Chemical Engineering 160/260Polymer Science and Engineering

Lecture 6 - Mechanism and Kinetics ofLecture 6 - Mechanism and Kinetics ofFree Radical Chain PolymerizationFree Radical Chain Polymerization

January 29, 2001January 29, 2001

Outline

!! Mechanism of Radical Chain PolymerizationMechanism of Radical Chain Polymerization

"" Fundamental steps (initiation, propagation, termination)Fundamental steps (initiation, propagation, termination)

"" Kinetic chain length and molecular weightKinetic chain length and molecular weight

!! Chain TransferChain Transfer

!! Energetic CharacteristicsEnergetic Characteristics

"" Activation energies and frequency factorsActivation energies and frequency factors

"" Rate of polymerizationRate of polymerization

"" Degree of polymerizationDegree of polymerization

!! AutoaccelerationAutoacceleration

General Comments on Chain Reactions

!! Polymerization is possible only if Polymerization is possible only if ∆G < 0∆G < 0 for the for thetransformation of monomer to polymer. This will dependtransformation of monomer to polymer. This will dependonly upon the initial and final states, not the nature of theonly upon the initial and final states, not the nature of theintermediate (free radical, anion, intermediate (free radical, anion, cationcation).).

!! SubstituentsSubstituents on a vinyl group will influence reactivity on a vinyl group will influence reactivitythrough through inductive, resonance,and inductive, resonance,and steric steric effectseffects..

!! Susceptibility to a particular chain mechanism depends onSusceptibility to a particular chain mechanism depends onthe degree of the degree of stabilization of the propagating centerstabilization of the propagating center..

!! Radicals are “free” speciesRadicals are “free” species, but anionic and cationic end, but anionic and cationic endgroups have groups have counterions counterions that influence reactivity.that influence reactivity.

!! High polymer is formed immediatelyHigh polymer is formed immediately in a chain in a chainreaction. Increasing the reaction time simply increases thereaction. Increasing the reaction time simply increases theamount of high polymer produced.amount of high polymer produced.

Effect of Substituents on Chain Mechanism

Monomer Radical Anionic Cationic Hetero.

Ethylene + - + +Propylene - - - +1-Butene - - - +Isobutene - - + -1,3-Butadiene + + - +Isoprene + + - +Styrene + + + +Vinyl chloride + - - +Acrylonitrile + + - +Methacrylate + + - + esters

• Almost all substituents allow resonance delocalization.• Electron-withdrawing substituents lead to anionic mechanism.• Electron-donating substituents lead to cationic mechanism.

Mechanism of Radical Chain PolymerizationInitiation:

I → 2R •kd

R• + CH2=CHY → RCH2C •

H

Y

|

|

slow

fast

Propagation:

+ CH2=CHY →RCH2C •|

|

H

Y

RCH2CHYCH2C •|

|

H

Y

RCH2CHYCH2C • + CH2=CHY → R(CH2CHY)2CH2C •|

|

H

Y

|

|

H

Y

(thermal or photochemical bond cleavage)

(addition of hundreds orthousands of monomers)

always thesame identityand reactivityfor head-to-tailreaction

Mechanism of Radical Chain PolymerizationTermination: (Reactions are similar for radical and cationic.)

Coupling (molecular weight is effectively doubled)

Disproportionation (molecular weight is unchanged)

~CH2C • + • CCH2~ → ~CH2C-CCH2~|

|Y

H|

|Y

H|

|Y

H|

|Y

H

~CH2C • + • CCH2~ → ~CH2CH + C=CH~|

|Y

H

|Y

|H

|

|

Y

H|

|Y

H

ktc

ktd

Most anionic reactions have no inherent termination step.

Mechanism of Radical Chain PolymerizationInitiation:

Propagation:

Termination:

I → 2R •kd

− = =d I

dtR k Ii d

[ ][ ]

Mn • + M → M n+1 •kp

− = = •d M

dtR k M Mp p

[ ][ ][ ]

kp ~ 102 - 104 liter/mole sec

Mn • + Mm • → dead polymerkt

kt ~ 106 -108 liter/mole sec

kt = ktc + ktd

R k Mt t= •2 2[ ][M •] ~ 10-7 - 10-9 mole/liter

Note: [M+], [M-] ~10-2-10-3 mole/liter

Azonitriles:

Mn • + RN=NR → MnR + N2 + R •

Peroxides:

Mn • + RO-OR → MnOR + RO •

Magnitudes of Reaction Parameters

G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 274.

Rate of Polymerization

− = = •d M

dtR k M Mp p

[ ][ ][ ]

Define the rate of polymerization based upon monomer loss.

− = +d M

dtR Ri p

[ ]

0

Assume that kp and kt are independent of size of radical.

Steady-state assumption: The net rate of production offree radicals is zero so that the initiation and terminationrates are equal. This is usually true after about 1 minutereaction.

R R k Mi t t= = •2 2[ ] [ ]/

MR

ki

t

• =

2

1 2

R k MR

kp pi

t

=

[ ]

/

2

1 2

~

Rate of Initiation

− = =d I

dtR k Id d

[ ][ ]

[ ] [ ]exp( )I I k to d= −

ln[ ][ ]I

Ik to

d=

tk

II kd

o

o d1 2

1

2

0 693/ ln

[ ][ ]

.= =Half life:

R fk Id d= 2 [ ]

Unimolecular decomposition:

In actual reactions, not all initiator decompositions areeffective in initiating polymerization. An efficiencyfactor f is introduced to account for this.

