This document summarizes key concepts about step-growth polymerization from a lecture by Professor Paula Hammond. It discusses the kinetics and equilibrium considerations of step-growth polymerization, including how the average degree of polymerization (n_p) depends on reaction constants and monomer concentration over time. It also describes different experimental conditions that can be used to drive step-growth polymerization forward, such as removing byproducts like water, using acid catalysis, conducting reactions at high temperature, or performing polymerization in bulk or with solvent.

1. 10.569 Synthesis of Polymers
Prof. Paula Hammond
Lecture 3: Step Growth Polymerization, Types of Monomers, Kinetics and
Equilibrium Considerations, Closed vs. Open Systems
Kinetics of Step Growth Polymerization (Chapter 2)
A + B → polymer + byproduct
rate of polymerization
=
Rp
d M d a d b
Rp k a b
dt dt dt
− − −
⎡ ⎤ ⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦ ⎣ ⎦
= = = = ⎡ ⎤⎡ ⎤
⎣ ⎦⎣ ⎦
Assume r =1, where r is the stoichiometric ratio.
b
a
r =
a b
=
⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦
Terminology n
p varies with t → o
n
a
p
a
⎡ ⎤
⎣ ⎦
=
⎡ ⎤
⎣ ⎦
( )
n
X p. 50
2
d a
k a
dt
− ⎡ ⎤
⎣ ⎦ = ⎡ ⎤
⎣ ⎦
2
d a
kt
a
− ⎡ ⎤
⎣ ⎦ =
⎡ ⎤
⎣ ⎦
1 1
o
kt
a a
− =
⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦
1
o
o
a
a kt
a
⎡ ⎤
⎣ ⎦
− = ⎡ ⎤
⎣ ⎦
⎡ ⎤
⎣ ⎦
1
o
a
a
⎡ ⎤
⎣ ⎦
π = −
⎡ ⎤
⎣ ⎦
in book, p
=
π (p. 46)
1
1
o
a
a
⎡ ⎤
⎣ ⎦
=
− π
⎡ ⎤
⎣ ⎦
1
1 1
1
o n
a kt p
= − = −
⎡ ⎤
⎣ ⎦ − π
Notes:
1.
1
M
t
∝
⎡ ⎤
⎣ ⎦ as time ↑, concentration of monomer ↓
2. n
p increases linearly with time
kf >> kr
LeChatlier’s Principle: remove water
a + b
kf
kr
c + d
a + b
kf
kr
c + d
To drive reaction forward
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date

2. Making esters:
COOH +
Keq
+ H2O
OH C O
O
COOH +
Keq
+ H2O
OH C O
O
Ester can hydrolyze with water and
go backwards (reverse rxn) → drug delivery
2
eq
COO H O
K
COOH OH
⎡ ⎤ ⎡ ⎤
⎣ ⎦
=
⎡ ⎤⎡ ⎤
⎣ ⎦⎣ ⎦
M
= =
⎣ ⎦
10.569, Synthesis of Polymers, Fall 2006 Lecture 3
Prof. Paula Hammond Page 2 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date
Assume at t M
0 : o
⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦
o
COOH OH M
= π = π = π
⎡ ⎤ ⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦ ⎣ ⎦
Put in terms of π:
o o
COO
⎡ ⎤
⎣ ⎦
“ “
[ ] =
OH
( )
1
o o o
COOH OH M M M
= = − π = −
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ π
( )
( )
2
2 2
1
o
o
M
K
M
π⎡ ⎤
⎣ ⎦
=
− π
⎡ ⎤
⎣ ⎦
( )
2
2
1
K
π
=
− π
1
2
1
2
1
K
K
π =
+
In closed system, limited by K (reaction constant).
That also means rxn and polymer limited by K.
1
2
1
1
1
n
p K
= = +
− π
where n
p is the # average degree of polymerization (# of units in polymer)
Polyesterification: K: 1 ∼ 10
n
p ∼ 2 - 5 monomers
Polyamidation: K: 100 – 1000
n
p : 10 - 40
In between: removing some of the water
Open Driven System
Removing byproduct
- H2O by temperature, low pressure, or N2 blowing of water
- Acid like HCl, base neutralization
( )
2 n
H O MW p
↔
⎡ ⎤
⎣ ⎦ How H2O affects n
p

