Chemistry Reference
In-Depth Information
followed from the change in volume of the reaction mixture if this relation is
known for the particular monomer
[9]
. Gas-liquid chromatography is also a con-
venient technique for following the rate of polymerization because the polymer
produced is not volatile and the amount of unused monomer can be measured
with ref
ere
nce to
sol
vent or other internal standard
[10]
.
The M
n
and DP
n
of the polymer produced can be measured as outlined in
Section 3.1.
Recall that corresponding instantaneous values of DP
n
and
R
p
are linked by
Eq. (8-64)
. If sufficient polymer can be collected for molecular weight measurements
from a polymerization that goes to only 5% or 10% convers
ion,
the average value of
[M] can be inserted into this equation with the measured DP
n
and
R
p
to estimate
k
p
ð
. If the ratio
k
td
/k
tc
is known or assumed, then
k
p
=
k
t
is available.
Alternatively, when the initiator in these experiments is an azo compound like
AIBN the initiator characteristics
f
and
k
d
are believed to be independent of the
other constituents of the reaction mixture. (This cannot be assumed for peroxide
or redox initiation.) Then, if
f
and
k
d
or their product is known from other mea-
surements with the particular azo compound,
k
p
=
k
tc
1
k
td
Þ
k
1
=
t
can be calculated
fro
m poly-
merization rate measurements and
Eq. (8-29) or (8-35)
. As well, DP
n
alone
provides an estimate of
k
p
=
k
1
=
2
t
from
Eq. (8-65)
when
fk
d
and the mode of termi-
nation are already known.
Note that all these calculations except those that rely on
Eq. (8-29) or (8-35)
make th
e as
sumption that chain transfer is negligible. Estimations of
k
p
=k
1
=
t
that
involve DP
n
data can be rendered unreliable because of unsuspected chain trans-
fer reactions.
The ratio
k
p
=
k
1
=
t
has appeared again and again in the equations that were
developed to this point in the text for free-radical polymerizations. It is not too
difficult to measure this parameter from steady rate experiments, as shown in this
section,
k
1
=
2
t
is known for many systems of practical interest.
Measurement of the separate values of
k
p
and
k
t
is more challenging, however,
and methods pertaining to
k
p
and
k
t
are described in
Section 8.12
.
and
k
p
=
8.11
Radical Lifetimes and Concentrations
The average lifetime
of the kinetic chain is given by the ratio of the steady-
state radical concentration to the steady-state rate of radical disappearance:
τ
M
½
1
τ
5
(8-93)
2
5
M
M
2
ð
k
tc
1
k
td
Þ½
2
ð
k
tc
1
k
td
Þ½
Substituting for [M
] from
Eq. (8-13)
,
τ
5
k
p
½
M
=
2
ð
k
tc
1
k
td
Þ
R
p
(8-94)
Also, with
Eq. (8-29)
for
R
p
and
Eq. (8-20)
for
k
t
,
