Chemistry Reference
In-Depth Information
These relations provide the unknown distribution functions
W
i
ð
r
;
y
Þ
and
W
II
i
directly.
Figure
3
presents the schemes for successive precipitation fractionation (SPF)
and successive solution fractionation (SSF). In both cases, by lowering the temper-
ature (or adding nonsolvent) a homogeneous polymer solution (called feed phase F)
splits into two coexisting phases, a polymer-lean sol phase I and a polymer-rich gel
phase II, which are then separated. In SPF (Fig.
3a
), the polymer is isolated from
phase II as fraction F1. Phase I directly forms the feed phase for the next fraction-
ation step, etc.
In case of SSF (Fig.
3b
), fraction F1 is obtained from phase I. Phase II is diluted
by adding solvent up to the volume of the original feed phase, corresponding, to a
very good approximation, to the same total amount of segments. This phase is used
as a feed phase for step 2, etc. In the last fractionation step, the polymer of phase I in
the case of SPF, or of phase II in the case of SSF, forms the final polymer fraction.
All coexisting pairs of phase I and II are presumed to be in equilibrium. Hence, it is
possible to apply all equations introduced above. To indicate the different separa-
tion steps 1,2,
ð
r
;
y
Þ
, the corresponding number is added as a subscript.
According to the remarks made above, the total number of segments in SSF
(Fig.
3b
) is the same to a very good approximation in all feed phases. This leads to
the following relations:
...
X
iþ
1
W
iþ
1
ð
f
i
X
I
i
W
II
r
N
;iþ
1
¼
r
I
N
;i
y
F
W
;iþ
1
¼
y
I
W
;i
:
r
;
y
Þ¼
ð
r
;
y
Þ
(32)
i
a
step 1
solvent
step 2
F1
F2
b
step 1
solvent
F1
Fig. 3 Schemes of successive
fractionation procedures: (a)
successive precipitation
fractionation (SPF), (b)
successive solution
fractionation (SSF).
F1
and
F2
are successive fractions
step 2
solvent
F2
