ORGANIC AND PHYSICAL CHEMISTRY OF POLYMERS phần 6 doc

308 CHAIN POLYMERIZATIONS
one. The increase in volume (µ =dV /dt) that results drives the surfactant of the
empty micelles toward the external envelope of the particles; micelles thus disap-
pear from the medium by becoming particles or by supplying surfactant molecules
to the already formed particles. As soon as all the micelles have been used up by one
of the mechanisms mentioned above (first period in Figure 8.10)—corresponding
to approximately 15% monomer conversion—the number of particles (N
p
) can be
considered constant until the end of the polymerization. The rate of polymerization
during this second period in Figure 8.10 can be expressed by the relation
R
p
= k
p
[M]
part
N
p
2
Thus it will be constant up to 70–80% conversion. Assuming that free radicals are
generated at constant rate (d[RM
•
]/dt =ρ =const)) and that all of them serve to
create particles, at the time t
1
corresponding to the total disappearance of micelles,
N
p
can be written as
N

p
= ρt
1
At t
1
, a particle created at t
0
will exhibit the volume
V(t
1
,t
0
) = µ(t
1
−t
0
)
with its volume at t
0
(when it was a micelle) being negligible.
The surface of its external envelope can be easily deduced from its volume:
a(t
1
,t
0
) = (36π)
1/3
[µ(t
1
−t

0
)]
2/3
0 time
1
1
2
3
extent of
monomer
conversion
Figure 8.10. Kinetics of the monomer conversion for an emulsion polymerization in a closed
batch reactor.
Because the number of particles generated for the period of time dt is ρdt, the total
external surface at time t
1
can be written
A
t
1
=

t
1
0
a(t
1
,t
0
)ρ dt = (36π)

1/3
0.6ρµ
2/3
t
5/3
1
ANIONIC POLYMERIZATION 309
Because this total surface can be directly related to the concentration [S] of the
surfactant and to its molar surface (a
s
),
A
t
1
= a
s
[S]
one obtains the following for the expression of N
p
:
N
p
= 0.53

ρ
µ

0.4

a

s
[S]

0.6
The Smith–Ewart model describes satisfactorily the polymerization of styrene,
isoprene, and methyl methacrylate; for these systems, it can be used to predict the
size of the latex particles and the corresponding molar masses. In contrast, it is
unsuited for the case of monomers partially water-soluble or polymers insoluble
in their monomer—that is, polymerization of vinyl chloride and vinyl acetate. It
accounts neither for the fact that styrene can be polymerized in absence of surfactant
nor for the fact that free radicals (RM
•
) can equally penetrate into a micelle or in
an already formed particle during the initial phase.
Fitch has thus proposed another model which considers that initiation and the
early stages of the propagation occur in the aqueous phase, with the chains precip-
itating only when a critical size is reached—that is, for degree of polymerization
of a few units to a few tens depending upon the hydrosolubility of the oligomer
formed.
8.6. ANIONIC POLYMERIZATION
This type of polymerization is a very old one, used at the beginning of the twentieth
century in Germany to produce a well-known synthetic rubber named “Buna”.
However, it is only in the middle of the 1950s that anionic polymerization took
all its importance when Szwarc shed a new light on this field and discovered that
it can be carried out in the absence of any transfer and termination. Szwarc called
such polymerizations “living” (see Section 8.4), and his discovery triggered an
intense research activity that culminated in the synthesis of unprecedented complex
macromolecular architectures (block copolymers, stars, etc.).
8.6.1. General Characteristics
The anionic polymerization is a chain reaction that can be schematized by

~~~~M
n
−
, Met
+
+ M ~~~~M
−
n+1
, Met
+
310 CHAIN POLYMERIZATIONS
where ∼∼∼∼M
−
n
represents a negatively charged or polarized species carried by
the growing chain, and Met
+
is a positive counterion (or a polarized species),
generally a metallic cation. Whatever the precise mechanism involved in this type
of polymerization, it proceeds via repeated nucleophilic reactions. In the case of
vinyl and related monomers, for the propagation to occur by nucleophilic addi-
tion, an activation of the monomer double bond is generally required (see, however,
“Remark,” page 312). Electron-withdrawing substituents (–CO–OR, –CN, etc.) or
those inducing a strongly positive polarization of the β-carbon atom of the double
bond, when neared by a nucleophilic active species,
N
,,,
etc.
fulfill this condition.
Anionic polymerization also applies to heterocyclic monomers. In this case,

it can occur either by nucleophilic substitution or by nucleophilic addition onto
a carbonyl group followed by an elimination (mechanism B
AC
2), and so on. A
negative enthalpy of polymerization is a necessary condition for the monomer
to be polymerized, and thus heterocyclic monomers must be strained enough to
undergo ring-opening and polymerization. Another constraint of prime importance
that affects the polymerizability of monomers—in particular, that of ethylenic
ones—is the extreme reactivity of species that propagate the process. In a first
approach—and without mistaking between the notions of nucleophilicity and
basicity—a carbanionic species can be considered as the conjugate base of a pro-
tonic acid whose pK
a
can be evaluated. Thus, the species formed in the anionic
polymerization of styrene
~~~CH
2
(C
6
H
5
)HC
−
is the conjugated base of the species
~~~~CH
2
(C
6
H
5

)HCH
whose pK
a
is around 41, a high value that mirrors an extremely low acidity. The
corresponding conjugated base is thus particularly strong; the comparison of a
pK
a
of 41 with that of water which is the conjugated acid of metal hydroxides
gives an idea of the very high reactivity of the conjugate base. This imposes
that monomers are free of electrophilic species that could potentially react with
nucleophilic growing chains. Depending upon the nature of the substituent A, this
nucleophilicity varies to a large extent.
Anionic polymerization is utilized only when the “living” character of the chain
growth can be ensured. In addition, initiators are selected for their ability to give a
complete initiation (f ∼1) and a short period of initiation compared to that of prop-
agation, allowing a controlled polymerization to occur. This situation is exploited
ANIONIC POLYMERIZATION 311
in macromolecular engineering to synthesize polymeric chains with well-defined
structure and narrow molar mass distribution.
8.6.2. Structure of the Propagating Species
The “living character” of the growing species formed in carbanionic polymerization
offers an opportunity to study comprehensively their structure. The concentration
of the reactive centers being always extremely low in the polymerization medium,
it is easier to carry out such structural studies on simple organometallic models of
the “living” ends. Some of these are used to initiate the polymerization and the
knowledge of the parameters that determine their reactivity is interesting by itself.
There is a close relationship between the structure of organometallic species
(∼∼M
−
n

,Met
+
) and their reactivity. In the case of species responsible for the
polymerization of ethylenic monomers, their nucleophilicity and thus their reactivity
are strongly determined by the electron density on the carbanionic site
A
~~~CH
2
HC
d−
, Met
d+
This electron density depends on the polarization of the C–Met bond and the
possible delocalization of the negative charge on the substituent A. So, the param-
eters that control the structure of the active centers responsible for the anionic
polymerization of ethylenic monomers are:
•
The nature of the substituent(s) carried by the double bond,
•
The nature of the counterion associated with the carbanionic species,
•
The nature of the solvent in which the reaction is carried out and the presence
of possible additives.
8.6.2.1. Effect of the Substituent A. If the substituent promotes a delocaliza-
tion of the negative charge [as is the case for styrene, vinylpyridines, (meth)acry-
lates, etc.], it entails a decrease of the intrinsic reactivity of the carbanionic species.
Thus, in the case of acrylates, the active center is an enolate of rather low reactivity:
CH
2
CH

