Handbook of Size Exclusion Chromatography and Related ...

case of a highly branched high-temperature metallocene, are found in the article by
Trainoff and Wyatt (26).
The improvement in branching analyses, especially since the work of
Zimm and Stockmayer and with the advent of SEC, has been significant.
Unfortunately, there still remain some problems. Foremost among them is the
requirement that a linear analog of the branched sample be available for the
calculation of the branching ratio of Eq. (11). This is often difficult to find. Then
there is the equally serious problem that an elution slice actually corresponds to
a single mass. Because of branching, there will be many different masses that
are branched to varying degrees yet have the same hydrodynamic size and thus
co-elute. Each slice, therefore, may contain a relatively large mass distribution
and not be monodisperse. Analyses based upon the assumption of
monodispersity must be weighed carefully, especially if anomalous results
are derived. This problem is very similar to MALS measurements of copolymers
whereby for heterogeneous copolymers, a given elution slice may contain a
broad range of molar masses.
Interestingly, the Zimm–Stockmayer paper contained two paragraphs about
viscometry and discussed how measurement of the ratio of intrinsic viscosities for
branched and linear molecules might provide a parameter similar to the g-factor of
Eq. (11), that is, a measure of the degree of branching in a sample. This hope has
been used extensively as the basis of the belief that viscometric measurements
could be used to quantitate branching. However, the last sentence of the
viscometry discussion (24) concludes with the statement “ ...clearly it is still
hazardous to draw inferences about branching from empirical viscosity–
molecular weight relationships, and the method based on evaluations of kr2 gl from
light scattering is much to be preferred.”
9 MASS AND SIZE DISTRIBUTIONS
An important result derivable from MALS measurements following chromatographic
separation is the ability to determine both differential and cumulative
distributions in both mass and r.m.s. size for each sample successfully separated.
Shortt (17) has described these and related quantities in depth in his 1993 article.
There are few measurements able to characterize a sample more precisely than the
differential weight fraction distribution. Indeed, because of the associated error
analyses, such quantitation has been used extensively in quality control
applications. Until Shortt’s article, the definitions were confusing and some
were erroneous (28) because of confusion with the meaning of the logarithm to
base 10.
In addition to the differential and cumulative distributions, an important
measure of a molecular species are the number-, weight-, and z-averages of the
© 2004 by Marcel Dekker, Inc.