Handbook of Size Exclusion Chromatography and Related ...

possibly with hydrodynamic volume (8). In this work, we shall limit our discussion
to copolymers containing only two repeating units types.
From the point of view of the SEC analysis, block copolymers are simpler
than statistical copolymers. This is because important properties such as the
specific refractive index increment or the hydrodynamic volume may be estimated
by simply averaging the corresponding homopolymer properties (6). Also, linear
copolymers are simpler than branched copolymers from the point of view of their
MWD determination. A long-branched copolymer of a given molar mass and
composition exhibits a smaller hydrodynamic volume than its linear homolog, and
the volume reduction is more pronounced with an increasing branching
functionality (9,10).
The molecular macrostructure of a linear copolymer is totally determined by
the bivariate distribution of molar masses and chemical composition (2–6). The
univariate distributions of molar masses and chemical composition are obtained by
appropriate integration of such bivariate distribution. A branched copolymer
molecule is characterized by the number of branches and their functionality (9–12).
In this work, we shall restrict our discussion to long-branched copolymers of
functionality 3. The branching distribution (BD) is represented by the mass of
molecules containing 1, 2,... branches/molecule vs. the number of branches
(11,12). The complete molecular macrostructure of a trifunctionally branched
copolymer is represented by a set of bivariate distributions of molecular weights and
chemical composition, with one bivariate distribution for each branched topology.
Presently, it is impossible to measure such detailed molecular macrostructure.
SEC is the main analytical technique for measuring the MWD of a polymer.
For copolymers, several problems complicate this determination (13–15).
Consider first the instantaneous mass. With homopolymers, the instantaneous
mass is proportional to the differential refractometer (DR) signal, except perhaps
for molar masses lower than 10,000g/mol, where the specific refractive index
increment shows a dependence on the molar mass (15,16). With copolymers, the
specific refractive index increment depends on the instantaneous composition, and
this last variable may change with hydrodynamic volume. Thus, the copolymer
mass cannot be determined from the DR signal alone (6,15). Errors in the
instantaneous mass affect not only the MWD ordinates. More importantly, it
affects derived variables that are obtained from a signals ratio where the
instantaneous mass is in the denominator. This is the case for the molar mass
(when determined through an in-line detector) and for the chemical composition
(when determined through a detector that responds to a single repeating unit type).
The difficulties with the DR spurred the development of other more “universal”
mass detectors such as the evaporative-light scattering detector or the on-line
densimeter. Evaporative detectors present some fundamental difficulties for
quantifying the instantaneous mass, but enable their interface with Fourier
Transform Infrared (FTIR) detectors. This allows the determination of the
© 2004 by Marcel Dekker, Inc.