chapter 3. chain-growth (addition) polymerization 3.1. free...

Semester 1 2007/2008

Chapter 3. Chain-growth (addition)

polymerization

3.1. Free-radical polymerization

3.2. Kinetics of chain-growth polymerization

3.3. Molecular weight and its distribution

3.4. Effects of temperature and pressure on

chain polymerization

Semester 1 2007/2008 Fisika Polimer

Ariadne L. Juwono

The polymerization of unsaturated monomers typically involvesa chain growth polymerization. Chain-growth polymerizations require the presence of aninitiating molecule that can be used to attach a monomer moleculeat the beginning of the polymerization.These 3 types of polymerization share 3 common steps:•Initiation,•Propagation and,•Termination.

The initiating species (initiator) may be a radical, anion, and cationic.

One act of initiation may lead to the polymerization of thousands ofmonomer molecules. Thus polymer molecules are formed from the beginning, and almost no species intermediate between monomerand high-molecular-weight polymer are found.

3.1. Free-radical polymerization & copolymerization


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InitiationInitiation consists of 2 steps:a. Dissociation step: the initiator forms two radical species.

The labile bond can be broken by heat of irradiation (uv, gamma).

b. Association step: addition of a single monomer molecule to the initiating radical.

A free-radical polymerization has 3 main steps:•Initiation of the active monomer,•Propagation or growth of the active chain by sequential addition of monomers,•Termination of the active chain to give the final polymer product.

3.2. Kinetics of free-radical polymerization


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I-I 2I•

kdkd= A exp (-Ea/RT),where: kd is the dissociation rate-constant,

Ea is the activation energy for dissociation

Dissociation

Example

benzoyl peroxide

2,2’-azobis(isobutyronitrite) (AIBN) cyanoisopropyl radicals


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Association

I • + M IM•

ka ka is the monomer associationrate constant

Example

benzoyl peroxide styrene


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PropagationA process of monomer units addition to the initiated monomer species.Additional monomers are added sequentially during subsequent propagation steps.Propagation continues until termination process occurs

I M• + M IM•

kp

I Mx• + M IMxM•

kp


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TerminationTermination occurs when 2 propagating radical chains of arbitrarydegrees of polymerization of x and y meet their free-radical ends.There are 3 mechanisms of termination:1. Combination2. Disproportionation3. Chain transfer


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CombinationTo give a single terminated chain of degree of polymerization x + ythrough the formation of a covalent bond between the 2 combiningradical chains.

I Mx-1 M• + MMy-1 I IMX-1M – My-1 Iktc

Example: termination by combination of styrene polymerization


Ariadne L. Juwono

DisproportionationOne terminated chain will have an unsaturated carbon group whilethe other terminated end is fully saturated.

I Mx-1 M• + •MMy-1 I I MX + I My

ktd

Example


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Chain transferTo give hydrogen abstraction from an initiator, monomer, polymer,or solvent molecule.

I Mx-1 M• + SH I MX-1 MH + S•ktr

Example


Ariadne L. Juwono


Ariadne L. Juwono

The rate constants vary in a wide range, because they depend on thereactivity of both the radical and the monomer.


Ariadne L. Juwono

Free-radical polymerization kinetics

I Mx• + M IMxM•

kp

Assumption: the propagation step has equal reactivity with other steps

Ro ≡ Rp = kp [I Mx• ] [M]

Where: Ro = the overall rate of polymerization in a free-radical pol,Rp = the rate of chain propagation

The propagation rate for free-radical pol’n is very rapid. Typical condition,a polymer having mol weight of 10 million can be formed in only 0.1 s.

Problem: the radical concentration is normally not known.Solution: assuming that the total radical population obtains a steady-stateconcentration over the most of the pol’n process.


Ariadne L. Juwono

The steady-state condition:the radicals are formed in the initiation step = the radicals are consumedin the termination step.

Ri ≡ Rt

The overall rate of initiation is controlled by the slower step, which isthe dissociation of the initiator.

[ ] [ ]I2kdt

IdR di =

•=

where: [I•] = concentration of the free radical,[I] = the concentration of the initiator,2 radicals are produced in each dissociation step.

[ ] [ ]I2fkdt

IdR di =

•=

where: f = fraction of effective initiator-radicals (0.3 – 0.8).

Some initiator-radicals may recombine with other radicals


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At this stage, consider only termination by combination and disproportionation so that :

I Mx • + I Mx • Pkt

where: P is the deactivated polymer,kt is the termination rate constant (kt = ktc + ktd)

[ ] [ ]2xtx

t IM2kdt

IMdR •=

•=

[ ] [ ]1/21/2

t

dx I

k

fkIM

=•

The termination rate equation:

The steady-state condition:

Remember that Ro ≡ Rp = kp [I Mx• ] [M]

[ ] [ ]MIk

fkkRp

1/2

1/2

t

dp

=The propagation rate equation:

,so that


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The polymerization rate: [ ] [ ]MIk

fkkR

1/21/2

t

dp0

=


Ariadne L. Juwono

The ratio of rate constant is a useful information about the thermo-chemistry of polymerization and is a function of temperature.If the rate constant for initiator decomposition and the initiator efficiencyAre known, the ratio of rate constant can be evaluated.