3
CH
O
O
−
,
Met
+
~~~~
The intrinsic reactivity of carbanionic active centers is increased by the presence of
electron-donating substituents and is conversely decreased by that of electron-with-
drawing ones. However, in the case of acrylates, the monomer double bond is more
activated by the electron-withdrawing character of its substituent than the reactivity
of the corresponding enolate is lowered by the same substituent; this explains the
312 CHAIN POLYMERIZATIONS
very high anionic polymerizability of these monomers. Thus, the intrinsic reactivity
of the monomer determines the global reactivity of the system—that is, its poly-
merizability. For example, methacrylic monomers (methyl methacrylate is shown
hereafter) are characterized by a lower polymerizability than that of acrylates, in
spite of the electron-donating effect of their methyl group presumed to increase the
electron density on the active center and thus its reactivity; as a matter of fact, this
–CH
3
group in α-position prevents (by its donor effect) a full polarization of the
double bond and thus decreases the monomer reactivity.
O
O
CH
3
CH

3
Methyl methacrylate
Styrene and butadiene are the two reference monomers in anionic polymeriza-
tion. Their high polymerizability is primarily due to the virtue of their double bonds
to undergo a positive polarization and an electron shift toward their substituent
when neared by a negatively charged active center.
Remark. Ethylene is a monomer with no possibility of activation of its
double bond. However, it can be polymerized by nucleophilic addition but its
anionic polymerizability is very low, the absence of any stabilizing substituent
next to the carbanionic site making the latter particularly reactive.
8.6.2.2. Effect of the Nature of the counterion. Examples of polymeriza-
tions that can be carried out with nonmetallic counter-ions (quaternary ammonium,
phosphonium ions, etc.) are scarce, the vast majority of them requiring the use of
alkali or alkaline-earth cations.
Lithium and magnesium cations exhibit a small ionic radius which explains the
partial covalent character of their bond with carbon atoms in nonpolar solvents,
provided that the carbanion is not too delocalized.
With cations of higher ionic radius, the interionic distance favors the separation
of charges, and thus the corresponding species can be considered totally ionized.
In polar solvating media as well as in the presence of solvating additives, the
ionic radius of the counterion affects its capacity to be solvated.
Large cations like cesium can by no means be solvated even by solvents known
for their strong solvating power.
Lithium is by far the most used counterion known; this is primarily due to the
practical and synthetic ease that is associated with the utilization of butyllithium
as initiator, but also to the virtue of this cation to generate different configurational
structures in the polymers formed. Indeed, lithium cations can generate either par-
tially covalent or totally ionic species with different regio- and stereospecificity,
depending upon the solvent in which it is dispersed.
ANIONIC POLYMERIZATION 313

8.6.2.3. Effect of the Nature of the Solvent and that of Potential
additives. Because of the very high reactivity of anionic reactive species, the
solvents used in anionic polymerization should not exhibit any acidic character;
thus basic or neutral solvents are generally chosen.
The functions of a solvent are manifold and, depending upon its structure, it can
fulfill one, two or three of these functions.
The first function is that of a diluent; the simultaneous generation of carbanionic
initiating/propagating sites and the monomer consumption by the latter can liberate
a considerable heat in the reaction medium that can be better removed if a solvent
is present. Solvents used as diluents are always aliphatic or aromatic hydrocarbons;
they do not modify or only to a little extent the structure of active centers.
Organolithium compounds are aggregated species whose degrees of aggregation
vary with the nature of the carbanion and sometimes with the range of concentration.
For instance, polystyryllithium ion pairs are aggregated as dimers like shown below:
HC
−
~~~~PS~~~~CH
2
CH
2
~~~~ PS~~~~
−
CH
Li
+
Li
+
,
,
In the latter case, only non-aggregated species—in equilibrium with aggregated

ones—are reactive and contribute to the propagation:
Active
Non active
2
K
ag
~~~~PS
−
, Li
+
2 ~~~~PS
−
, Li
+
The second potential function of a solvent is that of a solvating agent. Solvents
used for that purpose are ethers or tertiary amines whose basic character—according
to Lewis definition—entails a coordination to the Lewis acids that are the metal
cations associated with the nucleophilic species. This role of solvating agent can
also be played by additives (crown-ether, cryptands, tertiary diamines, etc.) used in
small amount in a hydrocarbon serving as diluent. Depending upon their geometry
or their concentration, such additives can either solvate externally the ion pairs [see
hereafter the case of polybutadienyllithium in the presence of tetramethylethylene-
diamine (TMEDA)],
NN
~~~~CH
2
HC
CH
CH
2

Li
+
TMEDA
314 CHAIN POLYMERIZATIONS
or cause a stretching of the carbon–metal bond (see hereafter the case of polystyryl-
lithium solvated by a crown-ether):
~~~~PS~~~~CH
2
HC
−
,
O
O
O
O
Li
+
Depending upon the size of the cation and the geometry of the solvating agent, such
solvation may be more or less effective. Stretching ion pairs increases considerably
their reactivity due to the easier insertion of monomer between the anion and the
cation.
When the dielectric constant (permittivity) of the solvent is sufficiently high, it
can play the role of dissociating agent. Such a solvent can then cause the charges to
separate more markedly and induce a partial dissociation of ion pairs into free ions,
K
diss
~~~~~M
n
−
, S

x
,Met
+
~~~~~M
n
−
+ S
x
,Met
+
where S
x
corresponds to X molecules of solvent coordinating to the metal cation.
The relation between the dissociation equilibrium constant (K
diss
)andtheper-
mittivity of the reaction medium (ε) can be written as
−ln K
diss
=−ln K
0
diss
+
e
2
(r
1
+r
2
)εkT

