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Lecture 4 & 5
Polymerization
Reactions
Polymer Science and Engineering
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PolymerizationReactions
Step(aka: Condensation)
Chain(aka: Addition)
Free Radical-Ionic-Coordination-Group Transfer
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Gives off a small molecule (often H2O) as a byproduct
StepwiseStepwise polymerization long reaction times
Bifunctional monomers linear polymers
Trifunctional monomers cross-linked (network) polymers
Condensation Polymerization Characteristics
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Polymerization mechanisms
- Step-growth polymerization
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Examples: Polyesters
Nylons
Polycarbonates
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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
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Polyester from a di-alcohol and a di-acid Example
Condensation Polymerization — Esterification
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Another polyester: PETE Terephthalic acid + Ethylene glycol
n.HOOC-C6H4-COOH + n.HO-CH2CH2-OH
-(-OOC-C6H4-COO-CH2CH2-)n + 2nH2O
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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
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Nylon 6,6 — 2 monomers: 6-carbon diamine + 6-carbon diacid ( hexamethylene diamine + adipic acid )
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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 + n HOOC-(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 C12H22O2N2 + 2H2O
72+16+28 + 72+10+64 144+22+32+28 +2x18
116 + 146 226 + 36 116x103kg 146x103kg 103 kg 226 226 513 kg HMDA + 646 kg adipic acid Note: 159 kg of H2O byproduct
Problem — Nylon 6,6
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Polymerization mechanisms
- Chain-growth polymerization
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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).
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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 (10-9 - 10-7 mol/L).
Growth rate of a chain is very high (103 - 104 units/s).
Chains with a degree of polymerization of 103 to 104 are being formed in 0.1 to 10 s.
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C
O
O O C
O
H3C C
CN
CH3
N N C
CN
CH3
CH3
Benzoyl PeroxideBenzoyl Peroxide
Azobisisobutyronitrile (AIBN)Azobisisobutyronitrile (AIBN)
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Initiation Kinetics
The rate of radical production is then given by:
]I[k2dt
]•R[dd
I 2 Rkd
R + M R1
ki
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The actual rate of initiation
Ri is expressed in terms of the rate of radical production that leads to actual polymer chains growing:
]I[fk2R di
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.
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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:
Mi + Mkp Mi+1
The rate of this reaction Rp can be expressed as:
]M][•M[kR pp
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TerminationChain growth stops by bimolecular reaction of two growing chain radicals:
• termination by combination (ktc)• termination by disproportionation (ktd)
The general kinetic equation reads:
2tt ]•M[k2R
Mi + Mj
ktcMi+j
Mi + Mj
ktdMi Mj+
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Termination
Every reaction consists of two steps:1) approach of both reactants2) 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.
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at 5 % conversion
Termination: which is faster?
1. + or +
2. + or +
in a viscous medium in a non-viscous medium
3. + or +
at 85 % conversion
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Polymerization Kinetics
The rate of polymerization in a chain growth polymerization is defined as the rate at which monomer is consumed.
pi RRdt
]M[d
Since for the production of high molar mass material Rp » Ri this equation can be re-written as:
•]M][M[kRdt
]M[dpp
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:
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2td
ti
•]M[k2]I[fk2
RR
This steady state assumption leads to:
t
d
k
]I[fk=•]M[
From which the differential rate equation is derived:
t
dpp k
]I[fk]M[k=R
At low conversion this means:
log(Rp) vs log[M] yields a slope = 1
log(Rp) vs log[I] yields a slope = 0.5
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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:
CH2 C
H
+ C
H
CH2 CH2 C
H
C
H
CH2
CH2 C
CH3
C O
OMe
+ C
CH3
C
CH2
O
OMe
CH2 C
CH3
C
H
O
OMe
+ C
CH2
C
CH2
O
OMe
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low conversion polymer chains are in dilute solution (no contact among chains)
“intermediate” conversion
High conversionchains are getting highly entangled; kp decreases.
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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
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Definition – The transfer of reactivity from The transfer of reactivity from the growing polymer chain to another the growing polymer chain to another species. An atom is transferred to the species. An atom is transferred to the growing chain, terminating the chain and growing chain, terminating the chain and starting a new one.starting a new one.
