Handbook of Size Exclusion Chromatography and Related ...

the double extrapolation to zero angle and zero concentration intercepts the
K*c=R(u) axis at avalue equal to the inverse of the molecular weight,
K*c
¼
R(u ¼0) c!0
1
(9)
Mw
Theinitialslopeatzeroangleisproportionaltothesecondvirialcoefficient,
and theinitial slope ofthegraphat zero concentration, divided by theintercept, is
proportional to the mean-square radius of gyration.
When combined with SEC, the light-scattering intensity can only be
measuredatasingleconcentrationforeachmolecularweightfractionelutingfrom
the column. Thus, to determine molecular weight, the second virial coefficient
must be known beforehand or must be assumed to be zero. In most cases, setting
the second virial coefficient to zero is avalid approximation because the eluting
polymer concentration is usually low.In general, the resultant error is less than
experimental error. Making this approximation and measuring the scattered light
intensityatanumberofangles,wecandeterminethemolecularweightandmeansquareradiusofgyrationforeachelutionslicebyextrapolationtozeroangle.The
datapointsthusobtainedapproximatetothezeroconcentrationpointsinFig.4.In
practice, the radius of gyration can only be determined for molecules greater than
about 20 nm in diameter; below this size it is extremely difficult to measure
variation in scattered intensity with angle.
If asingle low-angle scattering intensity is measured, typically ,108, then
for most polymer molecules scattering intensity in this region this can be
considered avalid approximation to the zero-angle intensity and no extrapolation
is required. The molecular weight is then proportional to the scattered intensity
divided by the concentration.
3 METHODOLOGY
3.1 Viscometry
3.1.1 Universal Calibration
Benoit and co-workers (15) showed that SEC separates polymer molecules by
hydrodynamic volume. The hydrodynamic volume can be expressed as the
product of intrinsic viscosity and molecular weight:
hn ¼[h]M (10)
It is therefore possibletogenerate auniversal calibration curveof polymer hydrodynamic
volume against elution volume that is valid for different types of
polymers as well as copolymers and branched polymers (Fig. 5). This is achieved
by using narrow molecular weight distribution standards with known molecular
© 2004 by Marcel Dekker, Inc.