Environmental Engineering Reference
In-Depth Information
v
ij
is the partial molar volume. While this approximation is valid for non-polar
components, it has been used in polar systems with reasonable success (Blanks and
Prausnitz
1964
; Mayoral and Gama-Goicochea
2013
). From Eqs. (
25
) and (
27
)we
have
where
RT
ʴ
i
(
)
2
27
v
ij
a
ij
(
T
)
=
a
ii
(
T
)
+
3
.
T
)
−
ʴ
j
(
T
.
(28)
The determination of solubility parameters is a difficult and laborious undertaking,
but correlations with other physical properties of the substance in question help. For
example, writing
2
2
2
2
ʴ
=
ʴ
d
+
ʴ
p
+
ʴ
h
,
(29)
2
d
2
p
where
ʴ
denotes the
dispersion
component of the total solubility parameter,
ʴ
2
its
polar
component, and
ʴ
h
its contribution from
hydrogen bonding
. The dispersion
component
ʴ
d
may be very well approximated by using the total solubility parameter
of a
homomorphic
molecule, i.e., a non-polar molecule most closely resembling the
molecule in question both in size and structure (
n
-butane is homomorphic to
n
-butyl
alcohol, for example). This is because the solubility parameter of the homomorphic
molecule is due entirely to dispersion forces. One still needs to determine either
ʴ
p
or
ʴ
h
(the other one is obtained by subtraction from the total solubility parameter
ʴ
using
Eq. (
29
), when known), and this is done through trial and error experimentation on
numerous solvents and polymers and by comparing similar and dissimilar structures
according to functional groups and molecular weights.
The total solubility parameter may be calculated from the cohesive energy
E
coh
or, equivalently, from the enthalpy of vaporisation
H
v
ap
H
v
ap
ʔ
E
coh
V
A
ʔ
−
RT
ʴ
A
=
=
,
(30)
V
A
by using atomistic dynamic simulations. To do this, periodic cells of amorphous fluid
structures may be constructed using regular available software such as the
Amorphous
Cell
program of
Materials Studio
. The dimension of the box is specified (e.g., 25 Å
on each side). Interatomic force-field interactions are set as initial conditions, and
the system is evolved according to Eq. (
1
).
The solubility parameter of a mixture of liquids is determined by calculating the
volume-wise contributions of the solubility parameters of the individual components
of the mixture, i.e., the parameter for each liquid is multiplied by the fraction that
the liquid occupies in the blend, and the results for each component added together.
In these multicomponent systems the
ˇ
-parameters are calculated by pairs. If, for
instance, we have a 3-component mixture of water
w
(or other solvent), electrolyte
e
, and an organic compound
o
,wehave
v
e
RT
]
2
ˇ
e
w
=
[
ʴ
e
(
T
)
−
ʴ
w
(
T
)
,
(31)
Search WWH ::
Custom Search