Chemistry Reference
In-Depth Information
As a “proof,” consider a mixture formed of a grams of a monodisperse poly-
mer A (with molecular weight M
A
) and b grams of a monodisperse polymer B
(with molecular weight M
B
). This blend, which we call mixture 1, contains
weight fraction (w
A
)
1
of polymer A and weight fraction (w
B
)
1
of polymer B.
ð
w
A
Þ
1
5
a
=ð
a
1
b
Þ
ð
w
B
Þ
1
5
b
=ð
a
1
b
Þ
and
The number average molecular weight
ð
M
n
Þ
1
of this mixture is
a
1
b
a
=
M
A
1
b
=
M
B
ð
M
n
Þ
1
5
(2-11b)
2
1
a
ð
a
1
b
Þ
M
A
1
b
ð
a
1
b
Þ
M
B
ð
M
n
Þ
1
5
(2A-1)
If mixture 2 is produced by blending c grams of A and d grams of B, then
similarly
ð
w
A
Þ
2
5
c
=ð
c
1
d
Þ
and
ð
w
B
Þ
2
5
d
=ð
c
1
d
Þ
while
2
1
c
ð
c
1
d
Þ
M
A
1
d
ð
c
1
d
Þ
M
B
ð
M
n
Þ
2
5
(2A-2)
Now we blend e grams of mixture 1 with f grams of mixture 2. The weight
fraction w
1
of mixture 1 is e/(e
1
f) and that of mixture 2 is w
2
5
f/(e
1
f). The
weight fraction of polymer A in the final mixture is w
1
(w
A
)
1
1
w
2
(w
A
)
2
5
w
A
and
that of polymer B is w
1
(w
B
)
1
1
w
2
(w
B
)
1
5
w
B
.
1
5
w
A
e
e
1
f
a
a
1
b
f
e
1
f
c
c
1
d
w
1
ð
w
A
Þ
1
1
w
2
ð
w
A
Þ
2
5
(2A-3)
1
5
w
B
e
e
1
f
b
a
1
b
f
e
1
f
d
c
1
d
w
1
ð
w
B
Þ
1
1
w
2
ð
w
B
Þ
2
5
(2A-4)
The number of average molecular weight of the final blend is
2
1
w
A
M
A
1
w
B
M
ð
M
n
Þ
blend
5
by definition
(2-11c)
