Chemistry Reference
In-Depth Information
Fig. 2.18
Membrane
osmometer
capillary
solution
solvent
membrane
of the measurements be extrapolated to zero concentrations to fulfill the requirements of theory. The
laws that govern the various relationships in these determinations apply only to ideal solutions. Only
when there is a complete absence of chain entanglement and no interaction between solute and
solvent is the ideality of such solutions approached. A brief discussion of some techniques used for
molecular weight determination follows
Ebullioscopy
, or boiling point elevation, as well as
cryoscopy
, or freezing point depression, are well-
knownmethods of organic chemistry They are the same as those used in determiningmolecular weights
of small molecules. The limitation to using both of these methods to determine the molecular weight of
macromolecules is that
DT
f
become increasingly smaller as the molecular sizes increase. The
methods are limited, therefore, to the capabilities of the temperature sensing devices to detect very
small differences in temperature. This places the upper limits for such determinations to somewhere
between 40,000 and 50,000. The thermodynamic relationships for these determinations are:
DT
b
and
½DT
b
=
c
c!
0
¼ RT
2
=rDH
b
M ½DT
f
=
c
c!
0
¼ RT
2
=rDH
f
M
boiling point rise elevation
freezing point depression
The above two determinations, because each molecule contributes equally to the properties of the
solutions, yield number averagemolecular weights. Howmuch this technique is used today is hard to tell.
A method that can be used for higher molecular weight polymers is based on
osmotic pressure
measurements
. It can be applied to polymers that range in molecular weights from 20,000 to 500,000
(some claim 1,000,000 and higher). The method is based on van't Hoff's law. When a pure solvent is
placed on one side of a semi-permeable membrane and a solution on the other, pressure develops from
the pure solvent side. This pressure is due to a tendency by the liquids to equilibrate the concentrations.
It is inversely proportional to the size of the solute molecules. The relationship is as follow:
M
n
¼ RT=ðp=CÞ
C¼
0
þ A
2
C
where
is the gas constant,
A
2
is a measure of interaction between the solvent and the polymer (second viral coefficient).
A
p
is the osmotic pressure,
C
is the concentration,
T
is temperature, and
R
capillary osmometer is illustrated in Fig.
2.18
. Rather than rely on the liquid to rise in the
capillary on the side of the solution in response to osmotic pressure, as is done in the static method, a
dynamic equilibrium
method can be used. Here a counter pressure is applied to maintain equal levels
of the liquid in both capillaries and prevents flow of the solvent. Different types of dynamic
membrane osmometers are available commercially. The principle is illustrated in Fig.
2.19
.
static
