Chemistry Reference
In-Depth Information
CHAPTER
3
Practical Aspects of
Molecular Weight
Measurements
Now what I want is, Facts. Facts alone are wanted in life.
—Charles Dickens, Hard Times
In this chapter, analytical metho
ds
that ar
e
commonly used for the measurements
of molecular weight averages (
M
n
and
M
w
) and molecular weight distribution
will be described. It is interesting to note that it is possible to determine one of
the average molecular weights of a polymer sample without knowing the molecu-
lar weight distribution. This is accomplished by measuring a chosen property of a
solution of the sample.
3.1
M
n
Methods
Most of the procedures for measuring
M
n
rely on colligative solution properties.
These properties include osmotic pressure, boiling point elevation, freezing point
depression, and vapor pressure lowering. They are all described thermodynami-
cally by the ideal solution (
Eq. 3-10
) or its analogs (Section 3.24) for real solu-
tions. At given solute concentration, these relations show that the effect of the
dissolved species on the chemical potential of the solvent decreases with increas-
ing solute molecular weight. Therefore, any colligative property measurement
must be very sensitive if it is to be useful with high-molecular-weight solutes like
synthetic polymers.
Membrane osmometry is the most sensitive and accurate colligative property
technique. Consider, for example, a polystyrene with
M
n
around 200,000.
Trial-and-error experience has shown that molecular weight measurements with
similar samples are best made by starting with solutions in good solvents (like tol-
uene in this case) at concentrations around 10 g/liter and making successive
dilutions from this value. The initial polymer concentration is then [(10 g/liter)
(mol/200,000 g)]
10
2
5
M
. At room temperature
RT
is of the order of 23 L-atm
and
Eq. (3-17)
indicates that the osmotic pressure would be about 10
2
3
atm. This
corresponds to the pressure exerted by a column of organic solvent about 14 mm
high. Modern membrane osmometers measure pressures with precisions of the
5
3
5
