Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.1 Simple solvent characteristics 113
E E E d p E h
= + + [4.1.22]
V V V V
or
1 1 1 1
δ = δ + δ + δ
2 2 2 2
d p h [4.1.23]
where:
δ total solubility parameter
δd, δp, δh components of the solubility parameter determined by the corresponding contributions to
the cohesive energy.
Hansen gave a visual interpretation of his method by means of three-dimensional
spheres of solubility, where the center of the sphere has coordinates corresponding to the
values of components of solubility parameter of polymer. The sphere can be coupled with a
radius to characterize a polymer. All good solvents for particular polymer (each solvent has
been represented as a point in a three-dimensional space with coordinates) should be inside
the sphere, whereas all non-solvents should be outside the solubility sphere. An example is
given in Section 4.1.7.
In the original work these parameters were evaluated by experimental observations of
solubility. It was assumed that if each of the solubility parameter components of one liquid
is close to the corresponding values of another liquid, then the process of their mixing
should readily occur with a more negative free energy. The solubility volume has dimensions
δd, δp,2δh. The factor 2 was proposed to account for the spherical form of solubility
volumes and had no physical sense. However, it is necessary to notice that, for example, Lee
and Lee 31 have evaluated spherical solubility volume of polyimide with good results without
using the factor 2. Because of its simplicity, the method has become very popular.
Using the Hansen approach, the solubility of any polymer in solvents (with known
Hansen’s parameters of polymer and solvents) can be predicted. The determination of polymer
parameters requires evaluation of solubility in a great number of solvents with known
values of Hansen parameters. Arbitrary criteria of determination are used because Hansen
made no attempts of precise calculations of thermodynamic parameters.
The separation of the cohesion energy into contributions of various forces implies that
it is possible to substitute energy for parameter and sum contributions proportional to the
second power of a difference of corresponding components. Hansen’s treatment permits
evaluation of the dispersion and polar contribution to cohesive energy. The fitting parameter
of the approach (the solubility sphere radius) reflects on the supermolecular structure of
polymer-solvent system. Its values should be higher for amorphous polymers and lower for
glass or crystalline polymers.
The weak point of the approach is the incorrect assignment of the hydrogen bond contribution
in the energy exchange that does not permit its use for polymers forming strong
hydrogen bonds.
Table 4.1.2. Solubility parameters and their components for solvents (after refs 37,40)
Polymer
δ,
(MJ/m 3 ) 1/2
δd,
(MJ/m 3 ) 1/2
δp,
(MJ/m 3 ) 1/2
δh,
(MJ/m 3 ) 1/2
Polyamide-66 22.77 18.5 5.1 12.2