Chemistry Reference
In-Depth Information
M
d
is the molar mass of the (diluent) gas;
R
is the gas constant;
w
the mass fraction
of the gas in the polymer;
C
p
is the heat capacity change associated with the glass
transition of the pure polymer; and
z
is the lattice coordination number. All
parameters of the model have physical meanings, except the number
z
. The value
of this parameter changes according to the state of the diluent:
z
D
¼
2 when the
diluent is in the liquid state and
z
1 when it is gas.
In order to compare the model calculations with experimental calorimetric data,
PS samples were modified in a transitiometer used, in this case, as a small reactor to
modify PS under equilibrium conditions in the presence of a chosen fluid. Mod-
ifications of PS have been done in the presence of N
2
and CO
2
, along isotherms at a
given pressure. For these two fluids, a final temperature of 398.15 K and a final
pressure of 80 MPa have been attained. The
T
g
of modified and nonmodified PS
samples were determined by temperature-modulated DSC (TMDSC). The solubi-
lities of the different gases were measured using the VW
pVT
sorption technique
[
48
,
49
] along different isotherms, and the mass fraction of the gas in the polymer
was then determined with the following equation:
¼
s
w
¼
1
;
(16)
s
þ
where
s
is the solubility of the fluid in the polymer, in milligrams of fluid per
milligram of polymer.
Using the values of
w
determined for each gas PS system, the Chow equation
(
15
) allows estimation of the variation,
T
g
, of the temperature of the glass transition
with pressure, along the different isotherms of the sorption measurements.
The use of the Chow model is delicate because the choice of the value of
z
, i.e.,
the state of the diluent, significantly influences the results. The
T
g
shift under CO
2
pressures is spectacular, showing the high plasticizing effect of CO
2
. The good
agreement of the literature data for the {CO
2
PS} system with the calculated values
[
78 80
] (as seen in Fig.
23
) can certainly be explained by the state of the diluent,
which is most probably in the critical state in the ranges of
T
and
p
considered.
Effectively, the critical temperature
T
c
and critical pressure
p
c
of CO
2
support the
hypothesis of the gas being in the near-critical region. Depending on the experi-
mental conditions in the vicinity of the critical point, the fluid can exist in one or the
other state (gas or liquid), or even in both. In the present case, literature data for the
{CO
2
PS} system have been obtained under a pressure
p
D
p
c
and at a temperature
T
T
c
for CO
2
; then two phases of the diluent can coexist in different proportions.
Despite the difficulty in determining exactly the variation of
T
g
, particularly under
supercritical conditions of a diluent fluid, the model of Chow is a useful guide for
prediction of the variation of the glass transition of a polymer modified by a high
pressure fluid. However, the exact determination of the glass transition depression,
D
T
g
, becomes more difficult when the pressure increases, especially near and above
the critical point of the diluent fluid. This means that when plotting
D
T
g
as a