3. COH + + H2O
OH C O
O
O
COH + + H2O
OH C O
O
O
( )
2 2
2
1
o
COO H O H O
K
COOH OH M
π
⎡ ⎤ ⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦ ⎣ ⎦
= =
⎡ ⎤⎡ ⎤ − π
⎡ ⎤
⎣ ⎦⎣ ⎦ ⎣ ⎦
10.569, Synthesis of Polymers, Fall 2006 Lecture 3
Prof. Paula Hammond Page 3 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date
2
1
1 1
eq
o
H O
K
M
⎡ ⎤
π ⎣ ⎦
= ⋅ ⋅
− π − π ⎡ ⎤
⎣ ⎦
1
1
n
p =
− π
1 1 1
1 1
1 1 1 1
n
p
π − π
= − = − = −
− π − π − π − π
( ) 2
1
eq
n n
o
H O
K p p
M
⎡ ⎤
⎣ ⎦
= ⋅ −
⎡ ⎤
⎣ ⎦
( )
2
1
o
eq
n n
M K
H O
p p
⎡ ⎤
⎣ ⎦
=
⎡ ⎤
⎣ ⎦
−
only get down to a certain water concentration
→ solve for best n
p possible
Polyesterification Using Acid Catalysis
COH + HA C OH
OH
O
k1
k2 +
A
-
COH + HA C OH
OH
O
k1
k2 +
+
A
-
-
Acid
catalyst
More active than COOH
[ ][ ]
COOH
HA
k
k
K
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=
=
2
1
12
C OH
OH
+
A
-
C OH
OH
+
+
A
-
-
k3
k4
C OH
OH
+
A
-
OH
+ C OH
OH
+
A
-
OH
k3
k4
C OH
OH
+
A
-
C OH
OH
+
+
A
-
-
OH
+ C OH
OH
+
+
A
-
-
OH
Slow step
(rate-determining step)

4. k5
k6
C OH
OH
+
A
-
OH
..
..
..
.. + H2O + HA
C O
O
k5
k6
C OH
OH
+
+
A
-
-
OH
..
..
..
.. + H2O + HA
C O
O
catalyst regeneration
[ ]
dt
COOH
d
Rp
−
= Rate of disappearance of carboxylic monomer
p
R ( )
3 2
k C OH OH
+
⎡ ⎤
= ⎡ ⎤
⎣ ⎦
⎣ ⎦
(from previous page)
3 12
k K HA COOH OH
= ⎡ ⎤⎡ ⎤⎡
⎣ ⎦⎣ ⎦⎣ ⎤
⎦
From equilibrium expression [HA] is constant because it’s regenerated.
'
p
d COOH
R k COO
dt
− ⎡ ⎤
⎣ ⎦
= = ⎡ ⎤⎡
⎣ ⎦⎣
H OH⎤
⎦ where '
3 12
k k K HA
= ⎡ ⎤
⎣ ⎦ constant
Self-catalyzed: [HA] = [COOH]
2
"
p
d COOH
R k COO
dt
− ⎡ ⎤
⎣ ⎦
= = ⎡ ⎤ ⎡
⎣ ⎦ ⎣
H OH⎤
⎦ K
where k k3 12
" =
3
"
p
d M
R k
dt
− ⎡ ⎤
⎣ ⎦
= = ⎡ ⎤
⎣ ⎦
M separate and integrate
"
2 2
1 1
2
o
k t
M M
= −
⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦
( )
1
o
M M
= −
⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦ π
( ) ( )
2 2 '
2
1
2 1
1
n o
p M
= = ⎡ ⎤
⎣ ⎦
− π
k t +
Much slower because of time-dependence ( t )
That’s why people add acid to drive reaction.
High Temperature
- increase k
- remove byproduct (evaporate H2O)
Bulk or mass conditions (no solvent)
- [M]o is maximum
- no need to separate product
10.569, Synthesis of Polymers, Fall 2006 Lecture 3
Prof. Paula Hammond Page 4 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date

5. 10.569, Synthesis of Polymers, Fall 2006 Lecture 3
Prof. Paula Hammond Page 5 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date
- viscosity η low until high π
- direct processing
Use solvent
- monomers are not miscible with each other but miscible with solvent
- allow high T
- dilute viscous media (carrier for viscous media)
→ improves processing
- improves heat and mass transfer