10.569 Synthesis of Polymers
Prof. Paula Hammond
Lecture 11: Radical Polymerization, Homogeneous Reaction Rate Kinetics
How to determine MW in free radical polymerization
Kinetic Chain Length
ν = # of monomers added per effective free radical
ν =
ν=
rate of chain growth
rate of chain growth
=
rate of chain initiation rate of chain termination
Rp
Ri
=
Rp
Rt
=
k p [M ]
1
2( fk d k t [I ]) 2
p n = ν if termination is by disproportionation process
p n = 2ν if termination is by coupling Generally, (if no chain transfer): p n = 2aν where ½ ≤ a ≤ 1
100%
disproportionation
100%
disproportionation
M n = M n ⋅ pn
molecular weight of
vinyl monomer unit
What happens more often?
• Coupling usually greater than disproportionation
• Percent of coupling increases if: steric factors prevent effective coupling:
CH3
CH3
C
C
CH3
CH3
or if: β-hydrogens are more reactive:
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
H
C
+
C
C
H
ν=
Consider
k p [M ]
1
2( fk d k t [I ]) 2
1
⎛ fk p [I ] ⎞ 2
⎟ [M ]
Rp = k p ⎜⎜
⎟
⎝ kt ⎠
Increase Rp by: [M]↑, [I]↑
But increase ν → [M]↑, [I]↓
Thus you want to increase [M]
Chain Transfer
1.
ktr
Mn
+ X' Y
Rtr =
d [Y ⋅]
= k tr [M ⋅][X '−Y ]
dt
Mn
ktr = transfer constant
X' + Y
Chain transfer can occur when there
are solvent impurities.
But sometimes using chain transfer
can be advantageous.
2. Y
+ M
ka
YM
3. YM
+ M
kp
Chain transfer agent → CTA
Used to decrease MW in polymerization
YMn
kp >> ktr and kp ≈ ka ⇒ Rp is the same p n ↓
slightly – moderately
depending on CTA kp << ktr and kp ≈ ka ⇒ Rp ∼ same p n ↓ dramatically kp >> ktr and ka < kp ⇒ Rp↓ slightly and p n ↓ slightly
kp << ktr and ka < kp ⇒ Rp↓ drastically and p n ↓ drastically Transfer Types:
1. to monomer: ktr,m
Mn⋅ + M → Mn + M⋅
2. to solvent
or impurity
Mn⋅ + S → Mn + S⋅
ktr,s
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 11
Page 2 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
or CTA
3. to initiator:
Mn⋅ + I → Mn + I⋅
ktr,I
All act to decrease p n : (assume coupling)
pn =
Rp
Rp
=
Rt
Rt
+ Rtr,m + Rtr,s + Rtr,I
+ k tr,m [M ⋅][M ] + k tr,s [M ⋅][S ] + k tr,I [M ⋅][I ]
2
2
Use resistor analogy: (resistors in series)
C = transfer constant
= relative rate const vs. Rp
Cm =
k tr,m
kp
, CS =
k tr,S
kp
, CI =
k tr,I
kp
since Rp = kp[M⋅][M]
1
pn
=
Ri
[S ] + C [I ]
+ Cm + C S
[M ] I [M ]
2R p
Additive effect of each constant
Rt
2R p
⎛ 1 ⎞
⎟ ↔ 1
⎜
⎜p ⎟
2ν
⎝ n ⎠o
Often only have transfer to CTA (or impurity)
1
pn
=
Ri
[S
]
+ CS
[M ]
2R p
1
( fk d k t [I ]) 2
k p [M ]
=
1
2ν
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 11
Page 3 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
For a given amount of initiator [I] and monomer [M]
⎛ 1 ⎞
⎟ + C S [S
]
=⎜
⎜
[M ]
pn ⎝ p n ⎟⎠ o
1
1
pn
Increase
Increas
e
MW
MW
Cs
1
pn
o
o
[S]
[M]
Useful to control MW is free radical with high kp and/or really low kt
Cs values for different compounds:
π orbitals
• alkanes (weakest)
• cyclic hydrocarbons
• benzenes, aromatics
H
unstable negative charge → H- extraction unlikely
Increasing radical stability
<
<
weakest
<
share e- cloud
with other C atoms
CH2
resonance
stabilization
CH2
High Cs values:
• weak C—H bonds
• stabilized by conjugation
O
O
N
C
• weak C—Cl, C—Br, C—I
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 11
Page 4 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
R
R
C
R
Cl
+ R
R
H
C
+ RCl
H
• weak S—S bonds, S—H
weakest
largest CS
CTA (chain-transfer-agents)
CS x 104
CS x 104
For styrene
Vinyl acetate
Benzene
0.023
1.2
Cyclohexane
0.031
7.0
0.42
17.0
n-butyl alcohol
1.6
20.0
CHCl3 (chloroform)
3.4
150.0
Tri-methyl amine
7.1
370
210,000
480,000
Heptane
n-butyl mercaptan
SH
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 11
Page 5 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.