Handbook of Size Exclusion Chromatography and Related ...

concentration at each elution volume fraction, and second is the effect of the
copolymer dn=dc on the light-scattering signal. If the composition is
heterogeneous, an apparent weight-average molecular weight M w is measured,
which depends on the solvent refractive index n0. To determine the true molecular
weight, the light-scattering intensity must be measured in at least three solvents
with different refractive indices (2,156). This can be understood from Eq. (7),
which shows that the scattered intensity depends on (dn=dc) 2 , for two components
this is the sum of the respective dn=dc values squared. The measured dn=dc,
however, is merely a straight summation. In an extreme case, the solvent refractive
index may lie between the refractive indices of the two components and the dn=dc
could be zero. However, such a copolymer would still scatter light and M w would
be infinite. If the composition distribution is homogeneous, as in a random
copolymer, or if the refractive indices of the two components are equal, then M w is
equal to Mw. When these conditions are obtained, SEC-LS can be applied
successfully to copolymers.
Grubisic-Gallot et al. (66) studied block copolymers of ethyl methacrylate
and deuterated methyl methacrylate by SEC-LALLS. The dn=dc values in
tetrahydrofuran were nearly equal, 0.084 and 0.079 mL/g, respectively. They
found good agreement between the measured molecular weight and the theoretical
value obtained using the molecular weights of the blocks. Malihi et al. (123) used
static measurements of a styrene–butylacrylate emulsion copolymer in a series of
solvents with different refractive indices to obtain the correct Mw and also to find
the best solvent for SEC-LS. The best solvent is that in which M w is closest to Mw
as determined from the multiple solvent measurements, that is, when the
component dn=dc values are relatively closest. They found good agreement
between SEC-LS results and static measurements.
Dumelow (121) used SEC-LALLS with dual concentration detectors to
study the variation in compositional heterogeneity with molecular weight in
polystyrene–polydimethylsiloxane block copolymers. The results showed that
some of the copolymers were in fact blends. The largest errors in the analysis were
found to arise if it were assumed that there was no molecular weight distribution at
each elution slice. By avoiding this assumption the results were improved.
The relationship between the radius of gyration and the lightscattering
asymmetry is also dependent on copolymer composition and is not the
same as for homopolymers. Unless dn=dc is equal for both components, the
spatial distribution of the component that scatters the most dominates the angular
distribution of scattered light and thus the measured radius of gyration (156).
4.2.3 Branching
Light scattering has been widely used to study branching. The molecular weight
of the branched polymer Mb is measured for each elusion slice, and the
© 2004 by Marcel Dekker, Inc.