Chemistry Reference
In-Depth Information
is not possible to characterize individual components a priori. The solubility
parameter scheme is therefore the model that is most often applied in practice.
Numerous attempts have been made to improve the predictive ability of the
solubility parameter method without making its use very much more cumbersome.
These generally proceed on the recognition that intermolecular forces can involve
dispersion, dipole
dipole, dipole-induced dipole, or acid
base interactions, and a
simple
value is too crude an overall measurement of these specific interactions.
The most comprehensive approach has been that of Hansen
[10,11]
, in which
the cohesive energy
δ
2
is divided into three parts:
δ
2
2
d
2
p
2
H
δ
5
δ
1
δ
1
δ
(5-31)
where the subscripts d, p, and H refer, respectively, to the contributions due to dis-
persion forces, polar forces, and hydrogen-bonding. A method was developed for
the determination of these three parameters for a large number of solvents. The
value of
δ
d
was taken to be equal to that of a nonpolar substance with nearly the
same chemical structure as a particular solvent. Each solvent was assigned a point
in
δ
H
space in which these three parameters were plotted on mutually per-
pendicular axes. The solubility of a number of polymers was measured in a series
of solvents, and the
δ
d
,
δ
p
,
δ
H
values for the various solvents which all dissolved a
given polymer were shifted until the points for these solvents were close. This is a
very tedious and inexact technique. More efficient methods include molecular
dynamics calculations
[12]
and inverse gas chromatographic analyses
[13]
.
The three-dimensional solubility parameter concept defines the limits of com-
patibility as a sphere. Values of these parameters for some of the solvents listed
earlier in
Table 5.3
are given in
Table 5.4
. More complete lists are available in
handbooks and technological encyclopedias. The recommended procedure in con-
ducting a solubility parameter study is to try to dissolve the polymeric solute in a
limited number of solvents that are chosen to encompass the range of subsolubil-
ity parameters. A three-dimensional plot of solubility then reveals a “solubility
volume” for the particular polymer in
δ
p
and
δ
H
space.
Three-dimensional presentations are cumbersome and it is more convenient to
transform the Hansen parameters into fractional parameters as defined by
[14]
δ
d
,
δ
p
,
f
d
5
δ
d
=δ
(5-31a)
f
p
5
δ
p
=δ
(5-31b)
f
H
5
δ
H
=δ
(5-31c)
The data can now be represented more conveniently in a triangular diagram,
as in
Fig. 5.4
. This plot shows the approximate limiting solubility boundaries for
poly(methyl methacrylate). The boundary region separates efficient from poor sol-
vents. The probable solubility parameters of the solute polymer will be at the
heart of the solubility region. The boundaries are often of greater interest than the
