Chemistry Reference
In-Depth Information
M
1
S
5
C
I
½
I
C
½
TH
2
ð
k
tc
1
k
td
Þ
1
C
M
1
½
(8-102)
1
1
1
½
M
½
M
k
p
With [M
]
R
p
/k
p
[M] from
Eq. (8-13)
,
1
S
5
5
1
C
I
½
I
1
C
M
1
C
½
TH
2
ð
k
tc
1
k
td
Þ
1
R
p
(8-103)
1
½
M
½
M
2
k
p
½
M
Note that any chain transfer effects of solvent are included in the general term
for transfer agent TH and that
transfer to polymer is not
included in this
expression.
We first consider the polymerization where each kinetic chain yields one poly-
mer molecule. This is the case for termination of the growth of macroradicals by
disproportionation and/or chain transfer (
k
tc
5
0). The situation is completely anal-
ogous to that for linear, reversible step-growth polymerization described in
Section 7.4.3. If we randomly select an initiator residue at the end of a macromole-
cule, the probability that the monomer residue that was captured by this primary
radical has added another monomer is
S
and the probability that this end is attached
to a macromolecule that contains
at least i
monomers is
S
i
2
1
. The probability that
this macromolecule contains
exactly i
monomers equals the product of
S
i
2
1
and the
probability of a termination or transfer step. The latter probability must be equal to
(1
S
) since it is certain that the last monomer under consideration will undergo
one of these three reactions. That is, the probability that a randomly selected mole-
cule contains
i
monomer units is
S
i
2
1
(1
2
S
). Since such probabilities are equal to
the corresponding mole fraction of this size molecule,
x
i
, we have the expression
x
i
5
ð
2
S
i
2
1
1
S
Þ
(8-104)
2
for the number distribution function. The weight distribution function
w
i
is also given
by direct analogy to that for linear, equilibrium step-growth polymerization as
2
S
i
2
1
ω
i
5
i
ð
S
Þ
1
2
(8-105)
The distribution described is a random one, with average degrees of polymeri-
zation (Section 7.4.3):
DP
n
5
1
=ð
1
S
Þ
(8-106)
2
DP
w
5
ð
1
1
SÞ=ð
1
2
SÞ
(8-107)
DP
w
=
DP
n
5
1
1
S
(8-108)
[As a check, note that in the absence of chain transfer, DP
n
from
Eqs. (8-106)
and (8-103)
equals the value from
Eq. (8-64)
with
k
tc
5
0.]
R
tr
(or high-molecular-weight
polymer would not be formed). In that case
S
.1 and
X
w
/X
n
will be .2 from
Eq. (8-
108)
.
For most addition polymerizations,
R
p
c
R
t
1
