Chemistry Reference
In-Depth Information
4.11 Thermodynamics of Equilibrium Polymerization
The effect of solvents on the equilibrium constants in anionic polymerization in solution has been
considered in thermodynamic terms [
407
].
Sawada [
407
] expressed the change in free energy for converting one mole of liquid monomer in
an anionic polymerization to one base-mole of an amorphous polymer,
DF
1c
, as follows:
DF
1c
¼ DF
m
DF
p
where,
DF
m
is the partial molar free energy of the monomer (per mole) in the equilibrium mixture,
relative to that of the pure liquid monomer, and
DF
p
is the partial molar free energy of the polymer
(per base mole) in the equilibrium mixture, relative to that of the amorphous polymer.
Flory [
409
] described
DF
m
and
DF
p
in a three component system of polymer, monomer, and
solvent as follow:
DF
m
=RT ¼
ln
'
m
Þ'
s
ðX
m
=X
p
Þ'
p
ðX
m
=X
p
Þþðw
ms
'
s
þ w
ms
'
p
Þð'
s
þ '
p
Þ
w
sp
ðX
m
=X
p
Þ'
s
'
p
'
m
þð
1
DF
p
=RT ¼
1
'
p
Þ'
m
ðX
p
=X
m
Þ'
s
ðX
p
=X
m
Þþðw
pm
'
m
þ w
ps
'
s
Þð'
m
þ '
s
Þ
w
ms
ðX
p
=X
m
Þ'
m
'
s
=n½
ln
'
p
þð
1
where,
'
i
is the volume fraction of component
i
,
X
i
is the number of segments per molecule for
component
is the
free energy parameter between any two components. The subscripts m, s, and p indicate monomer,
solvent and polymer, respectively. Flory puts the ration of molar volume as,
i
,
n
is the degree of polymerization,
R
is the gas constant,
T
is the temperature, and
w
v
i
=v
j
¼ X
i
=X
j
assuming that
v
p
/
v
m
¼ n
and expressing
w
pm
and
w
ps
in terms of molecular weight-independent
quantities
w
mp
and
w
sp
through the relationship:
w
pm
¼ w
mp
ðV
p
=V
m
Þ¼V
mp
n
w
ps
¼ w
sp
nðV
m
=V
s
Þ
The free energy of polymerization can then be written:,
DF
1c
=RT ¼
'
m
þ
þðw
ms
'
s
þ w
ms
'
p
Þð'
s
þ '
p
Þw
sp
ðV
m
=V
s
Þ'
s
'
p
ð
=nÞ
'
p
=n
ln
1
1
ln
1
ðw
mp
'
m
þ w
sp
'
s
V
m
=V
s
Þð'
m
þ '
s
Þþw
m
'
m
'
s
where,
'
m
is now the equilibrium volume fraction of monomer and the volume fraction of the
polymer is
'
p
.
Sawata points out [
407
] that by neglecting terms 1/
n
when
n
is large, and by replacing (
'
s
+
'
p
)by
(1
'
m
) and (
'
m
+
'
s
)by(1
'
p
) one gets a more general expression:
DF
1c
=RT ¼
ln
'
m
þ
1
þ '
s
ðw
ms
w
sp
V
m
=V
s
Þþw
ms
ð'
p
'
m
Þ