Chain Transfer agents are added to control Chain Transfer agents are added to control molecular weight and branchingmolecular weight and branching
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Branching: Chain Transfer to Polymer
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04/21/23 31
Qualitative Kinetic EffectsQualitative Kinetic Effects
FactorFactor Rate of RxnRate of Rxn MWMW
[M][M] IncreasesIncreases IncreasesIncreases[I][I] IncreasesIncreases DecreasesDecreaseskkpp IncreasesIncreases IncreasesIncreases
kkdd IncreasesIncreases DecreasesDecreases
kktt DecreasesDecreases DecreasesDecreases
CT agentCT agent No EffectNo Effect DecreasesDecreasesInhibitorInhibitor Decreases (stops!)Decreases (stops!) DecreasesDecreasesCT to PolyCT to Poly No EffectNo Effect IncreasesIncreasesTemperatureTemperature IncreasesIncreases DecreasesDecreases
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04/21/23 32
Thermodynamics of Free Radical PolymerizationThermodynamics of Free Radical Polymerization
GGpp = = HHpp - T - TSSpp
HHpp is favorable for all polymerizations is favorable for all polymerizations and and SSpp
is not! However, at normal is not! However, at normal temperaturestemperatures, , HHpp
more than compensates for the more than compensates for the negative negative SSpp term. term.
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The The Ceiling TemperatureCeiling Temperature, Tc, is the , Tc, is the temperature above which the polymer temperature above which the polymer “depolymerizes”:“depolymerizes”:
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Gp = Gp = Hp - THp - TSpSp
Hp Hp is favorable for all is favorable for all polymerizations and polymerizations and Sp Sp is not! is not!
At operational temperaturesAt operational temperatures, , Hp Hp exceeds the negativeexceeds the negative T TSp Sp term.term.
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At TAt Tcc , , GGpp= 0 = 0
Hp - Tc Hp - Tc SSpp = 0 = 0
HHpp = T = Tcc SSpp
TTcc = = HHpp/ / SSpp
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Ceiling Temperaturekp
kdpMx +M M (x+1)
● Depropagation has larger S● ∵ TS term increases with T ∴ T increase; kdp increase
● At T = Tc
(i.e. ceiling temperature) Rp = Rdp
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COMPARISONCOMPARISON
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39
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
block
graft
alternating
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Homopolymer
Alternating Copolymer
Random Copolymer
Block Copolymer
Homopolymer
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12
111 k
kr
21
222 k
kr
kk1111
kk1212
kk2121
kk2222
——MM11• + M• + M11 —M—M11••
——MM11• + M• + M22 —M—M22••
——MM22• + M• + M11 —M—M11••
——MM22• + M• + M22 —M—M22••
}}
}}
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Case 1: r1=0 and r2=0•Each comonomers prefers to react with the other.•Perfectly alternating copolymer.
Case 2: r1 > 1 and r2 > 1•Each comonomers 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.
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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
"0.04
Maleic anhydride
0.015
Note: Data are for free radical copolymerization under standard condition
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11 r then homopolymerization growth is preferred
01 r then only reaction with 2 will occur
f1, f2 : mole fractions of monomers in feed
F1, F2 : mole fractions of monomers in polymer
][
][1
21
121 MM
Mff
][][
][1
21
121 MdMd
MdFF
……④
Monomer Reactivity and Composition
Reactivity Ration
Composition
22221
211
212
111
2 frfffr
fffrF
From , ③ ④
…… ③
……⑤
characterizes the reactivity of the 1 radical with respect
to the two monomers, 1 and 21r
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][][
][][
][
][
][
][
221
211
2
1
2
1
MrM
MMr
M
M
Md
Md
1
2
1
rr
][][
][][
][
][
211
211
2
11 MMr
MMr
M
Mr
][
][
2
11 M
Mr
211
111 ffr
frF
1
21
22
12
11 k
k
k
k
22
21
12
11
k
k
k
k
Ideal Copolymerization
Ideal Copolymerization
The two monomers have equal reactivity toward both propagating species
random copolymer
121 rr where