1. Polymerization Reactions
Polymer Science and Engineering I
Lecture 5
Polymerization Reactions

3. Condensation Polymerization

5. Condensation Polymerization Characteristics
Gives off a small molecule (often H2O) as a byproduct
Stepwise polymerization
long reaction times
Bifunctional monomers  linear polymers
Trifunctional monomers  cross-linked (network) polymers

6. Polymerization mechanisms
- Step-growth polymerization

7. Condensation Polymerization
Examples:
Polyesters
Nylons
Polycarbonates

8. Polyesters from a hydroxy-acid
Acid and base functionality on one monomer:
e.g., n . HO-CH2CH2CH2CH2COOH 
-(-CH2CH2CH2CH2COO-)n- + nH2O
General reaction:
n . HO-R-COOH  -(-R-COO-)n- + nH2O

9. Condensation Polymerization — Esterification
Polyester from a di-alcohol and a di-acid
Example (Callister eq. 16.8):

10. Another polyester: PETE
terephthalic acid + ethylene glycol
n.HOOC-C6H4-COOH + n.HO-CH2CH2-OH 
-(-OOC-C6H4-COO-CH2CH2-)n + 2nH2O

11. Nylon 6 from polymerization of an amino acid
acid and base groups on one monomer
H2N-(CH2)5-COOH
n H2N-(CH2)5-COOH  (-(CH2)5-CONH)n + nH2O
6-carbon monomer  6-carbon mer

12. hexamethylene diamine + adipic acid
Nylon 6,6 — 2 monomers: 6-carbon diamine + 6-carbon diacid
hexamethylene diamine + adipic acid

13. Problem — Nylon 6,6
Calculate the masses of hexamethylene diamine and adipic acid needed to produce 1000 kg of nylon 6,6.
Solution:
The chemical reaction is:
nH2N-(CH2)6-NH2 + nHOOC-(CH2)4-COOH  -(-HNOC-(CH2)4-CONH-(CH2)6-)n + 2nH2O
The masses are in proportion to molecular weights. Per mer of nylon 6,6:
C6H16N2 + C6H10O4  C12H22O2N H2O
 x18 
116x103kg 146x103kg kg
513 kg HMDA kg adipic acid Note: 159 kg of H2O byproduct

14. Free Radical Polymerization

15. Polymerization mechanisms
- Chain-growth polymerization

16. Characteristics of Chain Reaction
each polymer chain grows fast. Once growth stops a chain is no longer reactive.
growth of a polymer chain is caused by a kinetic chain of reactions.
chain reactions always comprise the addition of monomer to an active center (radical, ion, polymer-catalyst bond).
the chain reaction is initiated by an external source (thermal energy, reactive compound, or catalyst).

17. Stages of Free Radical Polymerization
initiation (start)
propagation (growth)
chain transfer (stop/start)
termination (stop)
During initiation active centers are being formed.
During termination active centers disappear.
Concentration of active centers is very low ( mol/L).
Growth rate of a chain is very high ( units/s).
Chains with a degree of polymerization of 103 to 104 are being formed in 0.1 to 10 s.

18. Example Initiators
Benzoyl Peroxide
Azobisisobutyronitrile (AIBN)

19. Initiation Kinetics
The rate of radical production is then given by:

20. The actual rate of initiation
Ri is expressed in terms of the rate of radical production that leads to actual polymer chains growing!:
where f is the efficiency factor: the fraction of radicals that really leads to initiation.
The rate constant ki is NOT used in the mathematical description of the polymerization.

21. Propagation
This reaction is responsible for the growth of the polymer chain. It is the reaction in which monomer is added at the active center:
The rate of this reaction Rp can be expressed as:

22. Termination
Chain growth stops by bimolecular reaction of two growing chain radicals:
termination by combination (ktc)
termination by disproportionation (ktd)
The general kinetic equation reads:

23. Termination
Every reaction consists of two steps:
1) approach of both reactants
2) chemical reaction
The second step in the termination reaction is very fast.
This means that the rate of approach (significantly) determines the overall termination rate.

