Chemistry Reference
In-Depth Information
Here the MHS constants
K
and
a
for the GPC solvent are used with the expo-
nent
a
0
and the measured intrinsic viscosity [
η
0
] of a single polymer sample in the
non-GPC solvent.
This procedure is much less tedious than the method described in
Section 3.3.2
for measurement of MHS constants. It may not necessarily produce the same
K
and
a
values as the standard fractionation method described earlier. This is
because
K
and
a
are inversely correlated, as mentioned, and are also not
entirely independent of the molecular weight range of the samples used.
Essentially the same
K
and
a
should be obtained if the two samples used with
Eq. (3-103) or (3-106)
and the fractions used with
Eq. (3-71b)
have similar
molecular weights.
Because
Eq. (3-80)
defines
M
w
when
a
1, it is possible to estimate the
M
w
of a sample by measuring the
M
v
for the pol
ym
er in two or three solvents with
different
v
alues of the exponent
a
. A plot of
M
v
against
a
is linear and extrapo-
lates to
M
w
at
a
5
1
[23]
. This procedure is fairly rapid if single-point intrinsic
viscosities (
Section 3.3.4
) are used. It can be employed as an alternative to light
scattering although the latter technique is more reliable and gives other informa-
tion in addition to the weight average molecular weight. The GPC method out-
lined here is a c
on
venient procedure to generate the MHS constants for this
approximation of
M
w
from solution viscosity measurements.
It is possible in principle to derive
K
a
nd
a
from a single whole polymer sam-
ple for which [
5
] in the GPC solvent and
M
n
are known
[21]
. This method is less
reliable than the preceding procedure
wh
ich involved intrinsic viscosities of two
samples because the computations of
M
n
can be adversely affected by skewing
and instrumental broadening of the GPC chromatogram.
η
3.4.4
Branched Polymers
Equation (3-66)
links the intrinsic viscosity of a polymer sample to the radii of
gyration
r
g
of its molecules while
Eq. (3-99)
relates the hydrodynamic volume
V
of a solvated molecule to the product of its molecular weight and intrinsic viscos-
ity. The separation process in GPC is on the basis of hydrodynamic volume, and
the universal calibration described in
Section 3.4.3
is valid only if the relation
between
V
and
r
g
is the same for the calibration standards and the unknown
samples.
Branched molecules of any polymer are more compact than linear molecules
with the same molecular weight. They will have lower intrinsic viscosities
(Section 3.3.7) and smaller hydrodynamic volumes, in a given solvent, and will
exit from the GPC columns at higher elution volumes. Universal calibration (pre-
ceding section) cannot be used to analyze polymers whose branching or composi-
tion is not uniform through the whole sample. Generally useful techniques that
apply to such materials, as well as to the linear homopolymers that are amenable
to universal calibration, involve augmenting the concentration detector (which is
