1. Reading (Odian Book):
Chapter 2-1, 2-2, 2-4

2. Step Growth Polymerizations
Bifunctional monomers
AB monomers

3. Example Polymers via Step Growth Reactions
DacronTM, MylarTM

4. Importance of Equal Reactivity
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B
A—ba—B +
A—B +
A—ba—B +
A—ba—B +
A—ba—B +
A—B
FA° = # of A groups at the beginning
FA = # of A groups at any given time
p = conversion = 1 – FA / FA°
= 1 – (6 / 10)
Xn = average degree of polymerization
total # of molecules present initially
total # of molecules present at time t
Xn = ————————————————

5. Importance of Equal Reactivity
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B +
A—B
p = Xn = 1
A—ba—B +
A—B +
A—ba—B +
A—ba—B +
A—ba—B +
A—B
p = Xn = 1.67
A—ba—ba—ba—B +
A—ba—B +
A—ba—ba—B +
A—B
p = Xn = 2.5
A—ba—ba—ba—B +
A—ba—ba—ba—ba—B +
A—B
p = Xn = 3.33
A—ba—ba—ba—B +
A—ba—ba—ba—ba—ba—B
p = Xn = 5

6. MW and Conversion Xn Given that: [M] = [M]0 - [M]0 p Rewriting:
(1 – p) [M]
Knowing:
[M]0
[M] Xn 1
(1 – p)

7. Implications of Carothers Equation1
(1 – p) Xn =
Conversion Xn
50% 2
80% 5
90%
95%
99%
99.5%

8. Weight Average and Number Average Molar Masses

9. Accessibility of mutually reacting groups
Factors Involved in the Synthesis of High MW Linear Polymers via Step-Growth Reactions
High purity monomers
Di-functionality
Proper stoichiometry
Very high conversions
No side reactions
Accessibility of mutually reacting groups
In general:
Suitable for bulk reactions
Moderate viscosity during much of the reaction
Incredible effort ($$) goes to pushing the reaction forward in last stages

10. Methods for Polyester Synthesis
Direct reaction
Acid halide / hydroxyl
Transesterification
Melt acidolysis

11. Direct Reaction
“Le Chatelier’s Principle”

12. Mechanism

13. Overall Reaction Self-catalyzed Rp [OH] [COOH] [COOH]
Catalyzed by added acid ( [H+] = constant)

14. Equilibrium Considerations: Closed System
[ester] [H2O]
[RCOOH] [ROH]
Keq = ————————
Initial hydroxyl and carboxyl concentrations are [M]0
Concentration of ester equilibrium is p [M]0
where p = extent of equilibrium
The concentrations of hydroxyl and carboxyl equilibrium must therefore be: ( [M]0 – p [M]0)
Therefore
( p [M]0)2
( [M]0 – p [M]0)2
Keq = ————————
p2 [M]02
[M]02 ( 1– p )2
= ———————— p2
( 1– p )2
= ————

15. Equilibrium Considerations: Closed System
[ester] [H2O]
[RCOOH] [ROH]
Keq = ————————
Solve for p yields:
Knowing that: K½
1+ K½
p = ————
1 + K½ = Xn 1
(1 – p) Xn =

16. Effect of Equilibrium Constant on “p” and Degree of Polymerization: Closed System

17. Effect of Equilibrium Constant on “p” and Degree of Polymerization: Closed System
Indicates the limitation imposed by equilibrium on the synthesis of high MW polymer
@ Xn = 100 (corresponding to Mn ≈ 10k) can be obtained in a closed system only if K is 104!!!
Can not be done in a closed system for most polymers…
Therefore must drive the equilibrium
Polymer K
Polyesters
1 - 10
Polycarbonates 15
Transesterifications
0.1 – 1.0
Polyamidation

18. Open System
Extent to which one must drive the system in the forward reaction
can be seen by calculating the lowering of the small molecule condensate concentration that is necessary to achieve a particular MW
Knowing that
Solve for [H2O] 1
(1 – p) Xn =
[H2O] = p [M]0
( p [M]0)2
( [M]0 – p [M]0)2
Keq = ————————
p [H2O]
[M]0 ( 1– p )2
= ——————
p [H2O] (Xn)2
[M]0
= —————— 1
Xn2
[H2O] ——
K [M]0
Xn ( Xn – 1)
[H2O] = —————

19. Drive the Equilibrium Need to remove the small molecule condensate
H2O
HCl
Small molecule condensate needs to diffuse through and eventually out of the reaction mixture
Not easy because of high viscosity
Can lead to reactions becoming diffusion controlled

20. Effect of Water Concentration on Degree of Polymerization: Open, Driven System

21. How best to drive the Equilibrium?
Mixing is energy and capital intensive
Wiped film reactors to increase surface area
Increase diffusivity of the condensate
Raise the temperature to lower the viscosity of the melt
Potential for side reactions
Swell the melt with solvents
Supercritical CO2