Chemistry Reference
In-Depth Information
1
Introduction
Mutual solubility of polymers and volatile organic substances are of importance for
many applications in polymer chemistry and polymer engineering. Polymeriza-
tions, which should be performed in homogeneous phase, require the complete
miscibility of monomer, polymer, solvent (liquid or supercritical) and other addi-
tives. Subsequently, the extraction of the polymer product from the reaction
mixture requires a phase split (into two liquid phases or into a vapor and a liquid
phase) to obtain a polymer product of high purity on one side and the remaining
monomer on the other side. In this context, the devolatilization of polymers is of
particular interest. Another example is the use of polymer membranes for the
separation of two volatile organic compounds. Here, besides the knowledge of
diffusivity, the solubility (sorption) of the different components in the polymer
membrane is also an important prerequisite for an efficient process.
However, experimental data on polymer solubility are often scarce. Considerable
experimental effort is generally required for determining these properties of polymer
systems. Thermodynamics can provide powerful and robust tools for modeling of
experimental data and even for prediction of the thermodynamic behavior.
2 Equations of State
Equations of state are traditionally equations that give the pressure
p
as a function
of temperature, molar mixture volume, and composition
p
(
T
,
v
,
x
i
). A well-known
example is the van der Waals equation of state [
1
], which reads as:
RT
a
v
2
p
¼
b
(1)
v
This equation contains two parameters
a
and
b
that are related to the interaction
energy of the molecules and to the size of the molecules, respectively. Therefore,
they are called pure-component parameters and are usually determined by fitting to
experimental liquid-density and vapor-pressure data. Applying equations of states
to mixtures is, in most cases, done by applying a one-fluid theory. This means that
the parameters of a virtual “mixture molecule” are obtained by so-called mixing
rules from the model parameters of the pure components, e.g., by:
X
X
a
¼
x
i
x
j
a
i
a
j
ð
1
k
ij
Þ
i
j
X
(2)
b
¼
x
i
b
i
i
k
ij
in (
2
) is a binary parameter that corrects for deviations from the mixing rule of
the interaction energy parameter and needs to be fitted to binary data.