where K
0
diss
is the constant of dissociation of ion pairs in a medium of infinite
permittivity, r
1
and r
2
are the ionic radius of cation and anion, respectively, and
e is the electron charge. This relation shows that by increasing the apparent ionic
radius of the cation and that of the interionic distance, the solvating effect favors
the dissociation; most of high permittivity solvents exhibit also a strong solvating
power. The reactivity of free ions resulting from the dissociation of ion pairs
is extremely high and, even at relatively low concentration, they have a major
impact on the global kinetics of polymerization. In contrast to the case of free
radical polymerization, the same monomer can generate various propagating species
depending upon the nature of the initiator and that of the surrounding medium.
The various reactive species are ranked hereafter in the increasing order of their
reactivity,
R–Met < (R
d−
–Met
d+
)
x
< R
d−
–Met
d+
< R

−
,Met
+
S
y
Generally
inactive species Highly reactive species
< R
−
,Met
+
< R
−
,S
y
Met
+
< R
−
+ S
y
Met
+
where R represents the polymer chain and S represents a solvent molecule.
ANIONIC POLYMERIZATION 315
8.6.3. Initiation Step
The initiator has to be selected with care so as to ensure a short initiation step
(compared to that of propagation) and the absence of side reactions. The preference
must go to initiators that are more nucleophilic than the active species resulting
from their addition onto a monomer molecule.

Two types of reaction can be utilized to generate primary active centers.
The first one resorts to an electron transfer from a metal atom (generally an
alkali metal) to a molecule whose electron affinity is sufficiently high. The role
of the electrophilic entity can be played by the monomer molecule and, in this
case, the transfer of ns electrons from the alkali metal results in the formation of
a radical-anion based on the monomer molecule:
Met
+
Met +
A
A
,
Radical-anion
−
•
The species obtained can be represented by the electron distribution shown
hereafter,
CH
2
HC
−
, Met
+
A
and by recombination of the two free radical sites, a bicarbanionic species is formed:
HC
−
A
, Met
+

Met
+
,
−
HC
A
A
2
•
CH
2
CH
2
CH
2
HC
−
, Met
+
This direct initiation is rarely utilized because the formation of such a radical-anion
through the reaction between a solid (metal) and a liquid (monomer) is generally
slow. To overcome this limitation, an organic intermediate that cannot polymerize
itself but can accommodate electrons by transfer is generally utilized. More often,
these intermediates are polycyclic aromatic hydrocarbons; for example, naphthalene
is commonly used for this purpose; the reaction between naphthalene (in solution)
and sodium (solid) is schematized hereafter:
Na +naphthalene
−−−
−−−
•

(naphthalene)
−
, Na
+
The reaction must be carried out in a sufficiently solvating solvent (tetrahydrofuran,
dimethoxyethane, etc.) for the electron transfer to occur, and, after elimination of
316 CHAIN POLYMERIZATIONS
the metal in excess, a homogeneous and quasi-instantaneous initiation step can be
obtained upon addition of monomer:
+
CH
2
CH
2
CH
−−
HC
, ,
, Na
+
Na
+
Na
+
Na
+
+
,
CH
2

HC
−
2
−
•
•
The bicarbanionic species formed is persistent under conditions of “living” poly-
merization.
Na
+
,
−
CH-CH
2
-CH
2
Na
+
,
−
CH-CH
2
-CH-CH
2
-CH
2
-CH-CH
2
-CH
−

,Na
+
-CH
−
,Na
+
+ 2
etc.
Remark. Since two molecules of initiator lead to the formation of a sin-
gle chain, the relationship giving the degree of polymerization as a function
of the conversion must be modified. In the case of a monofunctional initia-
tion, the relation is
X
n
= [M
pol
]/[I], whereas for a difunctional initiation we
obtain
X
n
= 2[M
pol
]/[I] [M
pol
], representing the concentration of monomer
polymerized.
More usually—and in particular in industry—initiation is obtained by the
means of strongly nucleophilic Lewis bases. They are usually monofunctional and
monovalent organometallic species; compounds like benzylsodium or phenyliso-
propylpotassium (cumylpotassium) may be utilized in research laboratories, but

in industry it is exclusively the isomers of butyllithium (n-, sec-, tert-) that are
employed. They are strongly aggregated in hydrocarbon media (n-BuLi is hex-
americ, tert-BuLi is tetrameric, etc.) and they react only under their “unimeric”
(nonaggregate) form, the latter being in equilibrium with aggregates:
ANIONIC POLYMERIZATION 317
n-BuLi
6
6 n-BuLi

K
ag
k
i
+
A
A
n-BuLi
−
, Li
+
n-Bu
In hydrocarbon solution, the initiation is rarely instantaneous and mixed aggregates
can be formed which adds to the complexity of the kinetic expression of the
initiation step and that of the first propagation steps. In polar solvents or in the
presence of certain additives, such aggregation disappears and very reactive species
(free ions, solvated ion pairs, etc.) are generated that may provoke side reactions.
The above Lewis bases can also be utilized to initiate the polymerization of
heterocyclic monomers. However, the high reactivity of the latter authorizes the
use of weaker bases (for example, KOH) than those required for the polymerization
of vinyl and related monomers. In this way it is possible to limit side reactions and

thus to preserve the “living” character of the polymerization:
HO
−
, K
+
+
O
HO
O
−
, K
+
8.6.4. Propagation Step
With vinyl and related monomers, the mechanism of propagation is the same as
that of the initiation by Lewis bases:
A
+
A
HC
−
A
~~~~M
n
~~~~CH
2
~~~~M
n+1
~~~~CH
2
, Met