24. Termination: which is faster?1. + or + 2. + or +
in a viscous medium
in a non-viscous medium 3. + or +
at 5 % conversion
at 85 % conversion

25. Polymerization Kinetics
The rate of polymerization in a chain growth polymerization is defined as the rate at which monomer is consumed.
Since for the production of high molar mass material Rp » Ri this equation can be re-written as:
From the beginning of the polymerization:
increasing number of radicals due to decomposition of the initiator
increasing termination due to increasing radical concentration (Rt µ [M·]2)
eventually a steady state in radical concentration:

26. This steady state assumption leads to:
From which the differential rate equation is derived:
At low conversion this means:
log(Rp) vs log[M] yields a slope = 1
log(Rp) vs log[I] yields a slope = 0.5

27. The number average degree of polymerization Pn of chains formed at a certain moment is dependent on the termination mechanism:
* combination: Pn = 2
* disproportionation: Pn = 
chemistry:

28. Conversion Regimes low conversion
polymer chains are in dilute solution (no contact among chains)
“intermediate” conversion
High conversion
chains are getting highly entangled; kp decreases.

29. Trommsdorff effect Somewhere in the “intermediate” conversion regime:
* Polymer chains loose mobility;
* Termination rate decreases;
* Radical concentration increases;
* Rate of polymerization increases;
* Molar mass increases;
This effect is called: gel effect, Trommsdorff effect, or auto-acceleration

30. Chain Transfer
Definition – The transfer of reactivity from the growing polymer chain to another species. An atom is transferred to the growing chain, terminating the chain and starting a new one.
Chain Transfer agents are added to control molecular weight and branchning

31. Branching: Chain Transfer to Polymer

32. Qualitative Kinetic Effects
Factor Rate of Rxn MW
[M] Increases Increases
[I] Increases Decreases
kp Increases Increases
kd Increases Decreases
kt Decreases Decreases
CT agent No Effect Decreases
Inhibitor Decreases (stops!) Decreases
CT to Poly No Effect Increases
Temperature Increases Decreases
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33. Thermodynamics of Free Radical Polymerization
DGp = DHp - TDSp
DHp is favorable for all polymerizations and DSp
is not! However, at normal temperatures, DHp
more than compensates for the negative DSp term.
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34. Ceiling Temperature
The Ceiling Temperature, Tc, is the temperature above which the polymer “depolymerizes”:

35. . . . Thermodynamic rational
Gp = Hp - TSp
Hp is favorable for all polymerizations and Sp is not!
At operational temperatures, Hp exceeds the negative TSp term.

36. At and above Tc At Tc , Gp= 0  Hp - Tc Sp = 0 Hp = Tc Sp
 Tc = Hp/ Sp

37. Ceiling Temperature Depropagation has larger S
∵ TS term increases with T
∴ T  increase; kdp  increase
At T = Tc
(i.e. ceiling temperature)
 Rp = Rdp

38. Comparison

39. Coplymerization

40. Copolymers two or more monomers polymerized together
random – A and B randomly positioned along chain
alternating – A and B alternate in polymer chain
block – large blocks of A units alternate with large blocks of B units
graft – chains of B units grafted onto A backbone
A – B –
random
alternating
block
graft 40

41. Copolymers: Types Homopolymer Alternating Copolymer Random Copolymer
Block Copolymer
Homopolymer

42. http://www. extremetech

43. Example Copolymer

44. } Reactivity Ratios —M1• + M1  —M1• —M1• + M2  —M2• —M2• + M1  —M1•
k11
k12
k21
k22
—M1• + M1  —M1•
—M1• + M2  —M2•
—M2• + M1  —M1•
—M2• + M2  —M2• }

45. Reactivity and Type of Copolymers
Case 1: r1=0 and r2=0
Each comonomer prefers to react with the other.
Perfectly alternating copolymer.
Case 2: r1 > 1 and r2 > 1
Each comonomer prefers to react with others of its own kind.
Tendency to form block copolymers.
Case 3: r1 * r2=1
There is no preference due to the chain ends.
Random incorporation of comonomers.
"Ideal" copolymerization.

46. Typical Reactivity Ratios
r1 and r2 for pairs of monomers. r1 r2
Styrene
0.80
Isoprene
1.68
"
0.52
Methyl methacrylate
0.46 55
Vinyl Acetate
0.01
0.04
Acrylonitrile
0.4
Maleic anhydride
0.015
Note: Data are for free radical copolymerization under standard condition

47. Monomer Reactivity and Compostion
Reactivity Ration
characterizes the reactivity of the 1 radical with respect
to the two monomers, 1 and 2
then homopolymerization growth is preferred
then only reaction with 2 will occur
Composition
f1, f2 : mole fractions of monomers in feed
F1, F2 : mole fractions of monomers in polymer
…… ③
……④
From ③, ④
……⑤

48. Ideal Copolymerization
where
The two monomers have equal reactivity toward both propagating species
random copolymer

49. Ideal Copolymerization1 F1 1 f1

51. End