Chemistry Reference
In-Depth Information
and from
Eq. (3-84)
,
K
1
=ða1
1
Þ
X
w
i
J
a=a1
1
½η 5
(3-102)
i
If two samples of the unknown polymer are available with different intrinsic
viscosities, then
X
X
i
ω
1
i
J
a=a1
1
½η
1
½η
2
5
ω
2
i
J
a=ða1
1
Þ
(3-103)
1
i
2
i
Here the
w
i
are available from the ordinates of the gel permeation chromato-
gram and the
J
i
from the universal calibration curve of elution volume against
hydrodynamic volume through
Eq. (3-94) or (3-98)
. The intrinsic viscosities must
be in the GPC solvent in this instance, of course. A simple computer calculation
produces the best fit
a
to
Eq. (3-103)
, and this value is inserted into
Eq. (3-101)
to calculate
K
. These MHS constants can be used with
Eq. (3-97)
to translate the
polystyrene calibration curve to that for the new polymer.
Note that this procedure need not be restricted to determination of MHS con-
stants in the GPC solvent alone
[22]
. The ratio of intrinsic viscosities in
Eq. (3-
103)
can be measured in any solvent of choice as long as the
w
i
and
J
i
values for
the two polymer samples of interest are available from GPC in a common, other
solvent. The first step in the procedure is the calculation of
K
and
a
in the GPC
solvent as outlined in the preceding paragraph. The intrinsic viscosities of the
same two polymers are also measured in a common other solvent. The data per-
taining to this second solvent will be designated with prime superscripts to distin-
guish them from values in the GPC solvent. In the second solvent,
J
i
½η
i
M
i
(3-100a)
For a species of given molecular weight
M
i
,
Eqs. (3-100a) and (3-100)
yield
J
i
½η
0
i
J
i
=½η
i
(3-104)
With
Eq. (3-70)
J
i
5
M
a
0
2a
i
K
0
=
J
i
ð
K
Þ
(3-105)
Then for the non-GPC solvent,
Eq. (3-103)
becomes
½η
0
1
X
X
ω
1
i
J
a
0
=ða1
1
Þ
=
ω
2
i
J
a
0
=ða1
1
Þ
½η
0
2
5
(3-106)
As above, the
w
i
and
J
i
values are available from the GPC experiment and
intrinsic viscosities of the two polymer samples in the GPC solvent. The exponent
a
can be calculated as described in connection with
Eq. (3-103)
.
The computed best fit value of
a
in
Eq. (3-106)
can be now used to calculate
K
from:
X
ω
i
J
a
0
ða1
1
Þ
K
0
5 ½η
0
K
a
0
=ða
1
1
Þ
=
(3-107)
i
