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# Polymer Chemistry. The Basic Concepts - Himenz P.C.

Himenz P.C. Polymer Chemistry. The Basic Concepts - Copyright, 1984. - 736 p.
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n-mer in phase P, for large values of n, will be maximized if the volume
of the P phase is kept to a minimum compared to phase Q. Stated simply,
the longer chains are concentrated in one of the phases, while the
shorter chains are relatively unaffected by the phase separation and
distribute themselves evenly and in proportion to the volume of the
phases. As a practical matter, then, keeping the volume of the dilute
phase as large as possible allows the optimum partitioning of the largest
molecules into the smaller but more discriminating concentrated phase.
The relative amounts of various n-mers in a fractionated sample is
examined numerically in the following example.
Example 8.4
Evaluate A in Eq. (8.64), assuming the polymer with n = 200 is divided
equally between the two phases and taking the ratio of phase volumes R to
be 10-1, 10~2, and 10"3. Use these A values to evaluate the relative
amounts of n-mer in the two phases for polymers with n = 100, 400, 600,
and 800. Comment on the significance of the numerical results.
Solution
The ratio of Eq. (8.66) to Eq. (8.67) gives the ratio of the
concentrations of n-mers in phases P and Q: fn p/fn Q = ReAn. Taking this
ratio to be unity for n = 200 gives ReA(20°) = 1, which is readily solved
for A using the R values given. Once these A values are obtained, fn p/fn
q can be evaluated for the required n values. For the phase volume ratios
under consideration, the corresponding values of A are listed below; also
tabulated are the ratios fn P/fn Q for the various n's:
R = Vp/Vq: 10"1 io-2 10~3
An=200' 1.15 X 10~2 2.30 X 10"2 3.45 X 10"2
100 0.32 0.099 0.032
400 9.95 99.0 985
600 99.9 9850 9.77 X 10s
800 990 9.80 X 10s 9.69 X 10(r)
Note that phase P is more concentrated in polymer, although smaller in
volume than phase Q. It is apparent from these values that the
combination of large n's
540
Thermodynamics of Polymer Solutions
and large differences in the volumes of the separated phases gives rise
to the most efficient segregation of polymer between phases. Also note
that the requirement that 200-mers be evenly distributed between the
phases creates the situation in which 100-mers are present in higher
proportion in the more dilute phase.

Figure 8.5 illustrates the sort of separation this approach predicts.
Curve A in Fig. 8.5 shows the weight fraction of various n-mers plotted
as a function of n. Comparison with Fig. 6.7 shows that the distribution
is typical of those obtained in random polymerization. Curve Â shows the
distribution of molecular weights in the more dilute phase-the coacervate
extract-calculated for the volumes of the two phases in the proportion
100:1. The distribution in the concentrated phase is shown as curve Ñ; it
is given by the difference between curves A and B.
In practice, such a fractionation experiment could be carried out by
either lowering the temperature or adding a poor solvent. In either case
good temperature control during the experiment is important. Note that
the addition of a poor solvent converts the system to one containing
three components, so it is apparent that the two-component Flory-Huggins
model is at best only qualitatively descriptive of the situation. A more
accurate description would require a
n
Figure 8.5 Theoretical plots of weight fraction n-mers versus n for
unfractionated polymer (A), the dilute phase (B), and the concentrated
phase (C) (drawn with R = 10~2). (Adapted from Ref. 1.)
Polymer Fractionation
541
triangular phase diagram. The onset of precipitation is marked by the
appearance of turbidity. In keeping with the principle outlined above,
only a small volume of the precipitated phase is allowed to form. Then
the sample is allowed to stand undisturbed until the two phases can be
physically separated. This step can require quite a long wait.
This procedure is then repeated by decreasing the solvent goodness
even further by another decrease in temperature or addition of
precipitant. In this manner a set of fractions such as those shown in
Fig. 8.6 are obtained from the initial distribution. In Fig. 8.6 curve A
again represents the initial distribution. Eight fractions are obtained
by precipitating successive portions of the polymer of progressively
lower molecular weights as shown, until the dilute phase contains only
the lowest molecular weight fraction as a residue. The curves in Fig. 8.6
are calculated for a phase volume ratio of 1000:1.
Figure 8.6 shows that the individual fractions still contain a
considerable range of chain lengths, with this effect becoming less
pronounced in the later cuts. In addition, there is a definite overlap
among the fractions. Nevertheless, the approach results in a sharpening
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