Chemistry Reference
In-Depth Information
distributions will overlap. Various mathematical techniques have been used to
allow for such overlapping in the reconstruction of the molecular weight distribu-
tion of the parent polymer from the average molecular weights measured with
fractions.
Although refractionation may narrow the molecular weight distributions of
“primary” fractions, such operations are subject to a law of diminishing returns
because of the complications of
Eq. (5-32)
that have just been mentioned.
If the volumes of the polymer-rich and solvent-rich phases are V
0
and V,
respectively, then the fraction f
i
of i-mer that remains in the solvent-rich phases is
given by
φ
i
V
1
f
i
5
(5-33)
1
φ
i
V
0
5
Re
σ
i
φ
i
V
1
1
V
0
/V. Similarly, the fraction of i-mer in the polymer-rich phase is
f
i
5
where R
5
Re
σ
i
Re
σ
i
=ð
1
Þ
(5-34)
1
and
f
i
5
Re
σ
i
f
i
=
1
=
(5-35)
If the volume of the solvent-rich phase is much greater than that of the
polymer-rich phase (R
1), then most of the smaller macromolecules will remain
in the former phase (
Eq. 5-35
). Also, as i increases, the proportion of i-mer in the
polymer-rich phase will increase.
Dilute solutions are needed for efficient fractionation. When fractionation is
effected by gradual precipitation of polymer from solution, good practice requires
that the initial polymer concentration decrease with increasing molecular weight
of the whole polymer. A 10-g sample of a low-molecular-weight polymer should
be dissolved in about 1 liter of solvent while a high-molecular-weight polymer
might easily require 10 liters.
Temperature rising elution fractionation (TREF) is a useful technique for char-
acterizing the distribution of branches and other uncrystallizable entities in semi-
crystalline polymers. Recall that regularity of polymer structure is necessary for
crystallizability (Section 1.11.2) and branches and comonomer residues cannot
usually fit into crystal lattices. This method is particularly valuable with polyole-
fins like polyethylene, whose properties are affected by the distributions of both
molecular weight and branching
[17]
. The procedure involves dissolution of the
sample in a solvent, followed by slow cooling to deposit successive layers of less
and less crystallizable species onto an inert substrate, like silanized silica. The
material here consists of onion-skin layers of polymer, with the least regular (i.e.,
most branched) species on the outside. The foregoing procedure is then reversed,
as the precipitated polymer is eluted by flowing solvent at progressively increas-
ing temperatures. The concentration of eluting dissolved polymer and the corre-
sponding branch concentration can be monitored by infra-red detection at
different wavelengths
[18]
.
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