+
HC
−
, Met
+
In hydrocarbon solvents, active centers have a strong tendency to be aggregated;
as previously seen, it is the case for the polymerization of styrene initiated by an
organolithium compound, in bulk or in a hydrocarbon solvent:
(~~~~~~PS
−
,Li
+
)
2
2 ~~~~~~PS
−
,Li
+
K
ag
318 CHAIN POLYMERIZATIONS
Because only nonaggregated species are active, the kinetic equation for the prop-
agation step can be easily established:
K
ag
= [(~~~PS
−
,Li
+
)

2
]/[~~~PS
−
,Li
+
)]
2
[~~~~PS
−
,Li
+
] = {[(~~~~PS
−
,Li
+
)
2
]/K
ag
}
1/2
R
p
= −d[S]/dt = k
p
,
app
[~~~~PS
−
,Li

+
][S] = k
p
{[(~~~~PS
−
,Li
+
)
2
]/K
ag
}
1/2
[S]
where k
p,app
is the apparent rate constant of propagation and k
p
is the rate “constant”
of propagation, both of which vary with the concentration in potentially active
centers—that is, with [Li].
Because the equilibrium constant of aggregation (K
ag
) is very high, it cannot be
measured generally so that the above equation can be simplified as
R
p
= k
p
[Li]

1/n
[S]
where n is the degree of aggregation.
Remark. In the anionic polymerization of dienes, the degree of aggregation
varies with the concentration in organometallic species, which complicates
the kinetic treatment.
The addition of solvating agents in the reaction system causes a total disaggregation,
without appreciably modifying the permittivity of the medium. All organometallic
species are then active and the kinetics becomes first order in active centers:
R
p
= k
p
[Li][S]
The situation is similar if the polymerization is carried out in a solvent exhibiting
some solvating power but no dissociating effect. It is the case for dioxane, which
is particularly suitable for the study of the influence of the ionic radius of the
cation on the reactivity of the corresponding ion pairs. Because of its structure,
dioxane has indeed a chelating power and thus generates externally solvated ion
pairs with bigger alkali cations, modifying only to a little extent the interionic
distance. A similar behavior can be observed in a nonpolar solvent containing
chelating additives. Table 8.15 shows how an increase in the ionic radius of the
cation strongly increases the reactivity of ion pairs.
Indeed, an increase in the interionic distance decreases the electrostatic interac-
tion between the two electric charges and favors insertion of the monomer. If the
solvent exhibits both a solvating power and a dissociating capacity, the two effects
play a role. For instance, in tetrahydrofuran (THF), whose permittivity is equal to
7.8 at 20
◦
C, the solvation of ion pairs generates “loose” ion pairs, with each cation

being surrounded by several molecules of THF. Ion pairs are thus in equilibrium
ANIONIC POLYMERIZATION 319
Table 8.15. Rate constants of propagation of styrene for
various alkali counterions (solvent: dioxane, T =25
◦
)
Counterion (Met
+
) k
p±
(L·mol
−1
·s
−1
)
Li
+
0.94
Na
+
3.4
K
+
19.8
Rb
+
21.5
Cs
+
24.5

with free ions formed by dissociation, and the resulting overall reactivity combines
the contribution of the various species, each with its own reactivity:
~~~M
n
−
, ~~~M
n
−
, xTHF,xTHF+
~~~M
n
−
xTHF,+
K
solv
K
diss
Met
+
Met
+
Met
+
If i families of reactive species are simultaneously present in the reaction medium,
each one contributes through its own propagation kinetics:
R
pi
= k
pi
[C

∗
i
][M]
the additivity of their contribution being expressed by
R
p
=

i
R
pi
= [M]

i
k
pi
[C
∗
i
] = k
app
[C
∗
][M]
with [C*] =

i
[C
i
*].

If only free ions (C
∗
−
) and (solvated or not) ion pairs (C
∗
±
) are taken into
consideration,
[C
∗
] = [C
∗
±
] +[C
∗
−
]
the dissociation equilibrium
~~~~~~M
n
−
,Met
+
~~~~~M
n
−
+ Met
+
K
diss

can be written as
K
diss
= [C
∗
−
]
2
/[C
∗
±
] = [C
∗
−
]
2
/

[C
∗
] −[C
∗
−
]

320 CHAIN POLYMERIZATIONS
Equilibrium constants of dissociation can be measured by conductometry from
solutions containing different concentrations in organometallic species; they vary
with the charge density of the anion, the interionic distance, and the permittivity of
reaction medium and are generally very low. [C

∗
−
] can thus be considered negligible
as compared to [C*] and [C
∗
±
] can be assimilated to [C*], which means that
[C
∗
−
] =

K
diss
[C
∗
]

1/2
This leads to
R
p
=−d[M]/dt = k
app
[C
∗
][M] =

k
p±

[C
∗
] +k
p
−
K
1/2
diss
[C
∗
]
1/2

[M]
which can be written as
R
p
=

k
p±
+k
p−
K
diss
1/2
[C
∗
]
−1/2



 
k
app
[C
∗
][M]
The above relation shows that k
app
varies with [C*]; as for k
p±
and k
p−
they can
be determined from the k
app
versus [C*] plot (Figure 8.11) if K
diss
is known. As
mentioned above, K
diss
can be measured under given experimental conditions by
conductimetry on active solutions. For instance, the rate constant of propagation
of ion pairs, the rate constant of free ions, and the constant of dissociation for
polystyrylsodium (PS
−
,Na
+
) in tetrahydrofuran solution at 25

