Chemistry Reference
In-Depth Information
p
0
= fraction of reacted groups in the linear chains. J ? S used the symbol x,
but x has a different meaning in Flory's work and in other chapters of this topic,
hence Flory's symbol p
0
was used in this chapter.
b = effective link length of polymer chain, correlated with bond length
l according to Eq. (
5.4
) and with the end-to-end distance of a coiled chain
according to Eq. (
5.5
).
b
2
¼ l
2
ð
1
þ
cos a
Þ=ð
1
cos a
Þ
ð
5
:
4
Þ
L
2
av
¼ mnb
2
ð
5
:
5
Þ
From experimental data, [
2
]J? S obtained via Eq. (
5.3
) b = 4.4. A for
poly(ecamethylene adipate) and speculated that this relatively high value might
indicate partially hindered rotations.
For the calculation of the weight fraction of rings (q
w
in Ref. [
1
], w
r
in Ref. [
5
]).
J ? S presented the following definitions and equations:
C
m
þ
n
!
C
m
þ
R
n
ð
no byproduct involved
Þ
ð
5
:
6
Þ
C
m
þ
n
!
C
m
þ
C
n
ð
byproduct needed
Þ
ð
5
:
7
Þ
C
n
!
R
n
ð
byproduct eliminated
Þ
ð
5
:
8
Þ
Commenting on poly(decamethylene adipate) [
2
]J? S noted that the role of
water in Eqs. (
5.6
) and (
5.7
) was ignored, because it does not show up in the sum
of all three equations.
The mass action product was formulated according to Eq. (
5.9
):
K
1
¼ C
m
þ
R
n
=
C
m
þ
n
¼ R
n
=
p
ðÞ
n
ð
5
:
9
Þ
Taking into account the definitions (
5.10
) and (
5.11
), Eqs. (
5.12
) and (
5.13
)
were formulated correlating the weight fraction of rings with experimental data,
such as the monomer concentration (IMC) and conversion p
0
.
c ¼ N
=
N
o
V
ð
Þ
;
ð
5
:
10
Þ
the ''ground molar concentration''
with N
o
=
Avogadro's number
B
0
¼ B
=
N
o
ð
5
:
11
Þ
!
q
w
¼ w
r
¼
ð
B
0
=
c
Þ
X
1
ð
p
0
n
3
=
2
for A
2
monomers
ð
5
:
12
Þ
n¼1
!
q
w
¼ w
r
¼ 2
ð
B
0
=
c
Þ
X
1
ð
p
0
n
3
=
2
for a
2
þ
b
2
monomers
ð
5
:
13
Þ
n¼1
From Eq. (
5.13
)J? S calculated Figs.
5.1
and
5.2
. These diagrams illustrate
that w
r
increases with conversion and with dilution. Yet, 100 % rings can only be
