Chemistry Reference
In-Depth Information
One phase
miscible
Spinodal curve
UCST
Binodal curve
T
1
Two phases
Metastable
Unstable
*
*
2
A
2
A
2
B
2
B
φ
φ
φ
φ
Volume fraction polymer
FIGURE 5.3
Schematic representation of spinodal and binodal curves.
able to predict the upper critical solution temperature (UCST) phase behavior is
that
χ
decreases with increasing temperature (
Eq. 5-20
). Using a UCST mixture as
an example,
Fig. 5.3
shows that within the immiscible region, there exist
unstable and metastable regions. They are bounded by the spinodal and binodal
curves that meet at the critical temperature. At the critical temperature, the partial
second and third derivatives of the chemical potentials of the components are zero.
This leads to the following equation for the determination of critical
χ
.
2
1
2
1
1
r
2
χ
critical
5
r
p
1
p
(5-30)
For a mixture that contains two types of small molecules with comparable
sizes, r
1
5
r
2
5
2 (regular solution theory). For a mixture that contains
a solvent and a polymer, r
1
5
1,
χ
critical
5
1 and r
2
tends to be large,
χ
critical
5
0.5. When both
components in a mixture are polymers,
χ
critical
5
0. Here, mixtures that exhibit
χ
values above
χ
critical
would phase separate.
EXAMPLE 5-1
A blend consists of 40 vol% PE and 60 vol% PS. The degrees of polymerization, based on
the molar volume of ethylene, are 1000. At 300 K, the molar volumes of the repeating units
of PE and PS are 32.74 cm
3
/mol and 84.16 cm
3
/mol, respectively. From small angle reac-
tion scattering experiments, χ was measured to be 0.10 at 300 K.