◦
Care
k
p±
=80 L·mol
−1
·s
−1
k
p−
=65,000 L·mol
−1
·s
−1
K
diss
=1.5 ×10
−7
mol·L
−1
Thus, the proportion of free ions can be deduced from these values: for [C
∗
] ∼10
−4
mol·L, free ions represent only about 4%; in spite of that and because of their very
high reactivity, free ions contribute to an extent of ∼97% to propagation.
k
p
-K
diss

1/2
kp
±
k
app
[C*]-1/2
Figure 8.11. Determination of the rate constants of propagation on ion pairs (k
p±
)andonfree
ions (k
p−
).
ANIONIC POLYMERIZATION 321
Remarks
(a) The value of k
p±
measured in THF is different from that measured in
dioxane (Table 8.15). Indeed, in this last solvent, ion pairs are externally
solvated, which modifies only very little the interionic distance, whereas
in THF, ion pairs not only can be externally solvated but can partially
also be stretched (“loose” ion pairs) under the effect of the solvent and
these are more reactive.
(b) Addition of homoionic species in the reaction medium by using soluble
and highly dissociated salts causes a retrogradation of the dissociation
equilibrium of reactive ion pairs; it entails a deceleration of the propaga-
tion step. By combining the results of the kinetic study and the value of
the added homoionic salt dissociation constant, it is possible to calculate
the propagation rate constant of free ions (k
p−
).

The stereochemistry of the propagation step closely depends on the polarity of
the solvent and on the nature of the counterion. For polymerizations involving free
ions, the sp
2
hybridization of carbanionic species prevents any marked stereoreg-
ulation of the propagation step and the resulting polymers are atactic. In nonpolar
solvents, the carbanionic species exhibit generally an sp
3
hybridization; with Li
+
and Mg
++
as counterions, (meth)acrylic and similar monomers (2-vinylpyridine,
etc.) polymerize under stereoregulating conditions through the combined effect of
monomer coordination and steric hindrance. High contents in either isotactic or
syndiotactic triads (mm or rr < 0.90) can be obtained.
As for the propagation step of heterocyclic monomers (oxiranes, thiiranes, lac-
tones, lactams, etc.), the general phenomena are very similar to those observed with
vinyl and related monomers. Although propagating species differ by the nature of
the nucleophilic entities (oxoanions, thioanions, nitranions, etc.) involved, the cor-
responding ion pairs can also be prone to aggregation, solvation, and dissociation,
depending upon the nature of the solvent or that of additives introduced into the
reaction medium. Since the propagating species in the polymerization of heterocy-
cles are much less reactive than pure carbanions, it is often necessary to activate
them in order to bring about sufficiently high rates of polymerization. In general,
the kinetics is complex because of the aggregation of active centers independently
of the reaction media, and the degrees of aggregation vary with their concentration.
Moreover, the energies of activation of the propagation reaction are appreciably
different for ion pairs and free ions; depending upon the temperature, the contri-
bution of the various active species to the propagation can vary in a large extent

with respect to the kinetics.
As for the nature of the propagating active centers, the polymerization of oxi-
ranes (epoxides) and of ε-caprolactone occurs through alkoxides, that of thiiranes
322 CHAIN POLYMERIZATIONS
(episulfides) occurs through thiolates, and that of strained lactones occurs through
carboxylates. The corresponding reaction mechanisms are well-established (nucle-
ophilic substitution, nucleophilic addition on carbonyl, etc.). For example, as estab-
lished in the polymerization of ethylene oxide initiated by a potassium derivative,
the propagation occurs by the following mechanism (nucleophilic substitution):
+
O
~~~~O
O
−
, K
+
O
−
, K
+
~~~~CH
2
CH
2
The polymerization proceeds differently in the case of lactams, with the nucle-
ophilic species being carried alternatively by the monomer and the growing chains.
For the monomer to be inserted at the chain end, it needs to be activated through
proton abstraction and charge transfer before it can add onto the end-standing car-
bonyl group; such a mechanism is called activated monomer polymerization, and
it is an unusual process in chain polymerization:

+
N
C
O
NH
2
NH
2
−
O
C
N
O
C
C
O
HN
C
O
C
N
O
C
O
C
O
C
N
O
+

+
BH
+
C
NH
O
C
NH
O
C
NH
O
C
N
O
C
O
C
O
B
−
, Met
+
NH, Met
+
N
−
, Met
+
N

−
, Met
+
N
−
, Met
+
Met
+
,
Met
+
,
Anionic polymerization of caprolactam is industrially used to produce poly-
amide-6 (PA-6).
Anionic polymerization of N -carboxyanhydrides (Leuch’s anhydrides—NCA)
affords polypeptides; it proceeds by nucleophilic addition onto the carbonyl func-
tion, followed by an elimination releasing CO
2
:
ANIONIC POLYMERIZATION 323
HN
O
O
O
R
1
R
2
R

1
R
1
R
1
R
2
R
2
R
2
R
1
R
2
++
B
HN
B
O
R
1
R
2
CO
2
CO
2
HN
O

O
O
−
B
HN
O
O
O
+
B
O
O
H
N
NH
CO
2
CO
2
_
Relatively weak bases (primary or secondary amines, alkoxides, etc.) are used to
initiate the polymerization of such monomers.
8.6.5. Anionic Copolymerization
In this section, only “statistical” copolymerizations will be considered.
Differences in the reactivity of the growing species are more pronounced in
anionic polymerization than in free radical polymerization. In particular, alkoxides,
thiolates, carboxylates, and so on, generally do not initiate the polymerization of
(and do not copolymerize with) vinyl monomers. Even in the latter family, the
differences between the reactivity of active centers are such that only a very few
of them give “statistical” copolymers. Among those, the styrene/butadiene system

