Handbook of Solvents - George Wypych - ChemTech - Ventech!

122 Valery Yu. Senichev, Vasiliy V. Tereshatov
Figure 4.1.5. Volume of the increased swelling of crosslinked
polybutadiene urethane elastomer, χ H ≤ 085 . . Labels of points:
1-outside volume, points with coordinates corresponding to solvents; 2-inside
volume, points with coordinates corresponding to solvents; 3-the
points with coordinates corresponding to polymer. This is the center of the
volume. 4- points placed on a plane with coordinate δ =18 (MJ/m 3 ) 1/2 .
Number of solvent (not underlined number) corresponds to their position
in the Table 4.1.3. The underlined number corresponds to swelling ratio at
the equilibrium.
In accordance to the approach
of Blanks and
Prausnitz, the solubility area
is displayed as a plane with
two coordinates, λτ , . 8,9 The
parameters are related to
Hansen’s parameters by
2 2 ( )
λ= δ , τ= δ + δ
d p h
12 /
Solubility areas in this
approach are closed because
they are degenerated from
Hansen’s spheres (see below).
Another example of application
of degenerate
Hansen’s spheres was given
by Chen. 18 Instead of parameters
δ p, δ d the value χ H is used
which is calculated from the
difference of the polar and
dispersing contributions, δ p,
δ d. The zone of solubility is a
circle.
Lieberman 13 uses planes with coordinates δ, γ where γ is spectroscopic parameter (see
Section 4.1.3). These planes are open and have the areas of solubility, non-solubility and intermediate.
In Rider’s approach, the solubility area is a system of two quarters on a plane; two
other quarters are the areas of non-solubility (Figure 4.1.2). Coordinates of this plane are accepting
and donating abilities. Rider’s approach finds application for solvents with high
H-bond interactions.
Three-component systems. Crowley et. al. 2 proposed the three-dimensional solubility
volumes (Figure 4.1.3). Better known are Hansen’s three-dimensional solubility volumes
(Figure 4.1.4). In Hansen’s approach, the components of solubility parameters for
mixed solvents δ j are calculated from Eq. [4.1.56]:
=∑
δ δ ϕ
j ji i
i
[4.1.57]
The choice of a solvent for polymer is based on coordinates of polymer in space of coordinates
δ d, δ p, δ h and the radius of a solubility volume. For mixed solvents, their coordinates
can be derived by connecting coordinates of individual solvents. This can be used to
determine synergism in solvents for a particular polymer but it cannot demonstrate
antisynergism of solvent mixtures (a mixture is less compatible with polymer than the individual
solvents).