Chemistry Reference
In-Depth Information
homogeneous polymer specimen into components (called “fractions”) which dif-
fer in molecular size and have narrower molecular-weight distributions than the
parent material. Ideally, each fraction would be monodisperse in molecular weight
but such a separation has not been approached in practice and the various frac-
tions that are collected always overlap to some extent.
It should be noted that all the fractionation process does is provide narrower
molecular weight distribution materials. The molecular weight distribution of the
original material cannot be reconstructed until the average molecular weight of
each fraction is obtained by other independent measurements.
Fractionation depends on the differential solubility of macromolecules with
different sizes. It has been displaced in many cases by size exclusion chromatog-
raphy as a means for measuring molecular weight distributions, but it is still often
the only practical way of obtaining narrow fractions in sufficient quantities for
the study of physical properties of well-characterized specimens. It is also part
of the original procedure for the calibration of solution viscosity measurements
for the estimation of molecular weights.
The Flory
Huggins theory leads to some useful rules for fractionation opera-
tions. Only the results will be summarized here. Details of the theory and experi-
mental methods are available in Refs.
[15
,
16]
and other sources.
Consider a polymeric species with degree of polymerization i in solution. The
homogeneous solution can be caused to separate into two phases by decreasing
the affinity of the solvent for the polymer by lowering the temperature or adding
some poorer solvent, for example. If this is done carefully, a small quantity of
polymer-rich phase will separate and will be in equilibrium with a larger volume
of a solvent-rich phase. The chemical potential of the i-mer will be the same in
both phases at equilibrium, and the relevant Flory
Huggins expression is
ðφ
i
=φ
i
Þ
5
σ
i
ln
(5-32)
φ
i
and
where
φ
i
are the volume fraction of polymer of degree of polymerization i
in the polymer-rich and solvent-rich phases, respectively. Sigma (
σ
) is a function
of the volume fractions mentioned and the number average molecular weights of
all the polymers in each phase, as well as the dimensionless parameter
(
Eq. 5-
23
). Sigma cannot be calculated exactly, but it can be shown to be always posi-
tive
[15]
. It follows then from
Eq. (5-32)
that
χ
φ
i
.
φ
i
, regardless of i. This means
that all polymer species tend to concentrate preferentially in the polymer-rich
phase. However, since
φ
i
=φ
i
increases exponentially with i, the latter phase will
be relatively richer in the larger than in the smaller macromolecules.
Fractionation involves the adjustment of the solution conditions so that two
liquid phases are in equilibrium, removal of one phase and then adjusting solution
conditions to obtain a second separated phase, and so on. Polymer is removed
from each separated phase and its average molecular weight is determined by
some direct measurement such as osmometry or light scattering.
It is evident that both phases will contain polymer molecules of all sizes. The
successive
fractions will differ
in average molecular weights but
their
