# Polymer Chemistry. The Basic Concepts - Himenz P.C.

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after the initial reaction has gone to completion. In this case the

molecular weight of the polymer increases, since no new growth centers

are initiated. Because of this absence of termination, such polymers are

called living polymers.

While living polymers can be prepared, there are some substances like

water, alcohols, and carbon dioxide which are highly effective in

terminating chain growth:

BMn0A(r) + H20 -> BMnH + AOH

(6.W)

BMn0A(r) + C02 -> BMnCOO0A(r) (tm) BMn COOH + AC1

(6 .X)

In practice, it is very difficult to completely exclude water and C02, so

chain termination is often induced by these reactions.

An interesting situation is obtained when the catalyst-solvent system

is such that the initiator is essentially 100% dissociated before monomer

is added and no termination or transfer reactions occur. In this case all

chain initiation occurs rapidly when monomer is added, since no time-

dependent initiator breakdown is required. If the initial concentration

of catalyst is [AB]0,then chain growth starts simultaneously at [B"]0

centers per unit volume. The rate of polymerization is given by the

analog of Eq. (6.24):

Rp = = kp[B']o[M]

(6.96)

406

Addition or Chain-Growth Polymerizatior

which integrates to

[M] = [M]0e~kpl8 lo 1

(6.97

if [M] = [M]0 at t = 0. Since no termination occurs, the kinetic chain

length at any point during the reaction is given by the amount of monomer

reacted a that point, [M]0 - [M], divided by the number of chain-growth

centers:

_ [M]0 - [M]

v =--------------

[B ]0

Combining Eqs. (6.97) and (6.98) gives

Mi (i - e-kplâ 1î× [B]"

(6.98

(6.99

which approaches [M]0/[B]0 ast-*00.

The first living polymer studied in detail was polystyrene

polymerized witl sodium naphthalenide in tetrahydrofuran at low

temperatures:

1. The catalyst is prepared by the reaction of sodium metal with

naphthalen* and results in the formation of a radical ion:

Na

+

(c)

Na +

(6.Y

2. These green radical ions react with styrene to produce the red

styren* radical anions:

H

H

(c)

+ CH2=C

Ô

+

' (

•ÑÍ,-C:

I

Ô

(6.Z

3. The latter undergo radical combination to form the dianion, which

subse quently polymerizes:

H H H

!e (c) i i(c) ì

2*CH2-C:

:C-CH2-CH2-C:

Ô

Ô

Ô

Living

Polymei

(6.AA

Anionic Polymerization

407

In this case the degree of polymerization is 2v because of the

combination step.

The molecular weight distribution for a polymer like that described

above is remarkably narrow compared to free-radical polymerization or

even to ionic polymerization in which transfer or termination occurs. The

sharpness arises from the nearly simultaneous initiation of all chains

and the fact that all active centers grow as long as monomer is present.

The following steps outline a quantitative treatment of this effect:

1. The first monomer addition to the active center occurs by the

reaction

(6.BB)

for which the rate law is

(6.100)

2. Substitution of Eq. (6.97) into Eq. (6.100) yields

d[BMT]

^ -"-ó = " kp [M] 0 exp (- kp [Â'] 0t) dt

(6.101)

Since [BMi"] = [B]0 at t = 0, Eq. (6.101) can be integrated to

(6.102)

Consideration of Eq. (6.99) permits Eq. (6.102) to be written as

[BMf] = [B"]0 e~v

(6.103)

3. The species BM2G is formed by reaction (6.BB) and lost by

BM2GA(r) + M ->

(6.CC)

Therefore the expression for d[BM2~] /dt is given by

d[BM2"]

= êð[ÂÌÃ][Ì] -kp[BM2'] [M]

(6.104)

which becomes

408

Addition or Chain-Growth Polymerizatior

(6.105

by substitution of Eqs. (6.97) and (6.103). Differentiation of Eq.

(6.99 with respect to t shows that dv = kp [M]0e-kp^ 8 ^ot dt. Therefore

Eq (6.105) can be written as

(6.106.

4. This is a standard differential equation for which the solution is

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