Chemistry Reference
In-Depth Information
then, miscibility is predicted if the absolute value of the (
δ
1
2
δ
2
) difference is
zero or small.
The convenience of the solubility parameter approach lies in the feasibility of
assigning
δ
values a priori
to individual components of the mixture. This is
accomplished as follows.
Operationally, the cohesion of a volatile liquid can be estimated from the
work required to vaporize a unit amount of the material. In this process the mole-
cules are transported from their equilibrium distances in the liquid to an infinite
separation in the vapor. The cohesive energy density (sum of the intermolecular
energies per unit volume) is at its equilibrium value in the liquid state and is zero
in the vapor. By this reasoning, the cohesive energy density in the liquid state is
Δ
U
v
/V
0
, in which
U
v
is the molar energy of vaporization and V
0
Δ
is the molar
volume of the liquid.
From inspection of
Eq. (5-8)
, it is clear that the solubility parameter
δ
is the
square root of the cohesive energy density. That is,
V
0
1
=
2
δ
5
ðΔ
U
v
=
Þ
(5-11)
If the vapor behaves approximately like an ideal gas
2
V
0
δ
5
ðΔ
H
v
2
RT
Þ=
5
ðΔ
H
v
2
RT
Þρ=
M
(5-12)
where
ρ
is the density of liquid with molecular weight M. Thus the heat of vapori-
zation
.
Cohesive energy densities and solubility parameters of low-molecular-weight
species can be determined in a straightforward manner by direct measurement of
Δ
Δ
H
v
can serve as an experimental measure of
δ
H
v
or by various computational methods that are based on other thermodynamic
properties of the substance. A polymer is ordinarily not vaporizable, however,
and its
is therefore assessed by equating it to the solubility parameter of a sol-
vent in which the polymer dissolves readily. If dissolution occurs, it is assumed
that
δ
Δ
δ
1
5
δ
2
(
Eq. 5-10
). Experimentally,
δ
is usually taken as equal
to that of a solvent that will produce the greatest swelling of a lightly cross-linked
version of the polymer or the highest intrinsic viscosity of a soluble polymer sam-
ple. These two experimental methods may, however, give somewhat different
results for the same polymer, depending on the polarity and hydrogen-bonding
character of the solvent. Such solvent effects are mentioned in more detail in
Section 5.2.3
.
A more convenient procedure relies on calculations of
H
m
5
0 and
values rather than
experimental assessments. Solubility parameters of solvents can be correlated
with the structure, molecular weight, and density of the solvent molecule
[3]
. The
same procedure is applied to polymers, where
δ
X
F
i
=
M
0
δ
5
ρ
(5-13)
is the density of the amorphous polymer at the solution tem-
perature, M
0
is the formula weight of the repeating unit, and
In
Eq. (5-13)
,
ρ
Σ
F
i
is the sum of all
