1. Odian Book
2-6, 2-14 a-e

2. Viscosity and Molecular Weight
MW1.0
MW3.4
Property “X”
Viscosity
Critical MW for entanglements
Molecular Weight
“X” = tensile strength
density Tg
etc

3. How to control MW in Step Growth Polymerizations?
Conversion
Stoichiometry p Xn
p = 0.990, DP = 100
p = 0.995, DP = 200 = 1
(1 – p) Xn

4. Controlling MW in Step Growth Polymerizations= 1
(1 – p) Xn
Recall
And that the value of Xn at any given time equals:
We can define a stoichiometric imbalance ratio (r ≤1.0) =
[M]0
[M] Xn =
NA°
NB° r

5. Controlling MW in Step Growth Polymerizations
Total # of monomers present at the start is:
And we know that:
Substitute: =
NA° + NB° 2 =
NA°
NB° r =
NA° r
NB°
NA° + NA° / r 2 =
NA° ( 1 +1/ r)

6. Controlling MW in Step Growth Polymerizations
Since A and B groups react in a 1:1 proportion, the fraction of B groups that have reacted when the extent of reaction has reached ‘p’ is:
since:
Substitute:
= p NA° =
NA°
NB° r =
r NB°
NA°
= p r NB°

7. Controlling MW in Step Growth Polymerizations
The total # of chains at any given time equals what? The sum of unreacted A and B groups. And since each polymer molecule has two chain ends, the total number of chains is
Recall
Substitute:
[ NA° (1 – p) + NB° (1 – rp) ] 2 =
[M]0
[M] Xn
[NA0 (1 + 1/r) ] / r
[ NA° (1 – p) + NB° (1 – rp) ] 2 =
1 + r
1 + r - 2rp DP

8. How to control MW in Step Growth Polymerizations?
As p goes to 1.0 =
1 + r
1 - r DP

9. End Groups?
PES
50%
25%

10. Controlled MW Poly(ether sulfone)
Slight excess
Controlled MW and controlled end groups

11. Bismaleimides (BMIs) Excess diamine dianhydride polyamic acid
Δ cyclodehydration

12. Controlled MW Poly(ether sulfone): “Non-functional” End groups

13. How to control MW in Step Growth Polymerizations?
Stoichiometric Imbalance (r)
when A-A and B-B monomers are used, with a small addition of R-B
Degree of Polymerization at p = 1.0 is =
NA°
NB° + 2NB’° r’
Where NB’° = number of mono-functional B groups =
1 + r’
1 - r’ DP

14. Thermosets Xn → ∞ Need to know…ahead of time! Xn Gel point p
Beginning of network formation
Need to know…ahead of time!

15. Stages of Thermosetting Reactions
Soluble
Branched system
Soluble, processible
“Gel Point”
Onset of network structure
Xn → ∞
We need to know when this happens…
pcrit = ?
Network Densification
5% soluble fraction not uncommon for “fully cured” system p
% Sol Fraction

16. Predicting the Gel Point
2 (No - N)
No favg
Recall where N0 and N are the number of monomer molecules initially and at conversion p
Knowing that
By gel point DP → ∞
As favg↑ ; pcrit↓
# functional groups reacted
# functional groups initially p p = =
favg DP favg N0 N
p = DP = 2
favg
pcrit =

17. Gelation vs Vitrification
Characteristic of thermosets
Significant for processing
At or beyond the gel point, system is no longer processable
Vitrification
Distinct from gelation
Transformation from a viscous liquid to a glass
Onset of vitrification shifts rate of reaction from chemical control to diffusion controlled

18. Gelation vs Vitrification
Molecular Weight Tg