Chemistry Reference
In-Depth Information
Fig. 2.17
Cannon-Fenske
capillary viscometer
as the intrinsic viscosity. If they do not, then the two intercepts are averaged. The relationship of
intrinsic viscosity to molecular weight is expressed by the Mark-Houwink-Sakurada equation [
66
]:
½
c¼
0
¼ KM
a
where
are constants. Various capillary viscometers are available commercially. Figure
2.17
illustrates a typical capillary viscometer.
The logarithms of intrinsic viscosities of fractionated samples are plotted against log
K
and
a
M
w
or
log
of the Mark-Houwink-Sakurada equation are the intercept and the
slope, respectively, of that plot. Except for the lower molecular weight samples, the plots are linear
for linear polymers. Many values of
M
n
. The constants
a
and
K
K
a
and
for different linear polymers can be found in the
literature [
66
].
Actually, the Mark-Houwink-Sakurada equation applies only to narrow molecular weight distri-
bution polymers. For low molecular weight polydisperse polymers this equation is useful, because the
deviations due to chain entanglement are still negligible. On the other hand, chain entanglement in high
molecular weight polydisperse polymers affects viscosity and this equation does not really apply.
The determinations of molecular weights of polymers rely, in most cases, upon physical methods.
In some special ones, however, when the molecular weights are fairly low, chemical techniques can
be used. Such determinations are limited to only those macromolecules that possess only one
functional group that is located at the end of the chain ends. In place of the functional group, there
may be a heteroatom. In that case, an elemental analysis might be sufficient to determine the
molecular weight. If there is a functional group, however, a reaction of that group allows calculating
the molecular weight. Molecular weights above 25,000 make chemical approaches impractical.
In chemical determination each molecule contributes equally to the total. This determination,
therefore, yields a number average molecular weight. With the development of gel permeation
chromatography (discussed below), this method is hardly ever used today.
There are various physical methods available. The more prominent ones are ebullioscopy,
cryoscopy, osmotic pressure measurements, light scattering, ultracentrifugation, and gel permeation
chromatography (also called size exclusion chromatography). All these determinations are carried out
on solutions of the polymers. Also, all, except gel permeation chromatography, require that the results
