Chemistry Reference
In-Depth Information
the equation. For
m
1
the second term vanishes. To obtain the material balances for the polymer, (
52
) and
(
53
), in terms of the normalized distribution function
W
(
r
,
y
), one divides these
relations by the total amount of segments in a plate at
i
¼
m
Max
and
i
>
0, the first term becomes unity and for
m
¼
¼
0. This leads to:
mþ
1
;i
1
þ
m
1
;i
¼
m;i
;
X
I
W
I
ef
X
II
W
II
e
X
F
W
F
e 1
ð
f
Þ
ð
r
;
y
Þ
ð
r
;
y
Þ
ð
r
;
y
Þ
(55)
where the special cases discussed in the context of (
52
) apply analogously, and to:
m;i
¼
m;i
þ
m;i
:
X
F
W
F
X
I
W
I
f
X
II
W
II
ð
r
;
y
Þ
ð
Þ
ð
r
;
y
Þ
ð
r
;
y
Þ
1
f
(56)
As described above, the stationary state is approached by the stepwise calculation
of the composition of the coexisting phase using the equation given in
Sect. 3.1
,where
the information concerning all previous states is required in the actual calculation.
3 Results and Discussion
The suggested fractionation theory is based on the LLE of a copolymer solution;
therefore, first the calculation procedure related to the LLE is discussed. Addition-
ally, the calculation results are compared with experimental LLE data for ethylene
vinyl acetate copolymer (EVA) in methyl acetate taken from literature [
90
].
Subsequently, the theory is applied to stepwise fractionation using the cross-
fractionation procedure. After some model calculations to study the influence of
different operative fractionation parameters on the fractionation efficiency, the
theoretical results will be again compared with experimental data for the styrene
butadiene copolymer system in two different solvent systems, namely cyclohexane +
isooctane and benzene + methyl ethyl ketone [
75
].
Finally, the theoretical framework is applied to the simulation of column frac-
tionation according two different methods (BW fractionation and CPF). In both
types of fractionation, the influence of operative conditions on the fractionation
effect with respect to the molecular weight and the chemical composition is
investigated. Because of the lack of experimental data, no comparison with experi-
ments was possible.
3.1 Liquid-Liquid Phase Equilibrium of Copolymer Solutions
The copolymer fractionation aims at the production of fractions having a distribu-
tion as narrow as possible. For this reason, this chapter focuses on the distributions
in the sol and gel phases. Before any calculations can be carried out, the model
parameters must be chosen. The model parameters can be divided into:
