Chemistry Reference
In-Depth Information
where the subscript refers to the polymer type. Thus, at equal elution volumes
K
1
M
a
1
1
1
K
2
M
a
2
1
1
½η
1
M
1
5
5 ½η
2
M
2
5
(3-96)
1
2
and the molecular weight of polymer 2, which appears at the same elution volume
as polymer 1 with molecular weight
M
1
, is given by
1
1α
1
1
K
1
K
2
ln
M
2
5
1α
2
ln
M
1
1
a
2
ln
(3-97)
1
1
1
The polystyrene calibration curve of
Fig. 3.11
can be translated into that of
any other polymer for which the MHS constants are known
[19]
.
EXAMPLE 3-4
The Mark
Houwink
Sakurada constants
for polystyrene in toluene at 25
C are
10
23
cm
3
/g and a
K
5
4.17
3
5
0.65. And the corresponding constants for polypropylene in
10
23
cm
3
/g and a
the same solvent are K
0.73. Using the following mono-
disperse polystyrenes as calibration standards, construct a calibration curve for polypropylene
in gel permeation chromatography. Also estimate the molecular weight of a fraction of an
unknown polypropylene sample showing an elution volume of 150 cm
3
.
5
21.8
3
5
Elution volume (cm
3
)
Molecular weight of the polystyrene standards
10,000
160
50,000
145
100,000
132
500,000
120
Solution
10
23
cm
3
/g
PS in toluene at 25
C
K
PS
5
4.17
3
a
PS
5
0.65
10
23
cm
3
/g
PP in toluene at 25
C
K
PP
5
21.8
3
a
PP
5
0.73
1
1a
PS
11a
PP
1
11a
PP
ln
K
PS
K
PP
ln M
PP
5
ln M
PS
1
110:73
ln
4
:
17
3
10
23
110:65
110:73
ln
1
5
M
PS
1
21:8310
23
50:954 ln M
PS
20:956
M
PP
5
0:954
PS
2
exp ln
M
0
:
956
=expð0:956Þ
0:954
PS
5exp ln M
0:954
PS
50:384 M
