Chemistry Reference
In-Depth Information
This changes dramatically when considering liquid liquid equilibria. Smaller
polymers are more soluble than longer ones (see, e.g., Fig.
8
). This also means that
the phase boundary of polymer systems is strongly influenced by the molecular
weight distribution of the polymer. Figure
14
shows the cloud-point curve of a
polydisperse LDPE (
M
n
= 43 kg/mol,
M
w
= 118 kg/mol,
M
z
= 231 kg/mol) in
ethene in comparison with PC-SAFT results obtained by monodisperse calculations
using either
M
n
,
M
w
,or
M
z
as the polymer molecular weight. Although PC-SAFT is
in general able to describe the phase behavior of that system (see Fig.
8
), none of the
calculations is able to describe the experimental data in Fig.
14
.
Obviously, the polydispersity of the polymer also needs to be considered in
the phase-equilibrium calculations. Assuming a system containing a solvent 1 and a
polydisperse polymer 2, the phase-equilibrium conditions have to be applied to the
solvent as well as to every polymer species. Equation (
21
) becomes:
x
I
1
'
I
1
x
I
1
'
II
1
¼
for the solvent
(27)
x
I
2
x
I
2
p;j
'
I
x
I
2
x
I
2
p;j
'
II
2
j
2
j
¼
for each polymer species
(28)
with
x
2
being the mole fraction of the polymer (
x
2
=
1
x
1
), and
x
2
p,j
meaning the
mole fraction of polymer species
j
within the solvent-free polymer. The latter have
to fulfill the normalization condition:
Fig. 14 Phase equilibrium in the system ethene/polyethylene (LDPE;
M
n
= 43,000 g/mol,
M
w
=
118,000 g/mol,
M
z
= 231,000 g/mol).
Symbols
represent experimental data [
55
].
Lines
show
calculations using the SAFT model.
Dashed lines
show monodisperse calculations using
M
n
,
M
w
, and
M
z
, respectively.
Solid line
shows a calculation using two pseudocomponents as given in
Table
4
