Influence of the Processes Parameters on the Properties of The ...

Chapter 2.
<strong>Processes</strong> to Manufacture Foams and to Functionalize <strong>the</strong> Surface
where X is given by:
X
*
v1
* * *
( P1
P2
2
12
)
(2.13)
RT
1
P
For a pure component, where = 1, <strong>the</strong> chemical potential can be reduced to:
P
1
R
P1
R
(1
R
) ln(1
R
) ln
R
r1
RT T1
R
T1
R
R
r1
(2.14)
Equations neglecting <strong>the</strong> solubility <strong>of</strong> polymer in CO 2 , have been solved for <strong>the</strong> chemical potential
<strong>of</strong> CO 2 in <strong>the</strong> fluid phase. As mentioned above, <strong>the</strong> values <strong>of</strong> three characteristic parameters for each pure
component and <strong>of</strong> one binary interaction parameter for polymer-CO 2 mixture are required in <strong>the</strong> SL model.
The pure component parameter values were all found in <strong>the</strong> literature, as reported in Table 2.3.
Table 2.3: SL-EOS characteristic parameters for CO 2 and PLGA 50:50 .
Component P * (bar) T * (K) ρ * (kg / m 3 ) Reference
CO 2 5745.0 305 1.510 [Kiszka et al., 1988]
PLGA 50:50 5727.4 649.63 1.4516 [Liu and Tomasko, 2007a]
Below <strong>the</strong> critical point, <strong>the</strong> behaviour predicted by SL equation <strong>of</strong> state is that typical <strong>of</strong> a cubic
equation <strong>of</strong> state: at a given pressure, up to three roots, those are density values, and can be found from
equation 2.4. The Mathcad program proposed by Kennedy [2003] has been used to solve <strong>the</strong> equation set
2.4−13 and it is presented in Annex A-1.1
4.2 Plasticization <strong>of</strong> Polymers by CO 2
With <strong>the</strong> exception <strong>of</strong> a few polymers, such as poly(dimethylsiloxane) and some specially
syn<strong>the</strong>sized fluoropolymers, most high molecular weight polymers show poor dissolution in supercritical
CO2 [Adamsky and Beckman, 1994; Desimone et al., 1992]. In those circumstances, carbon dioxide acts as a
diluent ra<strong>the</strong>r than a solvent. As <strong>the</strong> content <strong>of</strong> CO 2 is increased in <strong>the</strong> polymer phase, <strong>the</strong> sorption and
subsequent swelling <strong>of</strong> an amorphous polymer can cause <strong>the</strong> depression <strong>of</strong> glass-to-rubber transition
temperature (Tg) <strong>of</strong> a polymer by 30°C or more [Tomasko et al., 2003; Condo et al., 1992; Wissinger and
Paulaitis, 1987].
Gas foaming takes advantage <strong>of</strong> <strong>the</strong> plasticizing properties <strong>of</strong> carbon dioxide. It is qualitatively
known for many years that <strong>the</strong> compression <strong>of</strong> solid materials with gases alter <strong>the</strong> phase equilibrium <strong>of</strong> pure
component, in particular, <strong>the</strong> dissolution <strong>of</strong> carbon dioxide lowers <strong>the</strong> T g <strong>of</strong> amorphous polymers, and in
some cases, significantly. The reduction <strong>of</strong> glass transition temperature is a <strong>the</strong>rmodynamic effect due to
intermolecular interactions between carbon dioxide and <strong>the</strong> polymer. Stronger interactions enhance T g
depression, as does chain flexibility. The use <strong>of</strong> this technique is, however, limited to amorphous polymers
or semi-crystalline polymers with low T g .
It was assumed that polymer segments remain completely immobile below Tg, while small
plasticizers (e.g., gas molecules) are able to move and fill <strong>the</strong> holes within <strong>the</strong> polymer matrix. Tomasko et
al. [2003] have shown that if a polymer is exposed to a pressurized gas, <strong>the</strong> glass transition temperature <strong>of</strong>
this one decreases monotonically. This analysis is based on <strong>the</strong> assumption <strong>of</strong> Wissinger and Paulaitis [1991
and Dimarzio and Gibbs [1963] that <strong>the</strong> conformation entropy is zero.
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