Handbook of Size Exclusion Chromatography and Related ...

If the intrinsic viscosity of the eluting unknown polymer is measured at each
elution volume using an on-line viscometer, universal calibration can be used to
calculate the molecular weight at each volume, and thus the molecular weight
distribution, without knowledge of the Mark–Houwink coefficients.
For branched polymers or copolymers, the molecules eluting at a given
volume may be polydisperse in molecular weight. Molecules with the same
hydrodynamic volume but different structure or composition have different
molecular weights. In this case the molecular weight in a given elution volume
increment measured by universal calibration is the number-average molecular
weight Mn (16).
Universal calibration is valid only when there are no enthalpic interactions
between the polymer sample and the column packing and the separation is entirely
a result of the size exclusion mechanism. Furthermore, chromatographic concentration
effects must be absent. Another consideration is that the molecular weight
of the standards used to construct the universal calibration curve must be known
accurately.
3.1.2 SEC-Viscometry Without a Concentration Detector
SEC-viscometry combined with universal calibration can provide measurements
of molecular weight distribution even when it is not possible to use a concentration
method (17), for example at temperatures at which a concentration detector can no
longer operate or in solvents in which there is no measurable difference between
solution and solvent refractive index, such as polyolefins in decalin.
The method requires that the Mark–Houwink exponent a for the polymer–
solvent system and the sample amount injected be known. The concentration at
each elution slice is then calculated from the viscometer output hsp, the universal
calibration curve, and the Mark–Houwink exponent. From the Mark–Houwink
equation and the definition of hydrodynamic volume in universal calibration, it can
be shown that the concentration at each elution volume increment is given
by (M. Haney, personal communication)
where
and
© 2004 by Marcel Dekker, Inc.
K ¼
ci ¼
P ( ln hr) i
P ci
( ln h r) i
[K 1=a (hn) i] a=(aþ1)
P ( ln hr) i=hni
P ci
1=a
(12)
(13)
X ci ¼ mDV (14)