Handbook of Size Exclusion Chromatography and Related ...

fractionated sample. They represent three moments of the distributions present. In
terms of the numbers of molecules present in each slice separated by, for example,
SEC, these quantities are given simply by
P
i
Mn ¼
niMi
P
i ni
(14)
Mw ¼
Mz ¼
P
Pi
P
i P
2 niMi i niMi
i
3 niMi niM 2
i
where ni is the number of molecules in slice i whose weight-average molar mass is
Mi. Since MALS measurements measure the concentration at each slice by the
concentration detector (DRI or UV) rather than the number density, Eqs (14), (15),
and (16) must be re-expressed in terms of the concentrations ci. Since M is
expressed in g/mol and c in terms of g/mL, ci ¼ niMi=NA with NA Avogadro’s
number. Thus we re-write these in terms of the measured concentrations to obtain
P
i ci
P
(17)
and
Mn ¼
Mw ¼
Mz ¼
i (ci=Mi)
P
i ciMi
P
i ci
P
Pi
2 ciMi i ciMi
(15)
(16)
(18)
(19)
The polydispersity of a sample is then defined (17) as the ratio of Mw=Mn,or
simply
P ¼ Mw
Mn
¼ X
i
ciMi
X
i
ci
Mi
(20)
Although an important quantity often referred to as an essential characterization
parameter, MALS software must present each result with its measured precision.
Once again, this complex calculation is based on the errors associated with both
mass and concentration at each slice measured.
Equation (20) is often misunderstood and exaggerated in its use as a
characterization tool. For example, it is a simple matter to calculate the
© 2004 by Marcel Dekker, Inc.