is the best known, being industrially produced (in solution) under the trade name
of SBR.
The existence of active centers under the form of various structures for each
comonomer, with each of these structures having its own reactivity, complicates
the kinetic treatment of such copolymerizations in comparison to the case of free
radical polymerization. The reactivity ratios formalism can be utilized, but only
apparent values of rate constants, valid only under specific experimental conditions,
can be obtained. It is thus unrealistic to discuss the meaning of these values.
As a matter of fact, anionic copolymerization is essentially utilized for the
preparation of block copolymers (see Section 9.2); in general, one operates by
sequential addition of the comonomers in the order of increasing electroaffinity.
8.6.6. Termination Reactions
Being mainly known and utilized for its “living” character, it may appear at first
glance misleading to mention the existence of termination reactions in the anionic
polymerization of vinyl and related monomers. They indeed occur, and the condi-
tions have to be found when necessary to minimize them so as to obtain the control
324 CHAIN POLYMERIZATIONS
of the polymerization. Otherwise, these termination reactions can also be exploited
for the purpose of functionalization of the chain ends.
8.6.6.1. Spontaneous Termination Reaction. They mainly depend on the
molecular structure of the active centers considered. With polystyryl sodium in
tetrahydrofuran solution, a hydride β-elimination is observed in a first step:
+
H
CH C
~~~~
,Na
+
H
−

, Na
+
CHCH
H
~~~~
This results in the formation of a labile H. Because of its acidity, this hydrogen
atom can react with ∼∼∼PS
−
,Na
+
still present:
+
H
CH CC
H
~~~~
,Na
+
Na
+
CH
2
CH
2
CH
2
CH
2
C
H

~~~~
H
CH CC~~~~
CH
H
~~~~
+
The newly formed carbanion is particularly well stabilized and is unable to reinitiate
and propagate the polymerization.
The mechanism of spontaneous termination occurring in the polymerization of
(meth)acrylic monomers is completely different; the termination affecting
∼∼∼∼MMA
−
,Li
+
active chains is mainly an addition reaction onto the carbonyl
groups of the antepenultimate units by the growing enolates, followed by an elim-
ination reaction:
C
C
CH
2
CH
2
CH
3
CH
3
C
C

O
CO
2
CH
3
H
3
C
H
3
C
CH
2
CH
2
CH
3
CO
2
CH
3
CO
2
CH
3
H
3
C
H
3

C
OCH
3
C
O
O
Li
+
Li
+
,
−
OCH
3
n
~~~~~~
C
C
C
C
O
~~~~~~
n
−
ANIONIC POLYMERIZATION 325
Because the resulting alkoxide is unable to add onto the double bond of MMA, the
net result is a termination of the chain growth process.
A way to limit these reactions consists of replacing Li
+
by a bulkier cation

(quaternary ammonium, phosphonium, etc.) or by adding in the reaction medium,
a solvating agent that increases the apparent radius of the lithium ion; the attack of
carbonyl groups by ion pairs can thus be thwarted, the probability of termination
reduced, and the control of polymerization improved in this way.
8.6.6.2. Reaction with Termination Reagents. Because of their very high
reactivity, carbanionic species react with many compounds—in particular, those
exhibiting an acidic character:
∼∼∼M
n
−
, Met
+
+A–H −→ ∼∼ ∼ M
n
H +A
−
, Met
+
Several atmospheric components can be utilized as terminating reagents:
with CO
2
~~~M
n
−
,
~~~M
n
COO
−
,

+ CO
2
~~~M
n
−
, + O
2
with O
2
~~~M
n
•
2~~~M
n
•
~~~M
n
•
+ O
2
,
~~~M
n
•
+ O
2
,Met
+
then: ~~~M
n

-M
n
~~~
or + O
2
~~~M
n
-O-O
•
~~~M
n
-O-O
−
,Met
+
•
−
•
−
Met
+
Met
+
Met
+
Met
+
Met
+
The existence of such reactions imposes a reaction medium free of any protic

and electrophilic impurity so that the polymerization can be carried out under
“living” conditions; the techniques of purification providing such purity are now
well-developed.
8.6.7. Group Transfer Polymerization
It is now widely admitted that group transfer polymerization, which was unveiled in
1983 by a team from DuPont de Nemours, belongs to the category of anionic poly-
merization. It applies to (meth)acrylic monomers whose Li-based anionic polymer-
ization suffers from the termination by attack onto carbonyl groups as previously
shown.
Group transfer polymerization of these monomers exhibits a “living” character
at ambient temperature and under normal experimental conditions.
The initiator is a silylated acetal of dimethylketene (1-methoxy-2-methyl-1-
trimethylsiloxypropene, indicated by TMS) which is active only in the presence
of a “catalyst.” The reaction pathway is represented hereafter:
CC
H
3
C
H
3
C
H
3
C
OSiMe
3
OR
1
+ n
Cat.

C
CH
3
CH
2
COOR
1
COOR
2
n
C
CH
3
(H)
H
H
2
CC
CH
3
(H)
COOR
2
326 CHAIN POLYMERIZATIONS
The degree of polymerization obtained is determined by the molar ratio of
[monomer] to the [initiator (TMS)], with the “catalyst” concentration determin-
ing the rate of polymerization. The “catalyst” can be a nucleophilic entity, with the
best effects being obtained with fluoride (F
−
)orbifluoride(HF

2
−
) anions derived
from salts soluble in the reaction medium, such as tris(dimethylamino)sulfonium
bifluoride and tetrabutylammonium fluoride. These “catalysts” are particularly well
suited to the polymerization of methacrylic monomers.
Lewis acids such as zinc halides or a dialkylaluminium chloride (AlR
2
Cl) are
preferentially used to catalyze the polymerization of acrylics.
When strongly nucleophilic entities are utilized as catalysts, the active centers
have been identified as enolates (as with alkali counterions). Due to the nature of
counterions—in particular, their size—their reactivity is strongly reduced com-
pared to that of enolates associated with lithium; moreover, they are only present
in low concentration, the major part of the active species being in a “dormant” sily-
lacetal form in fast exchange with the reactive enolates. The mechanism occurring
in such polymerizations can be represented as below:
8.6.7.1. Initiation
CC
O SiMe
3
OR
1
+−
−
FSiMe
3
C
C
O

R
1
O
+ F
H
3
C
H
3
C
CH
3
CH
3
then,
+
NBu
4
+
NBu
4
,
C
C
O
CC
CO
COOR
1
,

C
CO
R
1
O
OR
2
OR
2
H
3
CCH
3
+ H
2
C
CH
3
CH
3
CH
3
CH
3
CH
3
−
Remark. The mechanism of initiation reaction reveals the consumption
of the “catalyst.” It does not function as a true catalyst but rather like a
“co-initiator” whose presence is essential for the activation of the initiator.

