
shown in Eq. (18.1), where the mass fraction of sorbed SCF
(w
SCF
) is proportional to the partial pressure of the SCF,
P
SCF
.
w
SCF
¼ k
H
P
SCF
: (18:1)
The Henry’s law constant, k
H
, is independent of molecular
weight except at extremely low molecular weight (< 1kDa),
but is often a strong function of temperature, typically
showing an Arrhenius-like dependence. The slope of the
Arrhenius plot can be correlated with the enthalpy of dis-
solution of the SCF in the polymer [78]. An alternate cor-
relation based on corresponding states suggests that k
H
should scale with (T
c
=T)
2
, rather than with 1/T [79]. How-
ever, the proportionality constant for (T
c
=T)
2
scaling is not
a universal constant. Over the temperature range common
for SCF-polymer mixtures, little difference is detectable
between 1/T scaling and 1=T
2
scaling, so data are presented
here with the 1/T scaling. The solubility of the SCF in the
polymer may either increase with temperature (for polymer-
SCF pairs exhibiting UCST phase behavior), or solubility
may decrease with increasing temperature (for polymer-SCF
pairs exhibiting LCST phase behavior.) Hence, the Arrhe-
nius coefficient for k
H
may be either positive or negative.
Table 18.3 lists Henry’s law constants for rubbery and
molten polymers. The temperature dependence of the
Henry’s law constants are correlated with absolute tempera-
ture via the Arrhenius expression:
ln (k
H
) ¼
A
T
þ B, (18:2)
where k
H
(from Eq. (18.1)) has units of mass fraction per
MPa, and T has units of degrees Kelvin.
Care should always be exercised when using solubility
data for glassy or crystalline polymers (not included
here), because SCF sorption occurs preferentially in the
amorphous phase, which may additionally experience
swelling-related stress. Solubility data for CO
2
in solid
polymers is compiled in [5]. Often, the pressure dependence
of SCF sorption in glassy polymers follows a dual-mode
sorption model, with substantial deviations from Henry’s
law.
Solubility of SCFs in polymers is determined experimen-
tally by one of several general techniques. Gravimetric
techniques monitor the in situ weight gain of a polymer
sample exposed to a surrounding high pressure SCF. These
techniques require the application of a buoyancy correction
term to the raw data, since the polymer swells upon expos-
ure to the SCF. The swollen volume may be measured
experimentally, or it may be estimated using an equation
of state, typically the Sanchez–Lacombe model. Another
experimental technique measures mass gain of a polymer
exposed to an SCF by monitoring the change in resonant
frequency of an oscillating sensor, typically a quartz crystal.
The amount of SCF sorbed in a polymer may also be
determined by recording the pressure decay in a reservoir
of SCF in contact with the polymer.
18.3 MELTING POINT DEPRESSIONS
OF POLYMERS IN THE PRESENCE OF SCFS
The melting temperature (T
m
) of a semicrystalline poly-
mer is usually lower in the presence of a soluble SCF than it
is in the pure polymer at ambient pressure. When a polymer
crystallizes from an SCF-saturated solution, the resulting
three-phase (S–L–G), two-component equilibrium is univar-
iant, according to the phase rule, so T
m
is only a function of
pressure under these conditions. Experimental measure-
ments of the polymer melting point in the presence of an
excess of CO
2
typically exhibit the pressure dependence
shown in Fig. 18.3. The melting temperature decreases
approximately linearly with increasing pressure above am-
bient conditions, then it abruptly levels off to a near constant
value. Occasionally, some deviations from this behavior are
seen: (1) a small (1–28C) increase is T
m
is sometimes
recorded at low pressure, before the linearly decreasing
region occurs. This is attributed to annealing of small crys-
tallites; (2) at very high pressure, following the plateau zone,
T
m
sometimes begins to increase with increasing pressure;
and (3) the plateau zone where T
m
is constant is sometimes
missing, so that a region of linearly decreasing T
m
is fol-
lowed immediately by a region of linearly increasing T
m
.
The qualitative features of the SCF-saturated melting point
curves are similar for polymers and for sparingly soluble
low molecular weight crystalline compounds such as naph-
thalene and biphenyl [100].
The melting point of a polymer saturated with an SCF is
determined experimentally either visually, or else by high
pressure calorimetry, although the pressure range for the
latter is often limited by instrument constraints to a few
MPa. Table 18.4 presents values of dT
m
=dP in the linear
region (low pressure) for polymers saturated with an SCF. In
cases where an increase in T
m
occurred at very low pressure,
as in Fig. 18.3, the lowest pressure points were not included
in the linear least squares line fitting. When the experimen-
tal pressures were high enough so that the second (plateau)
region could be seen, this has been noted in the Comments.
18.4 SCF-INDUCED T
g
DEPRESSION
Sorption of an SCF in a polymer can lower its glass
transition temperature (T
g
) significantly below that seen at
atmospheric pressure. For a given polymer, the glass transi-
tion temperature depression is found to increase as the
amount of SCF sorbed increases [105]. Because CO
2
solu-
bility usually decreases with increasing temperature, it is
possible for a polymer/CO
2
mixture at elevated pressure to
undergo a liquid-to-glass transition as the temperature is
raised. This phenomenon, referred to as ‘‘retrograde vitrifi-
cation’’ [18], has been observed for poly(methyl methacry-
late) [105,106]. Table 18.5 reports the pressure dependence
of T
g
observed for polymers which have been exposed to
a high pressure SCF. T
g
depression curves look similar to
POLYMERS AND SUPERCRITICAL FLUIDS / 327