Chemistry Reference
In-Depth Information
since each molecular decomposition produces two radicals. The rate of initiation
R
i
is the rate of reaction (8-8). This can be expressed in terms of the rate of radi-
cal production as
R
i
5
2
fk
d
½
I
(8-10)
where
f
, the fraction of all radicals generated that are captured by monomers, is
called the
initiator efficiency
. This
term is discussed in more detail
in
Section 8.5.5
. Initiator efficiency is always
1.
The formulation of the rate of initiation in
Eq. (8-10)
contains
k
d
as the only
rate constant. The other rate constant
k
i
of reaction (8-8) is not required if
f
and
k
d
can be measured.
#
8.3.2
Propagation
By definition, a propagation step in a chain reaction is one in which products are
formed, and the site of the reactive center changes but the number of active cen-
ters is not changed. (This statement is qualified in
[2]
.) There are two major prop-
agation reactions under the conditions of most free-radical polymerizations. These
are addition and atom transfer reactions.
8.3.2.1
Addition Reactions
Successive monomer additions after the initiation step of reaction (8-8) can be
represented as
M
1
1
M
2
M
(8-11a)
-
M
2
1
M
3
M
(8-11b)
-
M
i
1
1
(8-12)
where M
i
represents the radical R
(M
)
i
2
1
M
. Each reaction in the sequence
involves the addition of a monomer to a monomer-ended radical, and each is
assigned the same rate constant
k
p
on the reasonable assumption that the rate of
the addition reaction does not depend on the size of the participating macroradi-
cal. Values of the propagation rate constant
k
p
for most monomers are of the
order of 10
2
M
i
1
M
-
10
3
liter/mol sec under practical polymerization conditions.
Reaction (8-12) is a bimolecular reaction as written, and
k
p
is therefore a
second-order rate constant with units of (concentration)
2
1
(time)
2
1
.
The rate of propagation
R
p
is given by
R
p
5
2
M
½
(8-13)
where [M
] stands for the sum of the concentrations of all monomer-ended radi-
cals in the system. This expression for
R
p
can be written as shown since the
radical concentrations can be lumped together if
k
p
does not depend on the size
of M
i
.
k
p
½
M