8.6.7.2. Propagation. It must be stressed here that the propagation reaction
which is represented hereafter occurs through monomer addition by the carbon
form of the enolate whereas the exchange of trimethylsilyl groups between dor-
mant and reactive chains resorts to the oxygen form (due to “oxophilicity” of silicon
atom).
The mechanism shown below is described as “dissociative” because the reactive
species are fully ionized. With weak nucleophilic catalysts, an “associative” mech-
anism was proposed implying a pentacoordination of the silicon atom (discussed)
ANIONIC POLYMERIZATION 327
and mainly covalent active species.
+ n
H
3
C
H
3
C
H
2
C
H
3
C
H
2
C
C
CH
3
CH

3
H
3
C
CH
3
CH
2
CH
2
CH
3
CH
3
CH
3
CH
3
CH
3
CH
3
CH
2
CH
2
CH
2
C
CO

COOR
1
COOR
1
COOR
2
COOR
1
COOR
2
OR
2
OR
2
OR
2
OR
2
OR
2
,
C
CO
propagation
C
n
C
,
C
CO

CC
O SiMe
3
~~~
or TMS
Dormant s
p
ecies
C
n
C
C
C OSiMe
3
+
NBu
4
+
NBu
4
−
In the case of catalysis by Lewis acids found to be suitable for acrylates, the
mechanism is completely different and propagation occurs by monomer activation.
8.6.8. Application of Anionic Polymerization
to Macromolecular Synthesis
The “living” character of anionic polymerizations combined with a short initia-
tion step—compared to that of propagation—affords polymers with low dispersity
index (D
M
=M

w
/M
n
< 1.1). An additional advantage of these systems is the accu-
rate control of the degree of polymerization of the polymers obtained, which merely
reflects the high efficiency (f ) of the initiators employed.
Such a good definition of the molecular dimensions associated with the persis-
tence of the active centers was extensively applied for the purpose of so-called
macromolecular engineering, to design and construct precision macromolecular
architectures. An account of the various possibilities is described in Chapter 9,
including those based on other “living” polymerizations.
8.6.9. Techniques of Anionic Polymerization
Due to the generation of the totality of active centers at the onset polymerization
and the very high polymerizability of vinyl and related monomers, there is no option
328 CHAIN POLYMERIZATIONS
but to carry out anionic polymerizations in solution. Generally, the solvents used
are hydrocarbons (aromatic or aliphatic) acting as diluents. At a smaller scale in
laboratories, ethers (tetrahydrofuran, dioxane, dimethoxyethane, etc.) are sometimes
used, for their solvating and dissociating effects in addition to their role as a
diluent.
The extreme sensitivity of (carb)anionic active centers toward electrophilic impu-
rities, along with their utilization in low concentration to obtain high molar masses,
requires a thorough purification of all reagents. Initially, this purification step
appeared to be a limitation to the industrial development of anionic polymerization;
now, it is not anymore the case as shown by the increasing number of industrial
applications of anionic polymerization.
Studies carried out recently on the control of the reactivity of propagating
species indicate that solvent-free processes may well be developed in the near
future.
8.7. CATIONIC POLYMERIZATION

Cationic polymerization has witnessed an intense development in the middle of
the twentieth century after it could be successfully applied to polymerize certain
ethylenic hydrocarbons such as isobutene, carbonyl monomers such as formalde-
hyde, or cyclic ethers such as oxiranes, tetrahydrofuran, and cyclosiloxanes.
Because of the very high reactivity of the cationic propagating species—in par-
ticular, with ethylenic monomers—the polymerization systems that are commonly
used in industry often entail side reactions and frequent structural irregularities in
the polymers formed.
The discovery of compositional and experimental conditions affording “living”
cationic polymerizations has attracted much interest in particular because some
of unsaturated and heterocyclic monomers concerned can only be polymerized by
cationic means.
8.7.1. General Characters
A cationic polymerization can be defined in a way exactly symmetrical to anionic
polymerization as schematized hereafter:
~~~~M
n
+
~~~~M
+
n+1
,A
−
,A
−
+ M
In this equation, ∼∼∼M
+
n
represents a positively charged (or polarized) species

carried by growing chains, and A
−
represents a negative counterion (or a nega-
tively polarized species) ensuring the neutralization of the positive charge. With
ethylenic monomers, the propagation reaction is an electrophilic addition onto the
polymerizable double bond; the first step is the coordination of the double bond
CATIONIC POLYMERIZATION 329
onto the carbocationic site:
~~~~M
n
CCC
~~~~M
n
CC
+
, A
−
C
+
, A
−
C
+
, A
−
CC
~~~~M
n
C
+

