142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

Dendrimers and Dendrimer-Polymer Hybrids 193
2.3
Size Exclusion Chromatography
SEC by itself is not an absolute MW determination method but the analysis of
the elution peak has been used extensively for estimating the molecular purity
of dendrimers. If the shape of the elution peak of a size exclusion chromatography
experiment is Gaussian, the total dispersion, s T of the curve is given by the
sum of squares [47]:
(s T ) 2 =(s c ) 2 +a(s d ) 2 (1)
where (s c ) 2 is the sum of the squares of dispersions due to the injector, column
spreading and detector, s d is the dispersion due to the polydispersity of the sample,
and a is the experimental slope of the calibration of the elution volume, V e,
against MW
V e =B–a ln MW (2)
(s d) 2 =ln(Mw/Mn). Mw/Mn is a measure of polydispersity of the sample. Since
experimentally s T has almost always been substituted for s d, SEC has rarely given
the true MW distribution, the deviation being larger the narrower the MWD
of the sample. This is especially the case for near-monomolecular dendrimers.
Methods have been described for obtaining the true MW distribution of narrow
MWD polymers by SEC [47]. Furthermore, when the calibration is performed
with a set of linear polymers, it can only be used directly with the same type of
linear polymers. When other polymers are analyzed, the principle of universal
calibration is invoked.
V e =B'–a' ln [h]M (3)
Analysis of polydispersity can still be made but only when the exponent in the
Mark-Houwink relation [h]=KM a is identical for the calibrating polymer and
the new polymer. As will be shown in the next section this is clearly not the case
for highly branched dendrimers. The validity of the universal calibration principle
for dendrimers has been questioned [48]. SEC analysis with multiple detectors,
especially with a low angle laser light scattering detector, obviously removes
many of these objections. The results of such experiments [48] will be described
in the next section. SEC does not have the capability for analyzing small
defects in a dendrimer sample. However, it is a quick method for quantifying the
monomer-dimer and higher multiple content.