Chemistry Reference
In-Depth Information
There exist other examples for inversions in the heats of dilution; in these cases
an analogous straightforward molecular interpretation appears difficult. For
instance, the system TL/PS shows an inversion [
44
] from endothermal in the
range of moderate polymer concentrations to exothermal at high
values at
37
C. In this case, the sign of the heat contributions of the two steps of dilution
are the same as in the previous case. However, here it is only w
H,cr
which increases
(linearly) with rising polymer concentration, whereas w
H,fc
decreases (more than
linearly). This combination of the two contributions leads to the opposite inversion,
namely from endothermal to exothermal upon an augmentation of
'
. Concerning
the molecular reasons for this behavior, one may speculate on the basis of the
present findings that the insertion of a TL molecule between two contacting PS
segments (belonging to different molecules) becomes energetically particularly
favorable in the limit of high polymer concentration.
So far, we have dealt exclusively with homogeneous systems; the following
considerations concern the possibilities of obtaining the parameters of the present
expression for w(
'
, T) from demixing data. The results will demonstrate that the
present approach is capable of modeling liquid/liquid equilibria and liquid/gas
equilibria with the same set of parameters, in contrast to traditional theories.
The first example refers to solutions of PS in CH. This is probably the system for
which the phase separation phenomena are studied in greatest detail [
45
], namely in
the temperature range from ca. 10 to 240
C and for molar masses from 37 to 2700
kg/mol. Figure
9
displays the experimental data [
45
] together with the modeling,
using (
32
) to describe the Flory Huggins interaction parameter as a function of
composition.
The system-specific parameters used for the modeling of the phase diagrams
were calculated from the critical data (T
c
and
'
'
c
) measured [
45
] for PS samples of
different molar mass. For this purpose, the critical conditions resulting for the
present approach [cf. (
36
) and (
37
)] were first simplified: The parameter l was
set at 0.5 (this does not imply a loss of accuracy for the system of interest) and the
interrelation between a and zl [cf. (
34
)] was used to eliminate the parameter a;
setting
E
0.847 (an average value for solutions of vinyl polymers in organic
solvents). This procedure reduces the number of parameters from four to only two
(z and n) and enables the calculation of their values from the critical temperature by
inserting the known numbers of segments
N
and the critical composition
¼
'
c
in the
two critical conditions and solving these equations. Because of the large number of
different molar masses, yielding different critical data, it is possible to model the
temperature dependencies of the parameters z and n. The observed maximum in z(T)
is expected because of the transition from an upper critical solution temperature
(UCST) behavior at low temperatures to a lower critical solution temperature
(LCST) behavior at high temperatures, in combination with the fact that z =0at
the theta temperature, irrespective of the sign of the heat of mixing; n(
T
) also passes a
maximum but at a much lower temperature (in the vicinity of the endothermal theta
temperature). Within the range of LCSTs, both parameters decrease with rising
temperature. The binodal and spinodal curves shown in Fig.
9
for the different PS
samples were calculated from the thus-obtained system-specific parameters using