CC
This reaction is all the more facile as the nucleophilic character of the monomer is
pronounced: electron-donating substituents increase the cationic polymerizability,
and in turn the intrinsic reactivity of the carbocationic site formed is reduced by
the effect of such substituents. Thus, as in anionic polymerization, an increase
of reactivity of the monomer has more influence on its polymerizability than a
decrease in reactivity of the corresponding active center. Because of the strong
Lewis acid character of the active species, for a monomer to be polymerized,
strongly nucleophilic sites must not be present.
The mechanism is similar in the case of carbonylated monomers or n-donor
heteronuclear double bonds with an attack by the cationic active center onto the
oxygen atom of the carbonyl group:
O
OC ~~~~M
n
~~~~M
n
OCO
C
+
, A
−
C
+
, A
−
+
Cationic polymerization is also utilized with heterocyclic monomers. In this case,
disregarding the thermodynamic constraints, polymerization proceeds by nucle-
ophilic attack of the hetero-element of a monomer molecule on the electron-deficient

α-carbon atom of the onium ion:
X
~~~~M
n+1
X
~~~~M
n
X
, A
−
, A
−
+
+
+
The heterocyclic monomers that are the most sensitive to electrophilic active centers
are of diverse nature:
O
OO
O
O
O
Oxiranes Oxetanes Other ethers and acetals
O
A
O
A
330 CHAIN POLYMERIZATIONS
but also aziridines, thiiranes, siloxanes, phosphazenes, and so on, all monomers
whose polymerization leads to polymeric materials with various molecular struc-

tures and thus of different physical properties.
Most of the concepts concerning the structure of active species—aggregation,
ionization, solvation, dissociation—which were described in the section on anionic
polymerization, apply to cationic polymerizations; in particular, the more pro-
nounced the ionic character of the species and the longer the interionic distance,
the more prominent the reactivity of active centers.
Solvents that can be utilized in cationic polymerization must be inert with respect
to strongly electrophilic active sites. They can play the role of diluent (aliphatic
hydrocarbons) and that of solvating agents for electrophilic species (nitroparaf-
fins) and/or of dissociating medium of ion pairs into free ions (dichloromethane:
ε
CH
2
Cl
2
=8.93 at 25
◦
C).
8.7.2. Initiation of Cationic Polymerizations
Numerous are the initiators that can be used in cationic polymerization, the
monomer polymerizability determining their choice.
8.7.2.1. Protonic Acids (Br
¨
onsted Acids):
A
−
, H
+
−→ A
−

+H
+
These acids are all the more efficient as they are dissociated in the reaction medium.
More important than the pK
a
in aqueous solution (of little interest), Table 8.16
gives the pK
a
values of various protonic acids in acetic acid and acetonitrile. It
can be noticed that acids which are reputed strong in aqueous solution are not
dissociated in organic media. The most used Br
¨
onsted acids to initiate cationic
polymerizations are:
Perchloric acid H–ClO
4
Trifluoromethylsulfonic (triflic) acid H–SO
3
–CF
3
Trifluoroacetic acid H–O–OC–CF
3
Hydroiodic acid H–I
Depending upon the nature of the solvent used and, in particular, its basicity which
represents its aptitude to trap protons, these initiators will be themselves more or
less good proton donors. Among all the systems shown in Table 8.16, perchloric
acid in acetonitrile solution is the best one.
Certain protonic acids add easily onto the monomer double bond, but when
the associated counterion is more nucleophilic than the monomer, they form a
covalent bond unable to propagate the reaction. Such a situation often occurs with

hydracids:
HCl +H
2
C
=
CHR −→ H–CH
2
–HRC
+
, Cl
−
−→ H
3
C–HRC–Cl
CATIONIC POLYMERIZATION 331
Table 8.16. pK
a
values for some protonic acids in two
different organic solvents
Protonic Acid In Acetic Acid In Acetonitrile
HSO
3
CF
3
4.7 2.6
HClO
4
4.9 1.6
HBr 5.6 5.5
H

2
SO
4
7.0 7.3
HCl 8.4 8.9
HSO
3
CH
3
8.6 8.4
HOOC–CF
3
11.4 10.6
HOOC–CCl
3
12.2 12.7
HOOC–CH
3
12.8 22.5
In the same manner, protonic acids are generally capable of the following reaction
with heterocycles,
A
−
, H
+
+
X
XH
, A
−

+
but depending upon the relative nucleophilicity of the associated anion and the
monomer, propagation may occur or not. Thus, HI initiates the polymerization of
aziridines (three-membered cyclic amines)
HI n
+
N
R
, I
+
−
NCH
2
CH
2
R
H
n−1
N
R
but can only protonate oxiranes:
+ HO CH
2
CHR I
HI
O
R
The protonic initiators that are the most used to polymerize heterocycles are triflu-
oromethylsulfonic (“triflic”) and fluorosulfonic acids.
The kinetics of initiation of the polymerization of ethylenic monomers by pro-

tonic acids
A
−
, H
+
+ HC CHR
H
3
C–HRC
+
, A
−
generally exhibits a first-order variation (expected) with respect to monomer and a
second-order variation with respect to protonic acid.
332 CHAIN POLYMERIZATIONS
This phenomenon is accounted for by a mechanism involving two acid molecules
in the transition state which corresponds, for the case of HCl, to
H
Cl
CC
H
Cl
The higher the rate constant of addition of acid molecule onto the monomer double
bond (k
i
), the greater the nucleophilicity of the monomer. Thus, the rate constant of
initiation by trifluoromethylsulfonic acid at 0
◦
C in dichloromethane (CH
2

Cl
2
)varies
from k
i
=10 L·mol
−1
·s
−1
for styrene, to k
i
=10
3
L·mol
−1
·s
−1
for α-methylstyrene
and k
i
=5 ×10
4
·Lmol
−1
·s
−1
for p-methoxystyrene; these three monomers are
ranked in the order of increasing nucleophilicity.
8.7.2.2. Lewis Acids. BF
3

,AlCl
3
,TiCl
4
,SnCl
4
,andSbCl
5
are the most gen-
erally used Lewis acids. In a few cases, it was shown that these Lewis acids can
initiate polymerizations by themselves. For example, aluminum halides self-ionize
from (generally) dimeric aggregates:
2AlCl
3
−−−→
←−−−
(AlCl
3
)
2
−−−→
←−−−
AlCl
2
+
, AlCl
4
−
and the cationic species (AlCl
2

+
) formed adds to the double bond to generate the
propagating carbocation:
AlCl
2
+
, AlCl
4
−
+H
2
C
=
CHR −→ AlCl
2
–CH
2
–HRC
+
, AlCl
4
−
Diiodine (I
2
) is also able to initiate by itself the polymerization of certain vinyl
monomers, and two mechanisms were proposed to account for this behavior. First
is an addition of molecular iodine to the double bond
I
2
+H

2
C
=
CHR −→ I–CH
2
–CHR–I
followed by an ionization of a C–I bond under the effect of I
2
in excess, the latter
playing the role of a co-initiator:
I–CH
2
–CHR–I+I
2
−−−→
←−−−
I–CH
2
–
+
CHR, I
3
−
The second mechanism proposes a self-ionization of I
2
,
2I
2
−−−→
←−−−

I
+
, I
3
−
followed by an initiation according to a mechanism close to that described for AlCl
3
.
Initiation by a Lewis acid can also occur by an electron transfer in analogy with
the examples of anionic polymerization: for instance, 1,1-diphenylethylene, which