R k MR

kp pi

t

=

[ ]

/

2

1 2

R k Mfk I

kp pd

t

=

[ ]

[ ]/1 2

R Ri d=

Kinetic Chain Length

ν = average number of monomer molecules consumed for each radical that initiates a polymer chain

ν = =R

R

R

Rp

i

p

tν =

•

•=

•

k M M

k M

k M

k Mp

t

p

t

[ ][ ]

[ ]

[ ]

[ ]2 22

R k M Mp p= •[ ][ ] ν =k M

k Rp

t p

2 2

2

[ ]

For initiation by thermal homolysis:

ν =k M

fk k Ip

d t

[ ]

( [ ]) /2 1 2Typically, the initiatorefficiency f is about 0.5.

Relationship Between Kinetic Chain Lengthand Molecular Weight

Coupling:

This is the most common mode for styrene, methylacrylate, and acrylonitrile.

Disproportionation:

Methyl methacrylate (MMA) has a combination ofcoupling and disproportionation. At 70 °C, MMAtermination is almost 100% by disproportionation.

Xn = 2ν (true only if there is nochain transfer)

Xn = ν(true only if there is nochain transfer)

Chain TransferChain transfer is a chain breaking reaction leading to adecrease in the size of the propagating polymer chain. Theactive center is transferred from the growing chain to adifferent species (chain transfer agent, initiator, monomer,or polymer). The new species may initiate polymerizationor may truncate it.

Mn• + XA → Mn-X + A•ktr

A• + M → M •

ka

R k M XAtr tr= •[ ][ ]

can initiate anew reaction

dead

Effect of Chain Transfer on Molecular Weight

XR

Rk M M k M S k M I

np

ttrM trS trI

=

+ • + • + •

2[ ][ ] [ ][ ] [ ][ ]

Ck

kMtrM

p

≡ Ck

kStrS

p

≡ Ck

kItrI

p

≡

1 2

X

R

RC C

S

MC

I

Mn

p

iM S I= + + +

[ ][ ]

[ ][ ]

12 2

2

2 3X

k R

k MC C

S

MC

k R

k fk Mn

t p

pM S I

t p

p d

= + + +[ ]

[ ][ ] [ ]

Define chain transfer constants:

Use the kinetic chain length approach to obtain the ratio ofthe polymerization rate to the sum of all termination rates:

Chain Transfer to Polymer

~CH2CH2CH2CH2|

CH2CH2

CH2

|CH2

•

456 Size of side chainafter backbiting

Short branches decrease crystallinity and are 20 - 50 timesmore prevalent than long branches. A typical polyethylenehas 5 n-butyl branches and 1 - 2 each of ethyl, n-amyl, andn-hexyl branches per 1000 carbons.

Consider a terminal free radical of polyethylene:

Long branches, formed by normal chain transfer to polymer,affect melt flow properties.

Transfer to Chain Transfer Agent

1 1X X

CS

Mn n o

S=

+

[ ][ ]

12 2

2

2 3X

k R

k MC C

k R

k fk Mn o

t p

pM I

t p

p d

= + +

[ ] [ ]

• Strong C-H bonds of aliphatics lead to small CS.• Acids, carbonyls, ethers, amines, and alcohols have higherCS values than aliphatics due to stabilization by O, N, C=O.• Weak S-S bonds lead to large CS.• Carbon-halogen bonds are very weak, with excellentradical stabilization.• Thiols have the highest CS due to the weak S-H bond.

Energetic Characteristics:Activation Energies and Frequency Factors

Assume that all rate constants (kd, kp, kt) are Arrhenius-like.

k AE

RT= −exp( )

A = frequency factorE = activation energy

G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 277.

Energetic Characteristics:Activation Energies and Frequency Factors

G. Odian, Principles of Polymerization, 3rd. Ed., 1991, p 275.

Methyl methacrylate is sterically hindered, leading to low Ap.

Energetics: Rate of Polymerization

R k Mfk I

kp pd

t

=

[ ]

[ ]/1 2

ln ln/ /

kk

kA

A

A

EE E

RTpd

tp

d

t

pd t

=

=− + −

1 2 1 2

2 2

E EE E

R pd t≡ + −

2 2

ln ln ln ( [ ]) [ ]/

/R AA

Af I M

E

RTp pd

t

R=

+ { } −

1 2

1 2

kk

kpd

t

1 2/

This isthe key.

composite activation energy,usually ~80-90 kJ/mole

Energetics: Degree of Polymerization

ν =k M

fk k Ip

d t

[ ]

( [ ]) /2 1 2

Xn = 2ν

coupling

ln( )

ln( )/ /

k

k k

A

A A

EE E

RTp

d t

p

d t

pd t

1 2 1 22 2

=

−

− −

E EE E

X pd t

n≡ − −

2 2

ln ln( )

ln[ ]

( [ ])/ /XA

A A

M

f I

E

RTnp

d t

Xn=

+

−1 2 1 2

composite or overallactivation energy

k

k kp

d t( ) /1 2

This is the key.

Temperature Dependence of Rate ofPolymerization and Degree of Polymerization

Weight-averagemolecular weight

Rate ofpolymerization

1T

Autoacceleration (Trommsdorff effect)

G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 289.

R k Mfk I

kp pd

t

=

[ ]

[ ]/1 2 Normally, Rp decreases with time

because [M] and [I] drop withextent of conversion.