Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.1 Simple solvent characteristics 105
where:
* * *
ε = ε ε
[4.1.13]
12 11 22
∗
ειι potential energy of a pair of molecules
This assumption is not justified in the presence of the dipole-dipole interaction and
other more specific interactions. Therefore the theory of regular solutions poorly suits description
of the behavior of solutions of polar substances. Inherent in this analysis is the assumption
of molecular separation related to molecular diameters which neglects polar or
specific interactions. The theory also neglects volume changes on dissolution. This leads to
a disparity (sometimes very large) between internal energy of mixing used in the theory and
the constant pressure enthalpy measured experimentally.
The correlation between these values is given by equation:
m
m
m
( ΔH ) = ( ΔU ) + T( ∂p ∂T)
( ΔV
)
p
V
/ [4.1.14]
V
where:
( ∂p/ ∂T)
V thermal factor of pressure which has value of the order 10-14 atm/degree for solutions
and liquids.
Therefore, even at small changes of volume, the second term remains very large and
brings substantial contribution to the value of (ΔH m ) p. For example, for a system benzene
(0.5 mol) - cyclohexane (0.5 mol):
m
( ) ( )
m 3
m
ΔV= 0. 65 cm , ΔH= 182 cal, ΔU=
131 cal
p
The theory also assumes that the ideal entropy is possible for systems when ΔH m ≠0.
But the change of energy of interactions occurs in the course of dissolution that determines
the inevitable change of entropy of molecules. It is assumed that the interactive forces are
additive and that the interactions between a pair of molecules are not influenced by the presence
of other molecules. Certainly, such an assumption is simplistic, but at the same time it
has allowed us to estimate solubility parameters using group contributions or molar attractive
constants (see Subchapter 5.3).
The solubility parameter δ is relative to the cohesion energy and it is an effective characteristic
of intermolecular interactions. It varies from a magnitude of 12 (MJ/m 3 ) 1/2 for
nonpolar substances up to 23 (MJ/m 3 ) 1/2 for water. Knowing δ of solvent and solute, we can
estimate solvents in which particular polymer cannot be dissolved. For example,
polyisobutylene for which δis in the range from 14 to 16 (MJ/m 3 ) 1/2 will not be dissolved in
solvents with δ=20-24 (MJ/m 3 ) 1/2 . The polar polymer with δ=18 (MJ/m 3 ) 1/2 will not dissolve
in solvents with δ=14 or δ=26 (MJ/m 3 ) 1/2 . These are important data because they help to narrow
down a group of solvents potentially suitable for a given polymer. However, the opposite
evaluation is not always valid because polymers and solvents with the identical
solubility parameters are not always compatible. This limitation comes from integral character
of the solubility parameter. The solubility depends on the presence of functional
groups in molecules of solution components which are capable to interact with each other
and this model does not address such interactions. The latter statement has become a premise
for the development of the multi-dimensional approaches to solubility that will be the
p
V