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

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

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

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

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)

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°

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

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

End Groups? PES 50% 25%

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

Bismaleimides (BMIs) Excess diamine dianhydride polyamic acid Δ cyclodehydration

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

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

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

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

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 definition @ gel point DP → ∞ As favg↑ ; pcrit↓ # functional groups reacted # functional groups initially p p = = 2 2 favg DP favg N0 N p = - DP = 2 favg pcrit =

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

Gelation vs Vitrification Molecular Weight Tg