Lecture 4 & 5

Polymerization

Reactions

Polymer Science and Engineering

PolymerizationReactions

Step(aka: Condensation)

Chain(aka: Addition)

Free Radical-Ionic-Coordination-Group Transfer

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

Polymerization mechanisms

- Step-growth polymerization

Examples: Polyesters

Nylons

Polycarbonates

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

Polyester from a di-alcohol and a di-acid Example

Condensation Polymerization — Esterification

Another polyester: PETE Terephthalic acid + Ethylene glycol

n.HOOC-C6H4-COOH + n.HO-CH2CH2-OH

-(-OOC-C6H4-COO-CH2CH2-)n + 2nH2O

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

Nylon 6,6 — 2 monomers: 6-carbon diamine + 6-carbon diacid ( hexamethylene diamine + adipic acid )

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

Polymerization mechanisms

- Chain-growth polymerization

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).

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.

C

O

O O C

O

H3C C

CN

CH3

N N C

CN

CH3

CH3

Benzoyl PeroxideBenzoyl Peroxide

Azobisisobutyronitrile (AIBN)Azobisisobutyronitrile (AIBN)

Initiation Kinetics

The rate of radical production is then given by:

]I[k2dt

]•R[dd

I 2 Rkd

R + M R1

ki

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.

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

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+

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.

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

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:

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

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

low conversion polymer chains are in dilute solution (no contact among chains)

“intermediate” conversion

High conversionchains are getting highly entangled; kp decreases.

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

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

Branching: Chain Transfer to Polymer

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

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.

The The Ceiling TemperatureCeiling Temperature, Tc, is the , Tc, is the temperature above which the polymer temperature above which the polymer “depolymerizes”:“depolymerizes”:

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.

At TAt Tcc , , GGpp= 0 = 0

Hp - Tc Hp - Tc SSpp = 0 = 0

HHpp = T = Tcc SSpp

TTcc = = HHpp/ / SSpp

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

COMPARISONCOMPARISON

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

Homopolymer

Alternating Copolymer

Random Copolymer

Block Copolymer

Homopolymer

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••

}}

}}

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.

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

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

][][

][][

][

][

][

][

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