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

Himenz P.C. Polymer Chemistry. The Basic Concepts - Copyright, 1984. - 736 p.
Download (direct link): polymerchemistry1984.djvu
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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-kpl 1 [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

+

' (
,-C:

I



(6.Z
3. The latter undergo radical combination to form the dianion, which
subse quently polymerizes:
H H H
!e (c) i i(c)
2*CH2-C:
:C-CH2-CH2-C:



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]
^ -"- = " kp [M] 0 exp (- kp ['] 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"]
= [][] -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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