Chemistry Reference
In-Depth Information
Substitution of x
i
for
f
i
in
Eq. (2-4)
shows that the arithmetic mean of the number
distribution is
X
A
5
x
i
M
i
5
M
n
(2-6)
i
This is the definition of number average molecular weight M
n
.
Equivalent definitions follow from simple arithmetic. Since
N
5
n
i
X
n
i
n
i
x
i
5
(2-7)
X
n
i
M
i
X
n
i
M
n
5
(2-8)
where n
i
is defined, as above, as the number of polymer molecules per unit volume
of sample with molecular weight M
i
. Also, if c
i
is the total weight of the n
i
molecules,
each with molecular weight M
i
,andw
i
is the corresponding weight fraction, then
c
i
5
n
i
M
i
(2-9)
w
i
5
c
i
X
c
i
5
n
i
M
i
X
n
i
M
i
(2-10)
and
X
c
i
X
c
i
M
i
5
1
X
w
i
M
n
5
(2-11)
M
i
Since polymer solutions are used for direct determinations of average molecu-
lar weights, the symbols n
i
and c
i
will usually refer respectively to the molar and
weight concentrations of macromolecules in such solutions.
Molecular weight,
M
i
FIGURE 2.2
A normalized differential number distribution curve.
