S
Surface reaction:
A S B  CS
Desorption of product C:
CS
CS

CAS 
rAD  k A  PA CV 

K

A 
rS  kSCASPB

PCCV 
rDC  kD  CCS 

K

D 
Postulated surface r ' A  rS  kSC ASPB  kSK APAC VPB
reaction is rate limiting
Ct  Cv  C AS  CCS  Ct  Cv  K APAC V 
PCC V
KD
r ' A  rS  kSC ASPB  kSK APAC VPB  rS 
1
KC 
KD
k  k SK A C t
C AS  K APAC V
CCS  PCCV KD
Ct

 Cv
1  K APA  PC KD
kSK APA CtPB
1  K APA  PC KD
kPAPB
 rS 
1  K APA  K CPC
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.