Polymer Synthesis
CHEM 421
• Odian Book
2-6, 2-14 a-e
MW3.4
MW1.0
Critical MW for
entanglements
Molecular Weight
“X” = tensile strength
density
Tg
etc
Viscosity
Property “X”
Viscosity and Molecular Weight
Polymer Synthesis
CHEM 421
How to control MW in Step
Growth Polymerizations?
• Conversion
Xn =
1
p = 0.990, DP = 100
p = 0.995, DP = 200
Xn
(1 – p)
• Stoichiometry
Polymer Synthesis
CHEM 421
p
Controlling MW in Step
Growth Polymerizations
• Recall
Xn =
Polymer Synthesis
CHEM 421
1
(1 – p)
• And that the value of Xn at any given time equals:
Xn =
[M]0
[M]
• We can define a stoichiometric imbalance ratio
(r ≤1.0)
r
=
NA°
NB°
Controlling MW in Step
Growth Polymerizations
Polymer Synthesis
CHEM 421
• Total # of monomers present at the
start is:
NA° + NB°
=
2
–And we know that:
r
=
NA°
NB° =
NB°
NA°
r
• Substitute:
=
NA° + NA° / r
2
=
NA° ( 1 +1/ r)
2
Controlling MW in Step
Growth Polymerizations
Polymer Synthesis
CHEM 421
• 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:
= p NA°
– since:
r
=
NA°
NA° = r NB°
NB°
– Substitute:
= p r NB°
Controlling MW in Step
Growth Polymerizations
Polymer Synthesis
CHEM 421
• 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
[ NA° (1 – p) + NB° (1 – rp) ]
2
• Recall
Xn =
[M]0
[M]
=
[NA0 (1 + 1/r) ] / r
[ NA° (1 – p) + NB° (1 – rp) ]
– Substitute:
2
DP =
1+r
1 + r - 2rp
How to control MW in Step
Growth Polymerizations?
• As p goes to 1.0
DP =
1+r
1- r
Polymer Synthesis
CHEM 421
End Groups?
Polymer Synthesis
CHEM 421
PES
50%
25%
25%
Controlled MW Poly(ether sulfone)
Polymer Synthesis
CHEM 421
Slight excess
Controlled MW and controlled end groups
Bismaleimides (BMIs)
Excess diamine
Polymer Synthesis
CHEM 421
dianhydride
polyamic acid
Δ cyclodehydration
Controlled MW Poly(ether sulfone): Polymer Synthesis
CHEM 421
“Non-functional” End groups
How to control MW in Step
Growth Polymerizations?
Polymer Synthesis
CHEM 421
• Stoichiometric Imbalance (r)
r’
=
NA°
NB° + 2NB’°
Where NB’° = number of
mono-functional B
groups
when A-A and B-B monomers are
used, with a small addition of R-B
• Degree of Polymerization at p = 1.0 is
DP =
1 + r’
1 - r’
Thermosets
Polymer Synthesis
CHEM 421
Xn
• Xn → ∞
– Gel point
» Beginning of network formation
• Need to know…ahead of time!
p
Stages of Thermosetting
Reactions
Polymer Synthesis
CHEM 421
1. Soluble
•
Branched system
•
Soluble, processible
2. “Gel Point”
•
Onset of network structure
•
Xn → ∞
•
We need to know when this happens…
•
pcrit = ?
3. Network
Densification
•
5% soluble fraction
not uncommon for
“fully cured” system
% Sol
Fraction
p
Predicting the Gel Point
• Recall
# functional groups reacted
p =
# functional groups initially
p
=
Polymer Synthesis
CHEM 421
2 (No - N)
No favg
where N0 and N are the number of monomer molecules initially and at
conversion p
• Knowing that
DP =
N0
2
p =
favg
N
• By definition @ gel point DP → ∞
• As favg↑ ; pcrit↓
pcrit =
2
favg
-
2
DP favg
Gelation vs Vitrification
Polymer Synthesis
CHEM 421
• Gelation
– 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
Gelation vs Vitrification
Tg
Molecular Weight
Polymer Synthesis
CHEM 421