The ratio of rate constant

2

i

2

p

t

2

p

[M]R

2R

k

k=

t

2

p

k

k


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The number-average degree of polymerization at any time:

t

pn

R

RX =

In steady-state:[ ]

[ ] 1/2dt

pn

)Ifk2(k

MkX =

Consider termination by combination, disproportionation, and chaintransfer:

trtdtc

pn

RRR

RX

++=

The rate of termination by chain transfer: Rtr = ktr [IMx•] [SH]

+=

[M]

[SH]C

)X(

1

X

1

0nn

p

tr

k

kC =The chain-transfer coefficient:


Ariadne L. Juwono


Ariadne L. Juwono

3.3. Molecular weight and its distribution

A case in vinyl polymersThese polymers have the same average molecular weight throughoutthe reaction.Assume that the terminations is by disproportionation of transfer.Define:

p : the prob of a growing chain radical will propagate rather thanterminate.

px-1 (1-p) : the prob of formation of an x-mer as a result of (x-1) propagation and termination.

tp

p

RR

Rp

+=


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DefineN = the total number molecules in the system,N0 = the initial number of initiator.xn = the number-average degree of polymerization

p1

1

c

c

N

Nx 00

n −===

N0 is the total number of units present and N = N0 (1-p)

1x2

0x pp)-(1NN−=

wx is the weight fraction of x-mers 1x2

0

xx pp)x(1

N

xNw −−==

The weight-average degree of polymerization:p1

p1xw −

+=

Similar to step polymerization


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In a case when a high polymer is formed, p ~ 1 and xw/xn = 2.In the case of termination by combination with the absence of transfer, xw/xn = 1.5 (f = 2).The meas of xw/xn would differ between the possibilities oftermination by combination and by disproportionation.→ difficult !!

A method is to measure the number of initiator fragments per molecule of polymer.

2x

x p)(ln xpw =pln

1-xn =

pln

2xw

−=

In general distribution function by Zimm (1948)

δyz1Z

x exz!

yw

=

+

y

zxn =

y

1zxw

+=


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In a case of autoacceleration in the polymerization of methylmethacrylate, xw/xn ~ 10, p > 0 and < 1.When chain transfer involves, the distribution of molecular weightshas a long, high-molecular-weight “tail”. The empirical function:

2yxzρ

1z

x exy

ρ

1zΓ

ρw −

+

+=

ρ

1n

y

ρ

1zΓ

x

+

=

+

+

=

ρ

1zΓy

ρ

2zΓ

x

ρ

1w


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For low-molecular-weight polymers, the empirical distribution functionis called the logarithmic normal distribution (Lansing, 1935)

2

20

2

2σ

)lnx(lnx

0

2

σ

ex

1

πσ

ew(x)

−−

−

= 2

σ

0n

2

exx = 2

3σ

0w

2

exx =

Other empirical equations were proposed by Wesslau (1956), Tung (1956),Gordon (1961), and Roe (1961)

For extremely narrow-molecular-weight polymers, the empirical distrfunction is described by Possion distribution (Flory, 1940)

1)!(x

µxe

1µ

µw(x)

2xµ

−+=

−−

1µxn +=2

n

w

1)(µ

µ1

x

x

++=


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The Gibbs free energy of polymerization: ∆Gp = ∆Hp – T ∆Sp

where: ∆Hp is the heat of polymerization, ∆Hp ≡ Ep - Edp (neg)Ep and Edp are the activation energies for propagation and depolymerization respectively,

∆Sp is the entropy of polymerization (neg).

For low temp polymerization, both ∆Hp and ∆Sp are negative and ∆Gp is also negative. As the temperature increases, ∆Gp become less negative. At certain temperature, the polymerization reaches equilibrium (rateof polymerization = rate of depolymerization)This temp is called the ceiling temperature (Tc).

∆Gp = 0p

p

c∆S

∆HT =

3.4.1. Free-radical polymerization thermodynamics

3.4. Effects of temperature and pressure on chain polymerization


Ariadne L. Juwono


Ariadne L. Juwono

The expression of the rate of propagation or the overall polymerizationrate by Arrhenius-type equation:

RT

E

pp

p

eAk−

=

where: Ap is the collision frequency factorfor propagation,Ep is the energy of activation forpropagation

The rate-constant ratio: RT

2E

Ep

t

p

t

p

t

eA

A

k

k−

−

=

Graph log (kp/√kt) vs 1/T → (Ep – ½ Et) and (Ap/ √At) can be evaluated.For most polymerization:

The increase in (kp/√kt) ~ 30 – 35% for every 10 ºC near RT ↔(Ep – ½ Et) ~ 20 – 25 kJ/mole.For most monomers:Ep ~ 30 kJ/mole, Et ~ 12 - 20 kJ/mole.


Ariadne L. Juwono

3.4.2. Effect of pressure on free-radical polymerization

Polymerization of styrene at high pressure (3000 atm) :The rate of dissociation of initiator <, the rate of polymerization >,The rate of overall polymerization 7 – 8 X >, the rate of termination <,The molecular weight >>

Eyring rate theory: ∆VP

RTlnK

T

−=

∂

∂

chapter 3. chain-growth (addition) polymerization 3.1. free...

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